where Wa represents the weight of the sample in air, Wb is its weight when immersed in xylene, and ρb is the density of xylene, taken as 0.865 g/cm³. Subsequently, the molar volume (Vm) was determined by dividing the molar mass (M) of the glass composition by its measured density (ρ).
The patterns in Fig. 2 show the XRD results of the prepared glass samples. The absence of sharp diffraction peaks indicates that the samples possess an amorphous structure. The broad variations in the patterns arise from X-ray scattering in the disordered glass, suggesting structural irregularities over a wide range. Consequently, the materials are confirmed to be non-crystalline and glassy. Typically, borate glasses exhibit a broad halo in their XRD patterns between 20° and 30°.
In this study, special attention was focused on the mid-infrared region (400-1600 cm⁻¹), where various vibrational modes associated with Bi-borosilicate glasses are observed, to elucidate the role of Bi₂O₃ in the prepared glass systems. The recorded spectra displayed multiple absorption bands across different spectral ranges, with minor shifts in both intensity and position. These bands often overlapped and broadened, making the direct interpretation of individual peaks challenging.
To address this, a deconvolution procedure was applied to the FTIR spectra, separating the overlapping bands into distinct peaks for clearer identification. The original FTIR spectra of the prepared glass samples are shown in Fig. 3(a), while a representative set of deconvoluted peaks is presented in Fig. 3(b). The identified peak positions and their corresponding assignments are summarized in Table 2.
The absorption bands detected in the 400-600 cm⁻¹ region are primarily attributed to the vibrational modes of heavy metal oxides in the glass framework. Specifically, the peaks near 484 cm⁻¹ and 437 cm⁻¹ correspond to the combined bending vibrations of Bi-O bonds in BiO₆ octahedral units within the borate network and the bending vibrations of Si-O-Si linkages in SiO₄ tetrahedra, respectively. The band observed around 876 cm⁻¹ is associated with di-borate units and B-O-B linkages in the borate network, while the peak near 698 cm⁻¹ reflects both B-O-B bending vibrations and the stretching modes of Bi-O bonds in BiO₃ units.
In the spectral range of approximately 797-1100 cm⁻¹, several absorption bands appear, which can be categorized into two groups based on the vibrations of silicate and borate tetrahedral units. Within the borosilicate network, the bands at 969 cm⁻¹ and 1101 cm⁻¹ correspond to the asymmetric stretching vibrations of Si-O-Si linkages and B-O-Si bonds, respectively. Additionally, the absorption bands at 876 cm⁻¹ and 1050 cm⁻¹ are associated with the stretching vibrations of BO₄ tetrahedral units.
Finally, the absorption region between 1200 and 1500 cm⁻¹ was deconvoluted into four distinct bands at 1244, 1317, 1385, and 1444 cm⁻¹. These are typically assigned to the B-O stretching vibrations within triangular borate (BO₃) groups.
The bands attributed to the borate network were utilized to interpret the infrared spectra obtained through the deconvolution process. The areas under the deconvoluted peaks were measured to calculate specific structural parameters, including the N₄ and non-bridging oxygen (NBO) ratios. The N₄ parameter, which offers essential information about the proportion of BO₄ units within the glass structure, was calculated using the following equation:
Figure 4 shows that the N₄ ratio increases with the rising Bi₂O₃ content. The incorporation of Bi ions into the glass matrix leads to the transformation of some BO₃ units into BO₄ units, resulting in an increased content of non-bridging oxygen (NBO) bonds. A comparable trend has been observed in previous studies on bismuth-doped borosilicate glasses. This observation is further supported by the reduction in optical band gap values and the corresponding rise in Urbach energy values as the Bi₂O₃ content increases.
The mass density (ρ) and molar volume (Vm) of glass samples are important parameters for investigating structural changes. These properties are influenced by several factors, including coordination number, network structure, cross-link density, and interstitial spaces. Figure 5 illustrates the relationship between ρ and Vm as a function of Bi₂O₃ content, while the corresponding values for the prepared glass compositions are listed in Table 3.
In general, the introduction of Bi₂O₃ into the glass network led to a significant increase in mass density, rising from 2.31 g/cm³ (0% mol Bi₂O₃) to 4.59 g/cm³ (20% mol Bi₂O₃), with an uncertainty of ± 0.005 g/cm³. This increase in ρ can be attributed to the substitution of lighter B ions (2.34 g/cm³) with heavier Bi ions (9.78 g/cm³). Moreover, replacing boron oxide with bismuth oxide increases the coordination number to six, compared with the three- or four-fold coordination typical of boron oxide, thereby enhancing the density.
In the prepared glass samples, the molar volume (V) also increased gradually with Bi₂O₃ content, from 27.33 cm³/mol at 0% Bi₂O₃ to 31.02 cm³/mol at the highest concentration. This expansion of V is likely due to the rise in non-bridging oxygen atoms (NBOs) with increasing Bi₂O₃ content, which opens up the tightly compacted borosilicate network. As a result, the glass structure becomes less compact, leading to a noticeable change in the internal network, consistent with predictions from IR analysis.
UV-visible spectroscopy is a powerful tool for investigating the optical properties of materials, including band gap and Urbach energies. Figure 6 presents the UV-visible diffuse absorbance spectra of the examined glass samples. As shown, all samples exhibit a similar spectral profile, with an absorption edge that progressively shifts toward longer wavelengths (red shift) as the Bi₂O₃ concentration increases in the glass matrix.
The absorption edge spans a broad wavelength range of 320-400 nm in the base glass, reflecting the amorphous nature of the prepared samples. Below 320 nm, the spectra display a saturation region, followed by a decrease in absorption beyond 320 nm, corresponding to valence-to-conduction band transitions. The degree of attenuation and curvature at the absorption edges is influenced by impurities and structural defects in the glass network. Notably, no optical transitions appear in the visible region, since such transitions generally arise from d-d electronic transitions, and this glass composition contains no d-orbital heavy metal oxides capable of producing them.
The optical spectra of non-crystalline materials typically exhibit three distinct regions: (i) a phonon-assisted constant absorption region, (ii) the Tauc region, corresponding to strong absorption due to inter-band electronic transitions, and (iii) the Urbach region, where the absorption coefficient shows an exponential dependence on photon energy.
The optical band gap represents the energy separation between the valence band maximum and the conduction band minimum. For amorphous materials, it can be determined using models based on the Tauc method, originally proposed by Davis and Mott, expressed by the following relation:
where hυ is the photon energy, q is a constant, E is the optical band gap, m refers to an index that has different values (1/2 for direct and 2 for indirect allowed transitions), and α is the absorption coefficient. The origin in selecting the best value among them depends on the optical transitions as well as the material type. When the condition (αhυ) is applied as Y-coordinate against photon energy (hυ) as X-coordinate, the band gap energy value is equal to the intersection of the first straight portion of the linear part of the spectrum with X-ordinate. Figure 7 shows the optical spectra for all prepared samples with determination of E Values. The band gap values are listed in Table 4 and noticed to decrease steadily with increasing the concentration of BiO from 3.44 eV for the Base sample (0 mol% BiO) to 2.39 eV for the highest concentration (20 mol% BiO).
As noted in the infrared analysis, increasing the Bi₂O₃ concentration promotes the formation of non-bridging oxygen (NBO) bonds within the glass structure. These NBOs introduce additional energy levels near the top of the valence band, facilitating the transition of valence electrons to these states. Consequently, the band gap energy decreases progressively with increasing dopant concentration.
In amorphous or poorly crystalline materials, the optical absorption edge exhibits an exponential relation between the absorption coefficient (α) and the photon energy (hυ), forming a characteristic tail. The Urbach energy (EU), which represents the width of these band tails, arises from structural disorder in the material. Networks with higher defect concentrations -- such as non-bridging oxygens (NBOs) and dangling bonds -- typically exhibit larger EU values. These defects introduce additional energy states within the bandgap, further confirming the amorphous structure of the glass samples.
To determine EU for our glass series, we use the simplified Urbach relation given in Eq. (4):
where k is a constant. By plotting hυ against Ln (α), the Urbach energy can be derived from the inverse slope of the linear region in the resulting graph. Higher E values indicate an increased likelihood of weak bonds transforming into defects, making Urbach energy a useful metric for defect concentration analysis.
As shown in Fig. 8; Table 4, the E values increased from 0.2164 eV (lowest Bi₂O₃ content) to 0.488 eV (highest Bi₂O₃ content). Notably, the trends for bandgap energy and Urbach tails were inversely correlated. The reduction in the optical bandgap may not reflect an actual decrease in bandgap energy but rather the influence of dopant-induced localized states. Consequently, samples with higher Bi₂O₃ content are more prone to defect formation, enhancing amorphous character, leading to increased Urbach energy and a reduced optical bandgap. The relationship between optical bandgap energy and Urbach tails as a function of Bi₂O₃ concentration is illustrated in Fig. 9.
The mass attenuation coefficient (µ), shown in Fig. 10, and the effective atomic number (Z), presented in Fig. 11, were evaluated for the manufactured borosilicate glass composites with varying Bi₂O₃ concentrations over the energy range of 0.015-15 MeV. The results show that µ decreases with increasing photon energy, while it increases with higher Bi₂O₃ content as boron is progressively replaced.
Figure 10 also highlights a marked enhancement in µ for all synthesized glass samples compared to Portland concrete, a commonly used radiation shielding material. The observed peak in µm around 0.1 MeV for the glass composition 30SiO₂-(50-x)B₂O₃-5CaO-10Na₂O-5LiF-xBi₂O₃ is attributed to intrinsic interactions between the glass samples and gamma radiation at this energy. At 0.04 MeV, gamma-ray interaction is dominated by the photoelectric effect, which strongly depends on both Z and photon energy. The probability of photoelectric absorption increases with higher Z and decreases with photon energy, following an approximate Z³/E³ relationship, where E denotes photon energy. The presence of high-Z elements such as bismuth (Z = 83) significantly enhances photon interaction through the photoelectric effect, particularly at lower energies.
Thus, the incorporation of Bi₂O₃ into the glass introduces high-Z elements that are highly effective at attenuating low-energy gamma rays via the photoelectric effect. This leads to an increased µ at 0.04 MeV, where strong interactions occur with the inner electron shells of Bi, further amplifying absorption.
From a radiation interaction perspective, substituting boron (B, Z = 5) with bismuth (Bi, Z = 83) leads to an increase in Z, thereby enhancing the shielding efficiencies of the glass. As Z rises, the effectiveness of the material in attenuating gamma radiation also improves, making it a more efficient shielding medium.
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Figure 12 presents the half-value layer (HVL) measurements for the fabricated glass systems. The results indicate that HVL increases with rising photon energy and decreases as bismuth (Bi) concentration increases. Consequently, incorporating higher Bi content enhances gamma-ray attenuation.
A comparison between the theoretical and experimental values of the mass attenuation coefficient (µ) at 0.662 MeV, as shown in Table 5, reveals a deviation of less than 10%. This suggests that computational methods can be effectively used to estimate attenuation parameters for various compositions before conducting costly experimental procedures.
The Phy-X/PSD software was employed to compute the buildup factors of the glass systems. Figure 13 illustrates the change in the Exposure Buildup Factor (EBF) with incident photon energy in the scale from 0.015 to 15 MeV. The results indicate that at low photon energies, the EBF values remain minimal, mainly because of the dominance of the photoelectric effect.
Notable peaks in the EBF are directly associated with various radiation-matter interactions, including Compton scattering, pair production, resonance absorption, and the photoelectric effect. These interactions vary significantly across different energy levels, resulting in certain energies where radiation accumulation becomes notably higher. Understanding these peaks is crucial for designing effective radiation shielding materials for diverse applications.
Specifically, the glass composition 30SiO₂-(50-x) B₂O₃-5CaO-10Na₂O-5LiF-xBi₂O₃ exhibits EBF peaks at ~ 0.03-0.04 MeV and at ~ 0.08-0.1 MeV. These peaks are attributed to the atomic and electronic structures of the material, which influence its interaction with gamma radiation at these specific energy levels.
These two peaks in the exposure buildup factor arise from different photon interaction mechanisms, explaining their contrasting behavior with increasing Bi₂O₃ content. The first peak, at low energies (~ 0.03-0.04 MeV), is dominated by the photoelectric effect, whose probability varies approximately as Z³/E³, making it highly sensitive to the effective atomic number (Z) of the glass. Introducing Bi (Z = 83) increases Z and enhances photon absorption, which suppresses multiple scattering and reduces buildup in this region. In contrast, the second peak (~ 0.08-0.1 MeV) falls within the Compton scattering domain, where the interaction cross-section depends primarily on electron density rather than Z. Since electron density changes less significantly with Bi substitution compared to the sharp variation in photoelectric absorption, the magnitude of this peak remains relatively constant across different Bi₂O₃ concentrations.
Table 6 compares the fabricated glasses with reported data for barite concrete, Portland concrete, and lead-doped borate glasses. Although the synthesized glass samples contain neither lead nor barium, their effective atomic numbers and mass attenuation coefficients at 0.662 MeV are comparable to those of lead-rich glasses. Furthermore, all developed glasses demonstrate superior gamma-ray shielding performance compared to both Portland and barite concrete.