1 Introduction

MoO3 is not a glass-forming oxide on its own, but it can combine with other glass-forming oxides as P2O5 to form glasses. Recently, several glass systems involving P2O5 and MoO3 were investigated [1,2,3,4]. IR spectroscopy has been extensively used for structural characterization of MoO3–P2O5 glasses [5]. Selvaraj and Rao [3] investigated PbO–MoO3–P2O5 glasses. Because of PbO's ability to act as a modifier with the structural units of PbO6, adding PbO to phosphate glass increases the glass's stability against devitrification and causes the glass to become chemically inactive [6].

Incorporating transition metal oxide (TMO) to glass improves electronic characteristics by allowing electrons to transfer between valence states. The physical and mechanical characteristics of the glass are improved dramatically by CdO. The physical and chemical properties of glass systems with oxidation states 4 or 6 (CdO4 or CdO6) are altered by CdO [6,7,8,9].

Many industries, such as medical physics and nuclear research, can benefit from nuclear technologies. The interaction of X-ray radiation and a neutron with the material is critical in a variety of radiation technologies and applications. Therefore, radiation shielding has gotten a lot of press. The appropriate precursors for radiation shielding could be specific glass compositions. Glass materials have a range of excellent compositional properties that make them suitable for these applications [10,11,12,13].

Over the last few decades, researchers have investigated several types of glasses for use as alternative shield materials in a variety of nuclear applications. In extension to their ability to absorb high-energy photons, they have a variety of intriguing physical characteristics like transparency, ease of preparation, and stability when exposed to an external field.

The authors of this article investigate the use of fabricated glasses in radiation shielding applications. These glasses have excellent optical characteristics and can be used as radiation shields. Some physical and radiation shielding features were evaluated to achieve this goal.

2 Materials and methods

The chemical composition of the materials used to fabricate glass samples is shown in Table 1. In the following reaction, five lead, phosphate-based glass samples were manufactured. PbO2 + CdO + MoO3 + 2(NH4)2HPO4 \(\frac{\Delta }{-(4{\text{NH}}_{3}+3{\text{H}}_{2}{\text{O}})} \,\to\,\)( PbO2 + CdO + MoO3 + P2O5) \(\,\to\, \text{glass samples}\). The classic melt quenching method was used to produce the glasses, which took 45 min at 1100 °C. To relieve thermal stress, the fabricated glasses were annealed at 400 °C for 2 h and then cooled gradually.

Table 1 Fabricated glasses with \(\text{mol}\%\)
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XRD patterns on a Rigaku-Top XRD were used to check the condition of the glasses. The spectrophotometer type (JASCO V-670) recorded UV–VIS–NIR spectra in the range of 2700–200 nm. The study's goal was achieved by estimating all effective parameters that judge the shielding effectiveness of the prepared glasses using the online version of the Phy-X/PSD software. These glasses were studied for their (MAC), (LAC), and (HVL). We calculated and discussed EBF and EABF.

3 Results and discussion

3.1 Physical investigation

Figure 1 displays the XRD for the glass samples. There were no peaks discovered; instead, a broad hump in the XRD confirmed that the glass samples were amorphous [14, 15].

Fig. 1
figure 1

XRD of fabricated glasses

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Figure 2 shows ρ & \({V}_{\text{m}}\) values of the fabricated samples. As the amount of MoO3 in the sample increased, the density increased. This is because MoO3 (143.938 g mole−1) has a higher density and molecular weight than CdO (128.41 g mole−1). The value of \({V}_{\text{m}}\) declined as MoO3 increased, as displayed in Fig. 2. This could be due to changes in the glass structure, such as a reduction in bond length between the glass network's structure [16, 17].

Fig. 2
figure 2

Density and molar volume of fabricated glasses

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3.2 Optical measurements

Figure 3 demonstrates the variation in UV–Vis absorbance of fabricated glasses in the 200–1200 nm range. As a result, the growth of BO is attributed to MoO3. The absorbance coefficient (α) of the prepared glasses [18,19,20,21,22,23,24] is displayed in Fig. 4.

Fig. 3
figure 3

UV–Vis of fabricated glasses

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Fig. 4
figure 4

Absorbance coefficient of fabricated glasses

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Energy bandgap \({E}_{\text{opt}.}\) was estimated using absorption UV–Vis regions by (\(\alpha \cdot h\nu {)}^{1/2}=B(h\nu -{E}_{\text{opt}.})\) , B is a constant that is not affected by energy. To calculate the indirect \({E}_{\text{opt}.}\) from the intercept, plot (\(\alpha \cdot h\nu {)}^{1/2}\) against \(h\nu\) as is shown in Fig. 5. Because oxygen bridges (BO) are established, which bind excited electrons more strongly than non-bridging oxygen, (NBO) \({E}_{\text{opt.}}\) increases with the increase in MoO3 as shown in Table 2. As shown in Fig. 6 Urbach energy has been calculated as \({\propto }_{0 }{\text{exp}} \left(\frac{h\upsilon }{{E}_{\text{u}}}\right)\) . Figure 7 depicts the \({E}_{\text{opt.}}\) and \({E}_{\text{u}}\) values.

Fig. 5
figure 5

Plot of (\(\alpha h\nu {)}^{1/2}\) against (\(h\nu\)) to estimate the bandgap

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Table 2 Optical parameter values
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Fig. 6
figure 6

Plot of \(ln\left(\alpha \right)\,\text{absorbance coefficient}\) against (\(h\nu\)) to estimate Urbach energy

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Fig. 7
figure 7

Bandgap and Urbach energy against MoO3

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According to these findings, increasing the amount of MoO3 has a significant impact on the \({E}_{\text{opt.}}\) and \({E}_{\text{u}}\). The values of \({E}_{\text{opt.}}\) and \({E}_{\text{u}}\) are presented in Table 2.

The refractive index of fabricated glass was determined by using the following formula: \({n}_{\text{D}}= \frac{{(1- R)}^{2}+{k}^{2}}{{(1+ R)}^{2}+ {k}^{2}}\), k = αλ/4π. \({n}_{\text{D}}\) of fabricated glasses is shown in Fig. 8. \({n}_{\text{D}}\) of these glasses increases as density rises, as previously stated.

Fig. 8
figure 8

Refractive index for fabricated glasses

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The following formulas were used to calculate molar polarization \({R}_{\text{m}}\), polarizability \({\propto }_{0}^{2-}\), and optical basicity \(\Lambda\) of glasses: \({R}_{\text{m}}=\langle {n}^{2}-1|{n}^{2}+2\rangle Vm, {\propto }_{m}=\left(3|4\pi N\right){R}_{\text{m}},\) and \({\propto }_{0}^{2-}=\frac{\left[\frac{Vm}{2.52}\left(\frac{{n}^{2 }-1}{{n}^{2}+2}\right)-\sum {\propto }_{cat}\right]}{{n}_{\text{o}}^{2-}}\) and \(\Lambda = 1.67\left(1- \frac{1}{{\propto }_{0}^{2-}}\right)\). Figures 9, 10, and 11 show the \({R}_{\text{m}}\), \({\propto }_{0}^{2-}\), and \(\Lambda\) of these glasses, respectively. As the \({n}_{\text{D}}\) increases these variables increase. Therefore, \({n}_{\text{D}}\) and \({R}_{\text{m}}\), \({\propto }_{0}^{2-}\), and \(\Lambda\) have a similar trend.

Fig. 9
figure 9

Molar refractivity for fabricated glasses

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Fig. 10
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Polarizability for fabricated glasses

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Fig. 11
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Optical basicity for fabricated glasses

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The dispersion of Eo and Ed were estimated by Wemple and Didomenico [25] as \({n}^{2} - 1= \frac{{E}_{0 } {E}_{\text{d}}}{{E}_{0 }^{2}-{ E}^{2}}\). As shown in Fig. 12, the plotting of (n2−1)−1 with (hυ)2 Eo and Ed was calculated from the slope and intercept. A list of these values can be found in Table 2. With the increase in Mo3+, Eo and Ed have been slightly increased. The optical energy Eopt represents \(E_{\text{opt}}=\frac{{E}_{\text{d}}}{2}\). Refractive Static index at an infinite wavelength (no) was estimated by \({n}_{0 }= \sqrt{1 +\frac{{E}_{\text{d}}}{{E}_{0}}}\) and the static dielectric \({\varepsilon }_{\infty }={n}_{0}^{2}\). The oscillator's wavelength (λo) and strength (So) were calculated using the following formula: \({n}^{2} - 1= \frac{{S}_{0 } {\lambda }_{0}^{2}}{1-(\frac{{\lambda }_{0}}{\lambda } )2}\). Table 2 lists the available items.

Fig. 12
figure 12

(n2−1)−1 against (hυ)−2

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3.3 Shielding properties

In this study, the radiation attenuation capacities of five different glass samples were assessed. Figure 13 depicts the MAC of the fabricated glasses as a function of photon energy. Furthermore, the MAC trend with photon energy in the range in MeV is readily apparent (0.015 to 15). As shown in Fig. 13, the MAC values decrease as photon energy increases. With an increase in the MoO3 ratio, it is more obvious that the MAC values decrease. In the intermediate photon energy zone, there is a stable or slightly changing behavior, while in the maximum photon energy zone, there is an increase in the MAC values. The photoelectric effect, Compton effect, and pair production effect, and cross-sections in the low, intermediate, and high energy zones, respectively, can be discussed [2, 26,27,28,29,30,31,32].

Fig. 13
figure 13

Mass attenuation coefficient for fabricated glasses

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Figure 14 shows the LAC plotted. The photon interaction probability per unit length of the absorber material or medium, measured in cm−1, was illustrated by LAC. As shown in Fig. 14, the LAC values decrease as photon energy increases and increase with the increase of MoO3. This increase is due to an increase in the density of the glasses. As a result, the LAC values increased, indicating an inverse trend for glasses.

Fig. 14
figure 14

Linear attenuation coefficient for fabricated glasses

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The HVL parameter is inversely proportional to LAC and defines the shield, absorber, or medium thickness that attenuates or absorbs 50% of the incident intensity. The sample with the lowest HVL has the greatest shielding capacity. As a result of this behavior, G1 is predicted to have the maximum HVL, while G5 will have the minimum. Among all fabricated glasses, G5 appeared to be the greatest material for shielding. As shown in Fig. 15, the trend (G1) > (G2) > (G3) > (G4) > (G5) ensured the best shielding capacity for fabricated glasses among all other glasses.

Fig. 15
figure 15

Half-value layer for fabricated glasses

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Finally, exposure and energy absorption build-up factors are the final parameters that demonstrate the effectiveness of the tested glasses (EBF and EABF). Figures 16 and 17 show the plots of both parameters. With the substitution of CdO for MoO3, the two parameters have a slight difference. The EBF and EABF were slightly reduced when the MoO5 molar ratios were increased from 0 to 5. This finding could be linked to or attributed to the investigated substance's effective atomic number. Furthermore, by increasing the MFP from 1 to 40 for all synthesized glasses, the two parameters introduced an increase in their values. The gamma photon energy has an impact on these parameters as well. As a result, the EBF and EABF variance behavior is primarily influenced by the three main interaction mechanisms discussed in the MAC section.

Fig. 16
figure 16

EBF variation of G1 & G5

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Fig. 17
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EABF variation of G1 & G5

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4 Conclusions

For optical and radiation shielding applications, the current study prepared and characterized lead cadmium phosphate glasses doped with different concentrations of MoO3. We replaced CdO with MoO3 during this study, which increased density and \({n}_{\text{D}}\) but a decrease in molar volume. UV–VIs spectroscopy has been used to evaluate the optical characteristics of fabricated glasses. \({E}_{\text{opt.}}\) values for the investigated glasses have increased while the \({E}_{\text{u}}\) values have decreased. As the \({n}_{\text{D}}\) increase \({R}_{\text{m}}\), \({\propto }_{0}^{2-}\), and \(\Lambda\) were increased. The values of fabricated sample dispersion parameters related to \({n}_{\text{D}}\) were determined. Phy-X/PSD was used to investigate the radiation shielding properties. MAC values improve as the MoO3 ratio rises. G1 has the maximum HVL value, whereas G5 has the minimum. The exposure and energy absorption build-up factor (EBF and EABF) values decreased slightly as the MoO3 content increased. As a result, among all other glasses, G5 glasses have the best shielding capacity.