*Article* **Optical Properties and Gamma Radiation Shielding Capability of Transparent Barium Borosilicate Glass Composite**

**Mohamed Ehab 1,\*, Elsayed Salama 2,\*, Ahmed Ashour 1, Mohamed Attallah <sup>3</sup> and Hosam M. Saleh <sup>4</sup>**


**Abstract:** In this study, both radiation shielding capability and optical properties of prepared SiO2- ZnO-Na2CO3-H3BO3-BaCO3 glass composite with different concentrations of barium carbonate (0–30 mol%) have been studied. Gamma attenuation properties, such as the mass attenuation coefficient (MAC), mean free path (MFP), and exposure build-up factor (EBF), are experimentally and theoretically investigated. The detected XRD patterns for the prepared glass composites confirm their amorphous nature. It is evident from the obtained data that all tested parameters, such as mass density, molar volume, refractive index, dielectric constant, refraction loss (%), and molar refraction, have been increased as BaCO3 mol% increased. At the same time, the results of the optical bandgap show a gradual decrease with increasing barium concentration. It was also found that the mass attenuation coefficients increased with BaCO3 concentration from 0.078 at zero mol% BaCO3 to 0.083 cm2/g at 30 mol%. Moreover, the half-value layer (HVL) and the exposure build-up factor (EBF) up to 40 mfp penetration depth were investigated in addition to the effective atomic number (Zeff) and the corresponding equivalent atomic number (Zeq) at the energy range of 0.015–15 MeV. The produced glass composite might be considered for many shielding applications based on the obtained results that require a transparent shielding material.

**Keywords:** mass attenuation coefficient; effective atomic number; build-up factor; borosilicate glass; radiation shielding

#### **1. Introduction**

Shielding materials have a significant role in radiation protection during the wide medical use of radioactive isotopes and X-ray machines and in many industrial applications, such as petroleum and gas extraction [1]. The shielding of ionizing radiation has significantly changed over the last 60 years. As a result of these ongoing developments in anti-ionizing radiation technology, the significance of composite materials for radiation shielding has been acknowledged. In shielding applications, composite materials are desirable because secondary radiation must be considered in radiation shielding design. Therefore, a functional shield's composition must be such that it can efficiently absorb both primary and secondary radiation rays. In addition to their ability to absorb all primary and likely secondary radiation, other properties might restrict the use of particular materials for radiation shielding, such as space, cost, mechanical strength, chemical stability, and thermal stability.

There is a continuing need for new materials to be employed as shielding materials under testing nuclear radiation exposure circumstances [2–5]. The most often utilized protective material so far is concrete [5–10], which is cement mixed with various additives,

**Citation:** Ehab, M.; Salama, E.; Ashour, A.; Attallah, M.; Saleh, H.M. Optical Properties and Gamma Radiation Shielding Capability of Transparent Barium Borosilicate Glass Composite. *Sustainability* **2022**, *14*, 13298. https://doi.org/10.3390/ su142013298

Academic Editor: Changhyun Roh

Received: 7 July 2022 Accepted: 9 October 2022 Published: 16 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

such as cellulosic waste [11,12], bitumen [13,14], glass [15], polymers [16–18], nanomaterials [19,20], and cement wastes [21,22]. However, the trouble in accomplishing homogeneity, the presence of water and the need for transparency of the shield have persuaded scientists to use glass rather than concrete [23–27]. Borate glasses are used for their exceptionally high transparency, low melting point, and thermal stability. The role of glass additives is different depending on the kind of the enhancement property. Adding sodium carbonate (Na2CO3) to the borate glass improves its glass nature characterizations by changing the coordination of the boron coordination group [19], while zinc oxide (ZnO) is added to borate glass to boost its thermal stability, reduce crystallization, and enhance the glass matrix's chemical resistance [28–32]. Heavy elements, such as lead, barium, bismuth, and tungsten are used to increase the borate glass density, which in turn greatly enhancing their radiation-shielding abilities [5,27,33,34]. Borated glasses doped with lead and other specific elements to enhance their densities and radiation attenuation characteristics are successfully produced [32,35–37]. Borosilicate glasses have further advantages, such as chemical durability, better heat stability, extremely low thermal expansion coefficients, and high capacities for substantial visible light transmission [38–41].

Due to its high atomic number and good attenuation coefficient, barium-based glasses have a very promising gamma radiation attenuation coefficient. Several borosilicate glass systems were tested as gamma-ray shielding materials doped with different metal oxides, such as PbO, BaO, Bi2O3, BaO, TiO2, and SrO at different concentrations, showed better shielding efficiencies compared with those previously used in the industry [26,27,42–46]. Adding iron (III) oxide to sodium-barium-vanadate glass has an impact on its physical, optical, mechanical, and radiation absorption features where significant effect on the interaction parameters of thermal neutrons and gamma radiation absorption are observed [47]. The prepared titanium borosilicate glass modified with various ratios of barium oxide showed that adding barium increased the attenuation parameters and enhanced the durability of the prepared sample [48]. The density of sodium zinc borate glasses doped with dysprosium and barium oxide was observed to increase from 2.30 to 4.02 g/cm3, and the glass's hygroscopic property considerably decreased with the addition of barium [49]. The addition of BaO to zinc barium tellurite glasses enhances its polarization by increasing the bond length, hence the glass network expansion resulting in volume.

The current work aims to prepare and investigate highly transparent, lead-free barium borosilicate glass composite to be used for gamma shielding applications.

#### **2. Materials and Methods**

The glass composite of 10 Na2CO3 − 20 SiO2 − 10 ZnO − (60 − x) H3BO3 − x BaCO3 (where x = 0, 5, 10, 20, and 30 mol%) was fabricated using the conventional fast meltquenching technique. High purity grade powders of Na2CO3, SiO2, ZnO, H3BO3, and BaCO3 were utilized as a starting material, as shown in Table 1. The compositions were mashed in an agate mortar and melted at 1100 ◦C for one hour in a porcelain crucible and twirled a lot until a homogenous bubble-free liquid was formed. The melts were poured into preheated stainless-steel molds and annealed at ∼400 ◦C for 4 h to reduce the cracking and thermal stresses of the samples and then left to cool to room temperature. The photos of the obtained samples before polishing are shown in Figure 1. The samples were then manually polished to obtain maximum flatness.



**Figure 1.** Photos of the prepared samples.

X-ray diffraction (XRD) was accomplished for the prepared glass powders by utilizing a Philips X'pert Pro X-ray powder diffractometer (Malvern Panalytical, Almelo, The Netherlands) at room temperature. The X-ray diffraction patterns were analyzed in 2θ scan from 10◦ to 90◦ with CuKα as a target and Ni as a filter (λ = 1.5418 Å) at 40 KV and 30 mA with a speed of scanning reaching to 0.3 s.

Fourier transformation of the infrared absorption spectra (FTIR) of the produced samples were measured in the spectral region 400–4000 cm−<sup>1</sup> using a JASCOFT-IR6200 spectrometer with the KBr pellet method.

The densities of the prepared glass specimens were measured at room temperature by a simple Archimedes technique that utilizes xylene as a submerged liquid according to the following formula [50]:

$$
\rho = \frac{\mathcal{W}\_{\text{a}}}{\mathcal{W}\_{\text{a}} - \mathcal{W}\_{\text{b}}} \rho\_{\text{b}} \tag{1}
$$

where Wa is the sample's weight in air, Wb represents its weight in xylene, and ρ<sup>b</sup> is xylene's density (ρ<sup>b</sup> = 0.863 g/cm3). Using the results of the mass density, the molar volume of the glasses can be calculated according to the following formula [51]:

$$\mathbf{V\_m} = \mathbf{M\_W}/\mathfrak{p} \tag{2}$$

where MW is the molecular weight, and ρ is the glass sample density. Subsequently, the refractive index of the prepared samples can be calculated by the following relation [39,51]:

$$\mathbf{m} = \left(\frac{\rho + 10.4}{8.6}\right) \tag{3}$$

Other features depending on the refractive index can be acquired, such as the dielectric constant, which can be calculated according to the following formula [52]:

$$
\varepsilon = \mathbf{n}^2 \tag{4}
$$

Additionally, the reflection loss (R) has been calculated by using the following Fresnel's formula [53]:

$$\mathbf{R} = \left(\frac{\mathbf{n} - 1}{\mathbf{n} + 1}\right)^2 \tag{5}$$

The ratio of molar volume to molar refractivity (RM), which is acquired and calculated via the following equation [52], is another structural correlation that can be used to forecast glass propensity that would be metallic or insulating.

$$\mathbf{R\_M} = \mathbf{V\_m} \left( \frac{\mathbf{n}^2 - 1}{\mathbf{n}^2 + 2} \right) \tag{6}$$

A recording double beam UV-VIS spectrophotometer (type JASCO Crop., V-770, Japan) encompassing the wavelength range from 200 to 1100 nm was used to evaluate the optical absorption spectra of the polished samples. The absorption coefficient and optical bandgap

of the samples were determined according to the optical absorption data. The optical absorption coefficient α (ν) was calculated utilizing the following equation [52]:

$$\mathbf{a}(\mathbf{v}) = 2.303 \mathbf{A}/\mathbf{d} \tag{7}$$

where A is the absorbance, and d is the thickness of the glass sample. Then, the optical bandgap (Eopt) is determined through the well-known relation [54]:

$$\alpha(\mathbf{v}) = \mathbf{B} \frac{\left(\mathbf{h}\mathbf{v} - \mathbf{E}\_{\mathrm{opt}}\right)^{n}}{\mathbf{h}\mathbf{v}} \tag{8}$$

where hν is the incident photon energy, and B is a constant relating to the band tailing's extent.

For direct allowed, indirect allowed, direct forbidden, and indirect forbidden transitions, respectively, the index n has the values 1/2, 2, 3/2, and 3. Since there is no transition symmetry in the case of indirect transitions, the electron's wave vector might change during the optical transition, and phonons will either take or give up the momentum shift. [55]. In the above-mentioned case, (αhν) 0.5 renders a linear relation with the photon energy. Extrapolating of the linear part of the overhead relation shows the optical bandgap Eopt where (αhν) 0.5 = 0 in case of indirect transition.

A NaI (Tl) scintillation detector (Teledyne Isotopes "2 × 2" NaI (Tl) Scintillation Detector, AL, USA) with an energy resolution of 8% at 662 keV was used to test the gamma-ray shielding properties of the set glass samples. The generated glass samples were measured at four distinct gamma energies under the correct geometrical constraints: 0.662 MeV from a Cs-137-point source, 0.239 MeV, 0.911 MeV from a 232 Th point source, and 1.332 MeV from a Co-60-point source. All these sources are provided by a spectrum techniques company. The investigated samples were polished and formed to have cylindrical shape of about 2 cm diameter and 1 cm thickness. During the measurements of the gamma attenuation coefficients, the sample was in contact with the point source, and the distance between the source and the detector was fixed at about 10 cm.

#### **3. Theoretical Background**

Modified Lambert-Beer law was utilized for the calculation of the linear attenuation coefficients as follows [23]:

$$\mathbf{I} = \mathbf{I}\_0 \times \mathbf{B} \times \mathbf{e}^{-\mu \mathbf{x}} \tag{9}$$

where I0 and I are the initial and transmitted photon intensities, respectively, μ is a linear attenuation coefficient (cm<sup>−</sup>1), and B (E, x) is the build-up factor depending on the thickness x (cm) of the used material and the energy E of the incident photon. The mass attenuation coefficient (μm) can be determined utilizing the measured linear attenuation coefficient and the mass density (ρ) values by the following relationship [36]:

$$
\mu\_{\rm m} = \frac{\mu}{\rho} \tag{10}
$$

The following formula can be used to determine μ<sup>m</sup> for a compound or mixture [54]:

$$
\mu\_{\rm m} = \sum\_{\rm i} \mathbf{w}\_{\rm i}(\mu\_{\rm m})\_{\rm i} \tag{11}
$$

where (μm)i is the mass attenuation coefficient of the examined mixture's ith element and wi stands for its weight percentage. The half-value layer (HVL) of the prepared glasses can be calculated by the following formula [53,56]:

$$\text{HVL} = \frac{0.693}{\mu} \tag{12}$$

where μ is the material's linear attenuation coefficient, which obviously relies on the material's type, mass density, and beam energy.

The National Institute of Standard and Technology (NIST) created a photon crosssections database called XCOM that contains the attenuation coefficients of all elements in the periodic table at various energies in order to calculate the values of the mass attenuation coefficients for the glass samples over a broad range of energies from 0.015 to 15 MeV [57]. The following equation was used to compute the mean free path (MFP) values using the linear attenuation coefficient [58]:

$$\text{MFP} = \frac{1}{\mu} \tag{13}$$

The effective atomic number of a material (Zeff) is defined as the ratio of an object's electronic cross-section (σa) to its effective atomic cross-section (σe). For the produced glass samples, the following relationship may be used to estimate the values of Zeff based on the obtained data of μ<sup>m</sup> [33]:

$$Z\_{\rm cff} = \frac{\sigma\_{\rm a}}{\sigma\_{\rm c}} = \frac{\sum\_{\rm i} \mathbf{f}\_{\rm i} \mathbf{A}\_{\rm i} (\boldsymbol{\mu}\_{\rm m})\_{\rm i}}{\sum\_{\rm i} \mathbf{f}\_{\rm i} \frac{\mathbf{A}\_{\rm i}}{\mathbf{Z}\_{\rm i}} (\boldsymbol{\mu}\_{\rm m})\_{\rm i}} \tag{14}$$

where Ai is the atomic weight, Zi is the atomic number, (μm)i is the mass attenuation coefficient for the ith element, and fi represents ith element fractional abundance concerning the number of atoms. To calculate the build-up factor, we must first obtain the Compton partial attenuation coefficient ((μm)comp) and total attenuation coefficient ((μm)total) values for the constituent elements and compounds of the examined glass samples in the energy range of 0.015–15.0 MeV. The values of the equivalent atomic number (Zeq) for the produced glass samples may then be computed by comparing the ratio (μm)comp/(μm)total at a certain energy with comparable ratios of elements at the same energy. The interpolation of the equivalent atomic number was determined using the following logarithmic interpolation algorithm [59] where the ratio (μm)comp/(μm)total lies between two subsequent ratios of elements:

$$Z\_{\rm eq} = \frac{Z\_1(\log R\_2 - \log R) + Z\_2(\log R - \log R\_1)}{\log R\_2 - \log R\_1} \tag{15}$$

where the atomic numbers of the pure elements corresponding to the ratios R1 and R2 are Z1 and Z2, respectively, and R is the ratio for studied glass samples at certain energy [60]. Using the general progressive (G-P) interpolation in the energy range of 0.015–15 MeV up to 40 mfp, the exposure build-up factors EBF were calculated for the prepared abovementioned glass samples utilizing the following equations as mentioned in Harima et al. (1993) [6,61,62]:

$$\mathbf{B}(\mathbf{E}, \lambda) = 1 + \frac{\mathbf{b} - 1}{\mathbf{K} - 1} (\mathbf{K}^\times - 1) \text{ for } \mathbf{K} \neq 1 \tag{16}$$

$$\mathcal{B}(\mathbf{E}, \mathcal{X}) = 1 + (\mathbf{b} - 1)\mathcal{X} \text{ for } \mathcal{K} = 1 \tag{17}$$

$$\mathcal{K}(\mathcal{E}, \mathcal{X}) = \mathcal{c}\mathcal{X}^{\mathfrak{a}} + \mathrm{d}\frac{\tanh\left(\frac{\chi}{\mathcal{X}\_{\mathbb{K}}} - 2\right) - \tanh(-2)}{1 - \tanh(-2)}\tag{18}$$

where E is the photon energy, X is the separation between the detector and the source as a function of MFP, B is the EBF value at 1 MFP, K (E, X) is the dosage multiplicative factor, and b, c, a, XK and d are the calculated G-P fitting parameters that rely on the attenuating medium and source energy. The prepared glasses' b, c, a, XK and d G-P fitting parameters can be interpolated logarithmically using the following equation-like method for the 0.015–15 MeV gamma-ray energy range up to 40 mfp [63,64].

$$P = \frac{P\_1 \left(\log \log Z\_2 - \log \log Z\_{\text{eq}}\right) + P\_2 \left(\log \log Z\_{\text{eq}} - \log \log Z\_1\right)}{\log \log Z\_2 - \log \log Z\_1} \tag{19}$$

P1 and P2 are the values of the G-P fitting parameters that correspond to the Z1 and Z2 atomic numbers at the specified energy, respectively. The American Nuclear Society's study criteria for G-P fit for the elements were used [65].

#### **4. Results and Discussion**

*4.1. XRD Analysis and FTIR*

The XRD patterns for the prepared glass samples were obtained and are shown in Figure 2. The absence of sharp peaks in the XRD results demonstrates that the prepared specimens have an amorphous nature. The two humps seen at 2θ◦ equal 25◦ and 45◦ for each sample and serve as a strong piece of evidence for the constructive interferences at variance of two and the aggregation of atoms in the glass matrix in two separate ways. A typical peak for borosilicate matrices was previously seen in several publications [45,66,67].

**Figure 2.** Patterns of X-ray diffraction for ZnO borosilicate glasses doped with BaCO3.

The FTIR transmission spectra of ZnO borosilicate glasses doped with different concentrations of BaCO3 are shown in Figure 3. Table 2 displays the results of the FTIR absorption bands and the associated vibrational modes.

Four distinct bands can be found in the observed data. The band located between 800 and 1200 cm−<sup>1</sup> represented the BO4 structural units. Two more bands were visible in the range of 600 and 800 cm−<sup>1</sup> and 1200 to 1600 cm−<sup>1</sup> and were returned to BO3 structural units. Finally, the band of metal ion vibrations was observed at 400 to 600 cm−1. The stretching relaxation modes of B–O bonds of trigonal BO3 band centered at 1364 cm−<sup>1</sup> is observed with a small shoulder edge around 1260 cm−<sup>1</sup> [68]. While the strong broad band from 1176–755 cm−<sup>1</sup> centered at 955 cm−<sup>1</sup> are attributed to asymmetric stretching of B–O bonds of tetrahedral BO4 units. The higher intensity observed may be due to the formation of Si–O–Si and B–O–Si bonds, which contribute vibrational modes at the BO4 band [70–72]. A moderate band centered around 700 cm−<sup>1</sup> may be due to bending vibrations of B–O–B of linkages in a borate network [73,74]. The band centered at 440 cm−<sup>1</sup> and the shoulder noticed at 500 cm−<sup>1</sup> may be attributed to vibrational modes of all metal cations Ba+2 and Zn+2 [75–77]. It is noticed that the increase in the BaCO3 mol% in the composite shifts the bands to a lower wavenumber, which denotes a reduction in the BO3 group and formation

of the BO4 in the glass structure. As a result, an increase in non-bridging oxygens (NBO) and a decrease in the degree of localization of electrons are produced.

**Figure 3.** FTIR for ZnO borosilicate glasses doped with BaCO3.


**Table 2.** The assigned infrared bands to the produced glass samples' spectra.

#### *4.2. Density and Molar Volume*

Figure 4 displays the mass densities and molar volumes of the produced glasses. Both the density and the molar volume show an equivalent trend increase with increasing the BaCO3 mol% in the composites. By increasing the BaCO3 mol% in the composite, the structure becomes more compact. The larger molecular weight of BaCO3 relative to the other elements may have contributed to the rise in density. On the contrary, the increases in molar volume may be related to the creation of non-bridging oxygen ions (NBOs), which tend to increase the randomizer in the network and convert triangular (BO3) structure units into tetrahedral (BO4) structure units [46,78].

**Figure 4.** Density and molar volume for ZnO borosilicate glasses doped with BaCO3.

#### *4.3. Optical Absorption Spectra*

A powerful technique used to express the optical transitions and electronic band configuration of the amorphous materials is the absorption edge in the region of UV-Vis. Therefore, the optical absorption spectra for set glass samples are shown in Figure 5. The consistency of each sample has been kept as small as possible to evade the inherent absorbance resulted from the long optical path length.

**Figure 5.** Absorbance versus wavelength for ZnO borosilicate glasses as a function of BaCO3 mol%.

The linear relation between (αhν) 0.5 and the photon energy is shown in Figure 6. Extrapolating of the linear part of the overhead relation shows the optical bandgap Eopt energies of 3.55, 3.42, 3.29, 3.21, and 3.13 eV. The values of optical bandgap performance show a gradual decrease with increasing barium concentration. The observed decrease in bandgap with improved BaCO3 mole% concentration could be attributable to potential flaws in the glass network as non-bridging oxygen (NBO) ranges rise. It also indicates the formation of new localized states formed between the valence and conductive bands. Finally, because of the usage of BaCO3 rather than boron oxide, the glass matrix is densified, which is well compatible with the resulting density and changes in the optical bandgap.

**Figure 6.** Optical bandgap for ZnO borosilicate glasses as a function of BaCO3 mol%.

The received data of the refractive index and its related parameters are summarized in Table 3. It is evident from the obtained data that all these parameters have the same trend. With increasing BaCO3 mol%, the parameters grew linearly. All estimated parameters confirm the role of barium oxide in the glass network. It has been observed that the refractive index increases as the BaCO3 mol% increases inside the structure grow. The compactness that rises in the glass samples can be linked to this boom in the refractive index.

#### *4.4. Mass Attenuation Coefficient*

Table 4 compares the values of the mass attenuation coefficient (μm) that were derived theoretically and experimentally. It has been established that there is a close correlation between experimental and theoretical values. Figure 7 displays the fluctuation of m for the produced glass samples with photon energies ranging from 0.015 to 15 MeV. The obtained values of μ<sup>m</sup> significantly boost the growth in BaCO3 concentration at the same photon energy while mimicking the chemical composition and photon energy. Based on the interaction of gamma radiation with the examined material, it is possible to explain the inverse relationship between m and the rise in energy for all samples. The photoelectric effect is the most common interaction at low photon energies (E), with an interaction probability proportional to E<sup>−</sup>3.5. While Compton scattering is the dominant interaction at intermediate energies, its probability of interaction is proportional to E<sup>−</sup>1. Pair production is most prevalent at very high photon energies over 1.022 MeV, where the chance of contact is proportional to E2. The little variation in the mass density of the prepared glass samples with an increase in BaCO3 concentration from 0 to 30 mol% is what causes the Compton mass attenuation fraction to remain constant. As a result, the mass attenuation coefficient of the produced glass samples has been significantly increased in low-energy areas where x-ray shielding applications are advantageous. The K-absorption edge of barium is what causes the observed peak at around 0.04 MeV (0.037 MeV).



**Table 4.** The mass attenuation coefficients (cm2/g) of the created glass samples, both theoretically and experimentally.


**Figure 7.** Mass attenuation coefficients of 10 Na2CO3 − 20 SiO2 − 10 ZnO−(60 − x) H3BO3 − x BaCO3 glass system in the energy ranges from 0.015–15 MeV and x = 0, 5, 10, 20, 30.

#### *4.5. Half Value Layer (VL) and Effective Atomic Number (Zeff)*

Figure 8 depicts the fluctuation in the produced glass composite's effective atomic number (Zeff) at energies between 0.015 and 15 MeV and at various concentrations of BaCO3. The observed increase in the Zeff with the increase in the barium concentration can be attributed to the higher atomic number for barium compared with boron (barium is added on the expense of boron) while the change in Zeff of the prepared glass composite in the investigated energy range 0.015–15 MeV can be explained based on the probability of gamma radiation interaction at each energy photon. At low energy range, photoelectric reaction dominates, with the probability proportional to Z4. As the incident photon energy increases, photo electric interaction probability will decrease, and therefore, Zeff will also decrease. At the intermediate energy range, Compton interaction dominates, with the probability proportional to Z. As the incident photon energy increases, Compton interaction probability will decrease (Compton interaction probability proportional with E−1), and therefore, Zeff will also decrease. At the higher energy range, more than 1.022 MeV pair production interaction dominates, with the probability proportional to Z2. As the incident photon energy increases, pair production interaction probability will increase, and therefore, Zeff will also increase [79]. At about 0.04 MeV, the ultimate Zeff value was detected in all the prepared glass samples. As discussed in the attenuation curve, maximum absorption occurred at the K-absorption edge of barium at about 0.037 MeV.

**Figure 8.** Zeff results of 10 Na2CO3 − 20 SiO2 − 10 ZnO − (60 − x) H3BO3 − x BaCO3 glass system.

The results of the calculated values of the half value layer (HVL) at the same energy range 0.015–15 MeV are shown in Figure 9. The discussion of these results is the same as mentioned in the case of the mass attenuation coefficients.

#### *4.6. The Exposure Build-Up Factor (EBF)*

As shown in Figure 10, the exposure build-up factor (EBF) values for the prepared glass samples (S0–S4) were calculated using the geometrical progression (G-P) method with depth penetration of up to 40 mfp and photon energies of up to 15 MeV. The picture also demonstrates that, according to the photoelectric effect interaction mechanism, the EBF values of the produced glass samples are negligible at low photon energies. Additionally, within the intermediate energy range when numerous scatterings about the Compton interactions has happened, the samples' EBF significances rise with the energy of the photons. The calculated EBF values for the pair formation process increase at high photon energies. Additionally, strong peaks can be seen at 0.04 MeV in Figure 8 due to the Kabsorption edge of barium (0.037 MeV).

**Figure 9.** HVL results of 10 Na2CO3 − 20 SiO2 − 10 ZnO − (60 − x) H3BO3 − x BaCO3 glass system.

ǻǼȱ

**Figure 10.** *Cont.*

**Figure 10.** EBF of the produced borosilicate glass composite at 0.015 to 15 MeV up to 40 mfp photon energies with (**a**) 0 mol% BaCO3, (**b**) 5 mol% BaCO3, (**c**) 10 mol% BaCO3, (**d**) 20 mol% BaCO3, and (**e**) 30 mol% BaCO3.

#### **5. Conclusions**

The glass composites 10 Na2CO3 − 20 SiO2 − 10 ZnO − (60 − x) H3BO3 − x BaCO3 in the current study have been made using the traditional melting procedure, where x = 0, 5, 10, 20, 30. The parameters for structural, optical, and gamma attenuation are established. With the addition of BaCO3, the molar volume and mass density measurements revealed an improvement in compactness. Different vibrational bonding modes, including B–O, B–O–B, and B–O–Si, were seen in the produced glasses according to the FTIR data. The effective atomic number (Zeff), mass attenuation coefficients (MAC), and exposure build-up factors (EBF) of the previously described prepared glass samples were computed at various photon energies between 0.015 and 15 MeV. The findings attained may recommend the manufactured glasses for applications requiring transparent shielding.

**Author Contributions:** Formal analysis, E.S.; Methodology, M.E., E.S., A.A. and M.A.; Supervision, E.S. and H.M.S.; Writing—original draft, M.E. and M.A.; Writing—review & editing, E.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

