1 Introduction

In last decades, heavy metal oxide (HMO) based glasses have gained significant attention due to their unique interesting electrical, optical, and magnetic properties. Additionally, these glasses have large exciton binding energy (BE) and wide bandgap. These properties make HMO based glasses potential candidates in several applications such as UV-emitting lasers, optoelectronic devices, gas sensors, and solar energy converters and gas sensors [1]. Boric oxide (B2O3) is an attractive oxide among the HMOs since it is one of the most common glass formers. Borate glasses exhibit more desirable physical and chemical properties, including a low melting point, strong clarity, chemical resistance, and thermal stability [1, 2]. Additionally, owing to their motivating nonlinear and linear optical properties, borate glasses of various compositions play a significant role in optical devices [3,4,5,6,7,8,9,10,11,12]. Through incorporating lead oxide into borate glass structures, such properties such as optical nonlinearity may be enhanced due to the strong polarizability of Pb2 + ions in glass networks [13]. Environments of Pb cations in oxide glasses have been also probed by X-ray studies [14]. On the other side, the interaction of PbO and B2O3 in the glass matrix has a dual impact on the glass network, acting as a glass former in the presence of high levels of boron oxide or lead oxide and as a network modifier at low concentrations. Thus, lead borate glasses exhibit a wide glass forming range, which is advantageous for the fabrication of structurally and optically diverse structures [15,16,17]. On the other hand, Lead borate glasses are known to be excellent candidate materials for optoelectronic, photoelectric, and optical switches for the reasons mentioned previously. The additive of alkaline earth oxides namely BaO or/and SrO into borate glass structure allows to increase the glass refractive index and thermal stability. Previously, Manikandan et al. [18] investigated effect of BaO on the optical and thermal properties of some tellurite glasses. The authors confirmed that optical properties of glasses were enhanced with increasing BaO content in their compositions. In addition, they reported that thermal stability of glasses improved with increasing BaO concentration making these glasses with BaO attractive candidates for amplifiers in the mid-IR and fiber lasers [9]. In other study, Elkhoshkhany et al. [19] evaluated structural properties, UV–Vis–NIR spectroscopy and thermal characteristics of oxyhalide–tellurite glasses with SrCl2. They reported that glass systems with Sr have high thermal stability and high index of refraction that makes them suitable as attractive candidates for optical fiber production. Recent research has shown that glasses are suitable for use as radiation filters owing to their unique properties, including their transparency to visible light and their capacity to absorb X-rays and neutrons [20]. By incorporating oxides into the glass matrix, the properties of the glasses against nuclear radiation shielding may be improved [21, 22]. Numerous scholars asserted that borate glasses continue to be the best option for radiation protection [10, 23,24,25,26,27,28,29]. The mass attenuation coefficient is the most useful gamma-ray attenuation parameter for evaluating the radiation shielding capability of materials. Numerous techniques, including Monte Carlo simulations and theoretical estimates using the XCOM and Phy-X/PSD systems, can be used to approximate the mass attenuation coefficients (MAC) [10, 26,27,28,29,30,31].

The main objective of this study is to determine potential synergistic effects of increasing SrO2 additive on B2O3–BaO–PbO–SrO2 glass system. To observe the direct effects of utilized chemical substitutions (i.e., B2O3/SrO2), MAC of glass samples were determined in this analysis using an experimental transmission setup. The obtained findings were compared to those obtained by Monte Carlo simulations (MCNPX v.2.6.0) and theoretical calculations (WinXcom program). The obtained MAC values were used to quantify other critical shielding parameters, including linear attenuation coefficients (LAC), half value layer (HVL), mean free path (MFP), tenth value layer (TVL), and effective atomic numbers (Zeff), as well as fast neutron removal cross sections values for novel lead–borate glasses. Along with their protecting properties against nuclear radiation, the physical and optical properties of the prepared glasses were studied.

2 Experimental and methods

2.1 Materials and measurements

By utilization of traditional and well-known method namely melt-quenching technique, commercial powders of high reagent grade of B2O3 of purity 99.96% Sigma-Aldrich, BaCO3 of purity 99.99% Sigma-Aldrich as a source of BaO, PbO of purity 99.9% Sigma-Aldrich, and SrO2 of purity 99.99% Sigma-Aldrich were utilized to synthesis samples of lead borate glasses series with the compositions:

  • 50B2O3–25BaO–25PbO–0SrO2 coded as BBPS0,

  • 45B2O3–25BaO–25PbO–5SrO2 coded as BBPS5,

  • 40B2O3–25BaO–25PbO–10SrO2 coded as BBPS10,

  • 35B2O3–25BaO–25PbO–15SrO2 coded as BBPS15,

  • 30B2O3–25BaO–25PbO–20SrO2 coded BBPS20, and

  • 20B2O3–25BaO–25PbO–30SrO2 coded as BBPS30.

For each glass sample, the required weights of chemical powers were determined by an electric digital balance with accuracy of ± 0.0001. Next, they mixed well and melted in a porcelain-crucible at 950 °C for 25 min. Next, the melt-liquid was poured into preheated molds. The produced glass samples were annealed for 5 h at 300 °C to erase thermal strains and then left to cool down gradually. The produced glasses were polished well to make the two opposite faces parallel and flat to be ready for the optical measurements. The details of manufactured glasses with their sample codes and compositions are presented in Table 1. On the other hand, manufactured samples with their general appearance are shown in Fig. 1. Shimadzu 7000 diffractometer device with Cu a radiation source (λ = 1.54060 Å) in the 2θ range of 10°–100° was used to perform the XRD of the glass samples to examine the state of the prepared glasses. Densities of the prepared samples measured by Archimedes’ technique using toluene (density, ρ = 0.867 g/cm3) as liquid for immersion with accuracy of ± 0.01 g/cm3 through the following Eq. (1):

$$ \rho _{{{\text{glass}}}} = \frac{{W_{1} }}{{W_{1} - W_{2} }}\rho _{{{\text{toluene}}}} . $$
(1)
Table 1 Chemical composition, density, and molar volume of the (50 − x)B2O3–25BaO3–25PbO–xSrO2: x = 0–30 mol% glasses
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Fig. 1
figure 1

An image of the prepared BBPS0–BBPS30 glass samples

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Here,

W1 = glass’s weight in air.

W2 = glass’s weight in liquid.

ρtoluene = toluene liquid’s density.

Molar volume (Vm) of each glass was calculated using Eq. (2):

$$ V_{{\text{m}}} = \frac{{M_{{W{\text{glass}}}} }}{{\rho _{{{\text{glass}}}} }}. $$
(2)

The optical absorption measurements for the (BBPS0–BBPS30) were carried out and drawn in wavelength from 190 to 1100 nm range by utilizing UV–Vis–NIR spectrophotometer of JASCO model V-570.

2.2 Methods

2.2.1 Monte Carlo simulations

The value of mathematical simulation methods in studies of nuclear radiation shielding remains a hot topic in the literature. Numerous scenarios are possible during numerical simulation, based on the characteristics and features of the running code. The section on Monte Carlo simulations will explore the technological aspects of Monte Carlo simulations utilizing the MCNPX [32] code. Each glass sample was modeled in this study using elemental mass fractions and densities (Table 1). Material definitions for fabricated composites encoded as BBPS0, BBPS5, BBPS10, BBPS15, BBPS20, and BBPS30 were entered into the MCNPX code's input register. The MCNPX’s substance description (Mn) entails many critical definition measures, including elemental mass fractions, atomic numbers, and mass numbers of components. Figure 2a–b illustrates the overall presence of the modeled simulation setup with the simulation package used to calculate mass attenuation and transmission variables. Finally, one of the detection tallies encoded in MCNPX code (F4 tally mesh) was implemented within the virtual detection area to record the attenuated rays from the glass samples. It should be remembered that the MCNPX simulations were run for each glass sample at various photon energies. As a physics library, the D00205ALLCP03 MCNPXDATA kit was introduced, which consisted of DLC-200/MCNPDATA.

Fig. 2
figure 2

a Simulation setup for MAC calculations b 3-D view of modeled simulation setup in MCNPX code (MCNPX Visual Editor)

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2.2.2 µ/ρ, HVL, and MFP, and Z eff

The total mass attenuation coefficient (μm = μ/ρ, usually in cm2/gram) is a fundamental concept used to describe the potential of a substance (in this case, Goethite glasses) to attenuate gamma radiation. Numerous methods, like XCOM, MCNP, Xmudat, and Geant4, may be used to obtain the _m factor. Fortunately, both of these techniques are based on the mixture law, as described in [33]:

$$ \frac{\mu }{\rho } = \mu _{{\text{m}}} = \frac{{N_{{\text{A}}} }}{M}\sigma _{{{\text{tot}}}} = \sum\limits_{i} {w_{i} \left( {{\mu \mathord{\left/ {\vphantom {\mu \rho }} \right. \kern-\nulldelimiterspace} \rho }} \right)_{i} } $$
(3)

wi denotes the weight fraction of the ith material contained in the glass sample. The μm values for Goethite glasses were obtained in our work using the XCOM software. Other shielding terms such as transmitting factors (e.g., MFP and HVL) and Zeff were then calculated using the following equations [34, 35]:

$$ {\text{MFP}} = {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \mu }}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$\mu $}} $$
(4)
$$ {\text{HVL}} = \left( {{{\ln 2} \mathord{\left/ {\vphantom {{\ln 2} \mu }} \right. \kern-\nulldelimiterspace} \mu }} \right) $$
(5)
$$ Z_{{{\text{eff}}}} = \frac{{\sigma _{a} }}{{\sigma _{e} }} = \frac{{\sum\nolimits_{i} {f_{i} A_{i} \left( {\frac{\mu }{\rho }} \right)_{i} } }}{{\sum\nolimits_{j} {f_{j} \frac{{A_{j} }}{{Z_{j} }}\left( {\frac{\mu }{\rho }} \right)_{j} } }} $$
(6)

3 Results and discussion

3.1 XRD and physical parameters

XRD spectra for fabricated glasses BBPS0–BBPS30 don’t illustrate any crystalline peaks as presented in Fig. 3, which confirm that glasses are in the amorphous nature.

Fig. 3
figure 3

XRD patterns of BBPS0–BBPS30 glass samples

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Equation 1 and Eq. 2 were used to evaluate ρglass and the corresponding Vm. The obtained data are collected in Table 1 and depicted in Fig. 3. From Table 1 and Fig. 4, one can observe that ρ value raises from 4.685 to 5.315 g/cm3 with increasing SrO2 content in the proposed glasses. This increasing in ρglass may be due to the partial replacement between the light B2O3 with molar mass (69.63 g/mol) and heavy SrO2 with molar mass of (119.619 g/mol). The Vm decrease with increasing SrO2 content in the proposed glasses as in Table 1 and Fig. 3. This decreasing may be attributed to (i) the amount of B2O3 with shorter atomic radii (1.589 Å) was larger than that of SrO2 with longer atomic radii (4.303 Å) and (ii) the number of NBO decreases with decrease B2O3 making glasses in less inter-atomic spacing and disordered formation.

Fig. 4
figure 4

Density and molar volume of BBPS0–BBPS30 glasses

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3.2 UV–Vis spectroscopy and optical properties

The UV–vis spectra for BBPS0–BBPS30 glasses are illustrated in Fig. 5. It is clear that the spectra haven’t color center and the absorption spectra are slightly shifter to longer wavelength with increasing SrO2 content in the glasses. With help of UV–vis spectra in Fig. 4, the cut-off wavelength (λcut-off, nm) which necessary to calculate the optical absorption coefficient α(λ) was evaluated for each spectrum and written in Table 2. It seen that the value of λcut-off increases with enhancement of SrO2 content in the glasses, λcut-off = 387, 404, 424, 445, 471, and 503 nm for BBPS0, BBPS5, BBPS10, BBPS15, BBPS20, and BBPS30 glasses, respectively.

Fig. 5
figure 5

Uv–Vis spectra for prepared BBPS0–BBPS30 glasses

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Table 2 λcut-off, \(E_{{{\text{gap}}}}^{{{\text{Direct}}}}\), \(E_{{{\text{gap}}}}^{{{\text{Indirect}}}}\) Average (n), and EU for BBPS0–BBPS30 glasses
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In the present work, the optical absorption coefficients α(ν) for each glass sample was estimated using the next relation via the absorbance (A) and sample thickness (d) [36]:

$$ \alpha (\nu ) = 2.303\left( {\frac{A}{d}} \right) = \left( {\frac{1}{d}} \right)\ln \left( {\frac{{I_{o} }}{I}} \right) $$
(7)

Tauc’s model [37] depends on the optical absorption coefficient α(hν) was used to determine the allowed gaps for optical energy bands of the proposed glasses. This model modified by Mott and Davis as [38]:

$$ \alpha (\nu )h\nu = {\text{C}}(h\nu - E_{{{\text{gap}}}} )^{{\text{m}}} , $$
(8)

where the transition probability depends on the constant C. The power m points to the type of electronic transition (m = 2 and 0.5 for indirect and direct allowed transitions) [38]. The variation of (αhν)2 and (αhν)1/2 with photon energy (hν) for BBPS0–BBPS30 glasses are shown in Fig. 6a and b, respectively. The optical energy gaps in direct transition (\(E_{{{\text{gap}}}}^{{{\text{Direct}}}}\)) and for indirect transition (\(E_{{{\text{gap}}}}^{{{\text{Indirect}}}}\)) were determined with help of the linear region of the graphs at the points (αhν)1/2 or (αhν)2 = 0. All obtained values of \(E_{{{\text{gap}}}}^{{{\text{Direct}}}}\) and \(E_{{{\text{gap}}}}^{{{\text{Indirect}}}}\) are collected in Table 2. Results reveal that the optical gap in both direct and indirect allowed shifts decrease with raising SrO2 content in the prepared samples as shown in the inset figures of Fig. 6a and b, respectively. The values in case of direct allowed transition were changes between 3.15 eV for BBPS0 glass and 2.38 eV for BBPS30 sample, while 3.07 eV and 2.28 eV for BBPS30, respectively in case of direct allowable transition. Utilizing the values of \(E_{{{\text{gap}}}}^{{{\text{Direct}}}}\) and \(E_{{{\text{gap}}}}^{{{\text{Indirect}}}}\), the average linear refractive on index (n) for all proposed glass samples was determined using the next relation [39, 40]:

$$ \left( {\frac{{n^{2} - 1}}{{n^{2} + 2}}} \right) = 1 - \left( {\frac{{E_{{{\text{gap}}}} }}{{20}}} \right)^{{0.5}} . $$
(9)
Fig. 6
figure 6

Variation of a (αhν)2 and b (αhν)1/2 with hν for BBPS0–BBPS30 glasses

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The obtained n values are listed Table 2. The n changes from 2.368 for BBPS0 sample to 2.606 for BBPS30. Generally, n for the proposed glasses increase with enhancing SrO2. Additionally, n is high, thus, the investigated glasses can be used as latent candidates in optical applications.

Urbach’s energy (EU) for all proposed glasses was calculated via the following relation [41]:

$$ \alpha (\nu ) = \bar{\alpha }(\nu )\exp \left( {\frac{{h\nu }}{{E_{{\text{U}}} }}} \right), $$
(10)

Here, \(\bar{\alpha }\left( \nu \right)\) is a constant. By taking logarithm for both sides of Eq. (10) and drawing ln(α) versus (hν), the values of EU can be obtained. The variation of ln(α) with hν is shown in Fig. 7, from the linear part of the curves, EU values can be evaluated. EU values recorded in Table 2 and plotted against SrO2 content in the inset figure of Fig. 7. The increasing of EU with increasing the amount of SrO2 in the prepared glasses due to increase of localized state concentration in the bandgap.

Fig. 7
figure 7

Variation of ln(α) with hν for BBPS0–BBPS30 glasses

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3.3 Nuclear shielding competence

The mass attenuation coefficients-MAC values (μm) of the prepared glasses at the energy ranges are between 0.02 and 20 MeV were derived from MCNPX simulation code and WinXCOM. Table 3 shows these obtained MAC data. From Table 3, it can be seen that MCNPX and WinXCOM, data are in well agreement to each other. Therefore, obtained outcomes verifies that MCNPX simulation is accurate to compute the μm values [42, 43]. Figure 8 compares the results of MAC. It can be noted that MAC values of the studied glass materials (encoded BBPS0, BBPS5, BBPS10, BBPS15, BBPS20, BBPS30) are reflective to the variation in the energy levels. If photon energies approach 20 MeV, the MAC values begin to decrease. Among the glass samples examined, BBPS30 had the highest MAC values. In the other hand, HVL-MFP and TVL are critical parameters to consider when predicting the performance of investigated materials in shielding applications. It should be remembered that these parameters represent the materials' thickness. Figures 9, 10, and 11 illustrate the variations of HVL, TVL, and MFP values as a function of incident hν, respectively. Given the inverse relationship between HVL and μ (HVL = ln2/μ), it is reasonable to assume that the sample with the greatest values of µ can offer the lowest HVL values [44, 45]. This situation has been confirmed by our findings that BBPS30 sample was reported with the minimum HVL values among the investigated glasses. On the other hand, TVL has similar inverse relationship with µ values (TVL = ln10/μ) [46, 47]. As a result, a similar pattern was seen for the BBPS30 sample, with the lowest TVL values among the examined glasses. The term MFP refers to the average distance traveled by an electron throughout the scattering process. When all target particles are at rest except one, the MFP may be calculated using the average distance between the particles as MFP = 1/µ. The smallest MFP can be interpreted as an indication of gamma-ray attenuation supremacy, since it suggests that the incident photon's average moving distance is also the smallest. The results indicate that BBPS30 has the lowest MFP values at the photon energies studied. Overall, the findings list the HVL, MFP, and TVL values associated with each material in ascending order as BBPS0 > BBPS5 > BBPS10 > BBPS15 > BBPS20 > BBPS30. The various photons with B, C, O, Sr, Ba, Pb that derived from high Z dependency have a reducing impact on the HVL, MFP and TVL values. For example, while SrO2 concentration in glass rise, HVLs for hν fall. The effective atomic numbers (Zeff) values for the investigated glass sample with various SrO2 concentration with respect to varying energy levels are reported in Fig. 12. From Fig. 12, possessing higher the Zeff values, BBPS30 serves better in terms of radiation shielding [48,49,50,51]. The fast neutron effective removal cross-section values (ΣR) for BBPS0, BBPS5, BBPS10, BBPS15, BBPS20, BBPS30 samples are given in Fig. 13. It should be noted that ΣR decline with increasing SrO2 concentration in the glass structure. The results show that the BBPS0 glass sample is better in terms of fast neutron shielding [19,20,21,22].

Table 3 MAC (μm = μ/ρ) of the prepared glass system obtained from MCNPX and WinXCOM
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Fig. 8
figure 8

Mass attenuation coefficient of the selected glasses with hν 0.02–20 MeV

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Fig. 9
figure 9

HVL of the prepared glass samples

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Fig. 10
figure 10

TVL of the prepared glass samples

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Fig. 11
figure 11

MFP of the prepared glass samples

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Fig. 12
figure 12

Effective atomic numbers of the prepared glass samples with hν

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Fig. 13
figure 13

Effective removal cross-section values of the glasses with density

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4 Conclusion

The major aims of this work were to investigate the physical, UV–Vis–NIR spectroscopy and nuclear shielding properties of novel borate glasses with nominal compositions 50B2O3–25BaO–25PbO–0SrO2: x = 0–30 mol% (BBPS0–BBPS30). From the obtained results, one can concludes the following points:

  1. 1-

    Densities of the fabricated glasses increased from 4.685 to 5.315 g/cm3, while molar volumes decreased from 29.869 to 29.152 cm3/mol.

  2. 2-

    The non-crystalline nature of the fabricated glasses is confirmed by utilization of X-ray diffraction (XRD) measurements.

  3. 3-

    Direct and indirect (\(E_{{{\text{gap}}}}^{{{\text{Direct}}}}\), \(E_{{{\text{gap}}}}^{{{\text{Indirect}}}}\))optical energy gaps, average of refractive index (n), and Urbach’s energy for (BBPS0–BBPS30) glasses were varied from varied from 3.15 to 2.38 eV, 3.07–2.28 eV, 2.268–2.606 eV, and 0.239–0.296 eV, respectively.

  4. 4-

    BBPS30 has maximum mass attenuation coefficient (μ/ρ) value which varies from 0.0420 to 60.259 cm2/g for hν 0.015 and 15 MeV.

  5. 5-

    The HVL, MFP, and TVL values corresponding to the materials were in a descending order BBPS0 > BBPS5 > BBPS10 > BBPS15 > BBPS20 > BBPS30.

  6. 6-

    The ∑R decrease with increasing the density of glass samples.

Therefore, results confirm that BBPS30 glass has superior shielding features against gamma-rays than the other material in the studied sample of glasses.