Introduction

The science and technology of radiation shielding is a major factor for the continued growth of nuclear energy applications and facilities around the world. The energy, medical, and research industries are just a few of the many industries that have benefited greatly from the peaceful usage of nuclear energy. Radiation protection technology also aids in assuring the public of the inherent safety of nuclear energy and radiation [1,2,3]. In general, in all radiation-based technology, the optimization of radiation operations and the limitation of dosage are cardinal objectives in all protective guidelines. These standards were created primarily to safeguard people and the environment from the consequences of uncontrolled radiation exposure [3, 4].

When creating the composition of glass, heavy metal oxides are frequently used in order to enhance the shielding potential of the glass system in question. Adding heavy metal oxides to a glass system can significantly increase the overall density of the glass, which is typically associated with improved shielding ability [5, 6]. Heavy metal oxides are metal oxides with a high density, and when they are added to a glass system, they can significantly increase the overall density of the glass system. Because of its high density and excellent attenuation capabilities, Bi2O3 is a heavy metal oxide that is widely employed [7]. Bi2O3 is also frequently utilized as a lead substitute due to the fact that it has qualities that are similar to lead when it comes to radiation shielding. Bi2O3 can be used as a glass intermediate in a variety of applications, including glass modification and glass formation, depending on the composition of the glass matrix. Bi2O3 is a chemical compound that is used in the production of glass. A glassmaker is responsible for forming the backbone of the glass structure, whereas a glass modifier affects the structure of the glass but does not contribute to its formation as a whole [8, 9].

Borate-based glasses have a wide range of glass forming regions, a low melting point, high thermal stability, strong bond strength, high rare earth ion solubility, smaller cation size, and high transparency [10,11,12,13,14,15,16]. It has a random network structure made up of trigonal BO3 units that, depending on the modifier oxide glasses type and concentration, can be transformed into tetrahedral BO4 units [17, 18].

Glasses incorporating alkaline, alkali, rare-earth, and/or transition metals perform well in a variety of applications [19,20,21,22,23], including solid-state electrolytes [19, 20], solid-state illumination [21], optoelectronic devices [22], and radiation shielding [24,25,26,27,28,29].

The objectives of this work are to explore the following interesting characteristics of high dense TeO2–ZnO–TiO2–Na2O–Bi2O3. In addition to the linear dielectric susceptibility (χ(1)), the electronegativity (χ*), and the non-linear refractive index (\({n}_{2}^{\mathrm{optical}}\)), the non-linear optical susceptibility (χ3) is also measured. Using two different tools (MCNPX [30] Monte Carlo simulations and Phy-X/PSD [31] software), the gamma-ray attenuation competencies of the investigated glasses are evaluated: linear (μ) and mass (μm) attenuation coefficients, half-value layer (HVL), effective atomic (Zeff), and exposure and energy absorption buildup factors (EBF and EABF).

Materials

Bismo-tellurite sodium titanium zinc glasses (B5–B15)

Bismo-tellurite sodium titanium zinc glass samples with chemical formula (80 − x)TeO2–10ZnO–5TiO2–5Na2O–xBi2O3, where x = 5 mol%, 8 mol%, 10 mol%, 12 mol%, and 15 mol% have been synthesized previously via using the conventional melt quenching process [32]. These glasses are selected in order to achieve the aims of this work. The investigated samples are named as (see Table 1):

  1. (i)

    75TeO2-10ZnO-5TiO2-5Na2O-5Bi2O3: B5 with density 5.401 (g/cm3)

  2. (ii)

    72TeO2-10ZnO-5TiO2-5Na2O-8Bi2O3: B8 with density 5.613 (g/cm3)

  3. (iii)

    70TeO2-10ZnO-5TiO2-5Na2O-10Bi2O3: B10 with density 5.762 (g/cm3)

  4. (iv)

    68TeO2-10ZnO-5TiO2-5Na2O-12Bi2O3: B12 with density 5.844 (g/cm3)

  5. (v)

    65TeO2-10ZnO-5TiO2-5Na2O-15Bi2O3: B15 with density 6.138 (g/cm3)

Table 1 Code, chemical composition, and density of the (80 − x)TeO2–10ZnO–5TiO2–5Na2O–xBi2O3, where x = 5, 8, 10, 12, and 15 mol%
Full size table

Results and discussion

Optical properties of B5–B15 glasses

These glasses (B5–B15), which were evaluated in this study, were found to have high electronegativity and low linear dielectric susceptibility (χ(1)), which were measured. The electronegativity (χ*) of a cation and an anion can be computed with the help of the electronegativity of the cation. Duffy [33] has proposed a relationship to find the χ* for complicated systems like the one under investigation (B2O3–TeO2–TiO2–Na2O–ZnO), which is depicted in Eq. (1). Additionally,

$$\chi^{\mathit\ast}\mathit=0.2688E^{optical}$$
(1)

where Eoptical is the optical energy bandgap. The values of Eoptival of B5–B15 glasses are listed in Table 2 [32]. When it comes to glasses, the linear dielectric susceptibility (χ(1)) is a characteristic that analyzes a material's ability to become totally polarized. The following Eq. (2) can be used to compute the χ(1) of glasses [33, 34]:

$${\chi }^{\left(1\right)}=\left({\left({n}_{2}^{\mathrm{optical}}\right)}^{2}-1\right)/4\pi$$
(2)

where noptical is the linear optical refractive index. Values of noptical of B5–B15 glasses are listed in Table 2 [32]. Figure 1a  and b depict the variation of the χ* and χ(1) with Bi2O3 content in the investigated B5–B15 samples. As seen in Fig. 1a and b, the values of χ* and χ(1) have an opposite trend. Therefore, behaviors of the χ* and χ(1) can be discussed as the modifications in the structure of B5–B15 glasses with adding of Bi2O3 helps to change the number of non-bridging oxygen (NBO) in the network structure [32].

Table 2 Eoptical, noptical, (χ*), (χ(1)), (χ3), and \(\left({n}_{2}^{\mathrm{optical}}\right)\) of the B5–B15 studied glasses
Full size table
Fig. 1
figure 1

Dependence of (a) χ* and (b) χ(1) on Bi2O3 concentration mol% of B5–B15 glasses

Full size image

The non-linear refractive index \(\left({n}_{2}^{\mathrm{optical}}\right)\) and non-linear optical susceptibility (χ3)) of the investigated B5–B15 glasses were calculated via Ticha and Tichy postulation [35]:

$$\chi^{\mathit3}\mathit(esu\mathit)\mathit=A\mathit/\mathit(\mathit4\pi\mathit)^{\mathit4}\mathit(n^{\mathit o\mathit p\mathit t\mathit i\mathit c\mathit a\mathit l}\mathit-\mathit1\mathit)^{\mathit4}$$
(3)
$$n_{\mathit n}^{\mathit o\mathit p\mathit t\mathit i\mathit c\mathit a\mathit l}\mathit{\left({esu}\right)}\mathit=\frac{\mathit{12}\mathit\pi\mathit\chi^{\mathit3}}{\mathit n^{\mathit o\mathit p\mathit t\mathit i\mathit c\mathit a\mathit l}}$$
(4)

where A = 1.7 × 10−10 is a constant. Values of the calculated χ(3) and \({n}_{2}^{\mathrm{optical}}\) for the investigated B5–B15 glasses are plotted as a function of Bi2O3 content in Fig. 2a and b, respectively. Also, values of χ(3) and \({n}_{2}^{\mathrm{optical}}\) are listed in Table 2. From Fig. 2a and b, it was seen that two non-linear optical parameters have a similar trend of the investigated glasses; this may be attributed to the increasing in the non-bridging oxygen (NBO) in glass structures [32].

Fig. 2
figure 2

Dependence of (a) χ3 and (b) \({n}_{2}^{\mathrm{optical}}\) on Bi2O3 concentration mol% of B5–B15 glasses

Full size image

Radiation protection properties of B5–B15 glasses

In this study, radiation shielding properties of five different glass samples (B5–B15) based on TeO2–ZnO–TiO2–Na2O–Bi2O3 chemical structure were investigated in a wide range of gamma-ray energy, i.e., from 0.015 to 15 MeV. As can be observed from the chemical compositions of the glasses, the amount of Bi2O3 reinforcement has been raised from 5 to 15% mole, while the quantity of TeO2 reinforcement has been lowered from 75 to 65% (see Table 1). Meanwhile, the adjustment described above resulted in an increase in the glass density from 5.401 to 6.138 g/cm3. Figure 3 shows the variation of glass densities. One can say that 10% mole increment of Bi2O3 in the glass composition resulted in a 0.737 g/cm3 total improvement in the glass density. Following the understanding of density change in the glass structures, we have utilized a detailed characterization using a well-known online platform, namely Phy-X/PSD [31], in terms of determining some fundamental gamma-ray shielding parameters, namely mass attenuation coefficients (µm), half-value layer (T0.5), mean free path (λ), effective atomic number (Zeff), exposure buildup (EBF), and energy absorption buildup factors (EABF), respectively. Figure 4 depicts the variation of mass attenuation coefficients (cm2/g) of investigated glasses as an incident photon energy (MeV) function. As it is seen from the figure, there is a sharp decrement in the low energy region, where the photo electric effect (PE) dominates all the photon–matter interactions. In the mid-energy region, the decrement was smoother than the low-energy region. This can be explained by the impact of Compton scattering (SC). However, the findings suggested that the B15 sample with the highest Bi2O3 content had the maximum µm vales across all photon energies examined. Due to the fact that µm is a density-independent parameter [36, 37], we may explain the preceding result in terms of elemental substitution between TiO2 and Bi2O3. The rising Bi2O3 content also boosted the glass sample’s total atomic weight from B5 to B15. As a result, the µm values of the glasses under examination significantly improved. On the other side, radiation protection studies need a thorough evaluation of the candidate shield materials used in radiation facilities in terms of determining the thickness, which may halve the intensity of incoming radiation. This is referred to as the half-value layer, and it is of considerable importance not only for radiation shielding investigations but also for medical diagnostic applications involving various modalities such as mammography. In this study, we determined the half-value layers of the glasses in a wide photon energy range. Half-value layer has an inverse correlation with any shielding material's linear attenuation coefficients. In other words, shielding materials having a greater number of linear attenuation coefficients may be referred to by their layer thicknesses with a lower half value. Thus, by demonstrating their superiority in gamma-ray attenuation, materials with lower half-value layers may halve the incoming gamma-ray intensity with smaller material thicknesses. In the current investigation, we determined the half-value layers of the glasses in the photon energy range of 0.015–15 MeV [37, 38, 39, 40]. Figure 5 shows the changes of half-value layer (cm) values of investigated glasses as a function of incident photon energy (MeV) and increasing Bi2O3 contribution in the glass structures (i.e., from 5 to 15% mole). The findings showed that B15 samples have the minimum half-value layer values at all photon energies. This is another clear example of the enhanced shielding qualities and the beneficial effect of increasing the quantity of Bi2O3 on the gamma-ray attenuation properties. The mean free part (λ) is a vital quantity in radiation sciences, notably in radiation shielding research. This is because the findings of provide unique knowledge in terms of a more accurate assessment of the mean distance for an incident gamma-ray interaction with the material environment. As a conclusion, one may propose that dropping the value results in a more attenuating environment for energetic gamma-rays. We measured the values of all the glass samples examined in this study. The shifting tendency in the mean free path (λ) values of the investigated glasses as a function of incoming photon energy and increasing Bi2O3 contribution is shown in Fig. 6. We noticed that the shortest λ values are given for the B15 sample, which is consistent with the sample’s smallest mean distance for adjacent gamma-ray interactions. It is necessary to assess an appropriate gamma-ray shield with a high effective atomic number. This is because the Z number of an element is related to the number of electrons in its atomic orbit. Given the critical role of electrons in orbit in interacting with gamma photons, it is predicted that elements or compounds with a high Z atomic number would have a greater number of electrons in orbit engagements. Given that increasing contact results in increased photon attenuation, a higher Zeff value may be interpreted as another indicator of improved gamma-ray attenuation capabilities. As seen in Fig. 7, B15 has the highest Zeff value of all gamma-ray energies. Additionally, as compared to the other glasses investigated, this condition is related with the greatest Bi (Z = 83) concentration in B15. Backscattering or photon reflection is a serious issue for researchers and suppliers of gamma-ray protection. It is a primary challenge in radiation shielding. As a response, successful geometry design is seen as a significant obstacle in this area. The buildup factor plays an important role for correct gamma attenuation measurements and may impact measurement precision. When gamma radiation travels through shielding substance, two different types of radiation are produced: un-collided photons and collided photons. As a conclusion, the accumulation factor is an essential statistic for determining the presence of gamma-rays. It is calculated as the proportion of total particles at a point to total particles that have not collided at that location. The shields with the lowest exposure (EBF) and energy absorption (EABF) buildup factors among the examined materials may be classified outstanding shielding substances. The exposure (EBF) and energy absorption (EABF) buildup factors of B5, B8, B10, B12, and B15 glasses were measured in this research. Figures 8 and 9 illustrate how the exposure buildup factor (EBF) and energy absorption buildup factor (EABF) values of glasses evolve as a function of incoming photon energy at various mfp values (from 0.5 to 40 mfp) (MeV). The (EBF and EABF) G–P fitting coefficients (b, c, a, Xk, and d) of B5–B15 samples are shown in Tables 3, 4, 5, 6 and 7. As can be seen, the EBF and EABF values decrease from B5 to B15, demonstrating that the shielding enhancement of glass samples has strengthened. On the other hand, changes in behavior in three photon–matter interaction domains were observed, namely low, medium, and high energy, as a result of the photoelectric effect, Compton scattering, and pair creation, respectively. Our findings suggested that the B15 sample has the lowest EBF and EBF values of all the glass samples examined.

Fig. 3
figure 3

Variation of glass densities (g/cm3)

Full size image
Fig. 4
figure 4

Variation of mass attenuation coefficients (cm2/g) of investigated glasses as a function of incident photon energy (MeV)

Full size image
Fig. 5
figure 5

Variation of half-value layer (cm) values of investigated glasses as a function of incident photon energy (MeV)

Full size image
Fig. 6
figure 6

Variation of mean free path (cm) values of investigated glasses as a function of incident photon energy (MeV)

Full size image
Fig. 7
figure 7

Variation of effective atomic number (Zeff) values of investigated glasses as a function of incident photon energy (MeV)

Full size image
Fig. 8
figure 8

Variation of exposure buildup factor (EBF) values of glasses at different MFP values (from 0.5 to 40 MFP) as a function of incident photon energy (MeV)

Full size image
Fig. 9
figure 9

Variation of energy absorption buildup factor (EABF) values of glasses at different MFP values (from 0.5 to 40MFP) as a function of incident photon energy (MeV)

Full size image
Table 3 (EBF and EABF) G–P fitting coefficients (b, c, a, Xk, and d) of B5 sample
Full size table
Table 4 (EBF and EABF) G–P fitting coefficients (b, c, a, Xk, and d) of B8 sample
Full size table
Table 5 (EBF and EABF) G–P fitting coefficients (b, c, a, Xk, and d) of B10 sample
Full size table
Table 6 (EBF and EABF) G–P fitting coefficients (b, c, a, Xk, and d) of B12 sample
Full size table
Table 7 (EBF and EABF) G–P fitting coefficients (b, c, a, Xk, and d) of B15 sample
Full size table

Conclusion

The objectives of this work are to explore the optical properties and gamma-ray attenuation competencies of bismo-tellurite sodium titanium zinc glass samples with chemical formula (80 − x)TeO2–10ZnO–5TiO2–5Na2O–xBi2O3, where x = 5, 8, 10, 12, and 15 mol%. Our findings revealed that:

  1. 1-

    Values of optical electronegativity (χ*) were varied from 0.715 for B5 glass sample to 0.677 for B15 glass sample.

  2. 2-

    Values of linear dielectric susceptibility (χ(1)) were varied from 0.400 for B5 glass sample to 0.430 for the glass sample.

  3. 3-

    Values of non-linear optical susceptibility (χ3) and non-linear refractive index (\({n}_{2}^{\mathrm{optical}}\)) were varied from 4.379 × 10−12 to 5.812 × 10−12 (esu) and from 6.719 × 1011 to 8.656 × 10−11 (esu) for B5 and B15 glasses, respectively.

  4. 4-

    The B15 sample with the highest Bi2O3 content had the maximum mass attenuation coefficient (µm) values across all examined photon energies, while B5 sample with the lowest Bi2O3 content had the minimum (µm).

  5. 5-

    Both half-value layer (T0.5) and mean free path (λ) followed the trend as follows: (T0.5, λ)B5 > (T0.5, λ)B8 > (T0.5, λ)B10 > (T0.5, λ)B12 > (T0.5, λ)B15.

  6. 6-

    The EBF and EABF values decrease from B5 to B15, demonstrating that the shielding enhancement of glass samples has strengthened.

  7. 7-

    The effective atomic number (Zeff) parameter followed the trend as follows: (Zeff)B15 > (Zeff)B12 > (Zeff)B10 > (Zeff)B8 > (Zeff)B5.

Our findings confirm that the enhancement of Bi2O3 content in the bismo-tellurite sodium titanium zinc glass samples play an important role of improvement both optical and gamma-ray protection properties.