Multiple Assessments on the Gamma-Ray Protection Properties of Niobium-Doped Borotellurite Glasses: A Wide Range Investigation Using Monte Carlo Simulations

provided the original work is properly cited. In this study, the monotonic eﬀect of Ta 2 O 5 and ZrO 2 in some selected borotellurite glasses was investigated in terms of their impact on gamma-ray-shielding competencies. Accordingly, three niobium-reinforced borotellurite glasses (S1: 75TeO 2 +15B 2 O 3 +10Nb 2 O 5 , S2:75TeO 2 +15B 2 O 3 +9Nb 2 O 5 +1Ta 2 O 5 , and S3:75TeO 2 + 15B 2 O 3 +8Nb 2 O 5 +1Ta 2 O 5 +1ZrO 2 ) were modelled in the general-purpose MCNPX Monte Carlo code. They have been deﬁned as an attenuator sample between the point isotropic gamma-ray source and the detector in terms of determining their attenuation coeﬃcients. To verify the MC results, attenuation coeﬃcients were then compared with the Phy-X/PSD program data. Our ﬁndings clearly demonstrate that although some behavioral changes occurred in the shielding qualities, modest improvements occurred in the attenuation properties depending on the modiﬁer variation and its magnitude. However, the replacement of 2% moles of Nb 2 O 5 with 1% mole of Ta 2 O 5 and 1% mole of ZrO 2 provided signiﬁcant improvements in both glass density and attenuation properties against gamma rays. Finally, the HVL values of the S3 sample were compared with some glass- and concrete-shielding materials and the S3 sample was reported for its outstanding properties. As a consequence of this investigation, it can be concluded that the indicated type of additive to be added to borotellurite glasses will provide some advantages, particularly when used in radiation ﬁelds, by increasing the shielding qualities moderately.


Introduction
Radiation is being used in a number of different ways in medicine, including the generation of energy for diagnostic and therapeutic applications. Because radiation cannot be eliminated, protective steps should be taken to minimize its harmful effects. Traditionally, lead (Pb) has the highest atomic number among materials that have a wide usage area in the field of radiation shielding. On the other hand, concrete with low cost, easy use, and good structural properties can also be used as an excellent shielding material. e fact that concrete shielding is primarily utilized in construction is far and by the most important disadvantage, owing to its massive structure and weight. e development of novel glass materials for efficient radiation shielding presents numerous untapped research opportunities. Radiation protection material design is heavily reliant on understanding the interactions between radiation and the materials used to protect against it. Pb or products containing Pb have a number of disadvantages, the most significant of which being their toxicity and consequent risk to users and the environment as well as difficulties faced during the attenuation of low-energy X-ray photons [1][2][3][4][5][6][7][8][9]. As a result, there has been an increase in recent years in the consideration of lead-free glasses as gamma-ray-shielding materials.
is is because many glass compositions have good radiation-shielding capacities and have unique properties such as optical transparency, compatibility for structural modifications as well as radiation absorption. Researchers have been developing various types of radiationshielding glass for several decades, including borate-, silicate-, phosphate-, boro-silicate-, and tellurite-based glass. Indeed, the glass former has an impact on the overall characteristics of the glass matrix. Researchers have been particularly interested in the combination of borate and tellurite, one of many glass-based oxides, due to the distinct properties of these two oxides, such as low melting point, nontoxicity, high refractive index, low phonon energy, chemical and thermal stability, high density, transparency over a wide spectral range, and corrosion resistance [10][11][12][13][14][15][16][17][18][19][20]. Various studies on the gamma-ray-shielding properties of tellurite glasses have been conducted in the literature [21][22][23][24][25][26][27][28][29]. In their pure form, tellurite glasses can crystallize readily and are therefore unstable. Consequently, the addition of other network formers and modifiers, such as alkaline-earth metals, alkaline metals, and transition metal oxides, helps stabilize the system [30]. Transparency, thermal stability, and optical transmittance are all enhanced by TeO 2 glasses containing a significant amount of B 2 O 3 [31]. In addition, using boron oxide is important in glass samples where the thermal expansion coefficient is desired to be low. On the other hand, it increases the resistance of the glass to chemical effects and gives it the ability to refract light. On the other hand, the fact that Nb 2 O 5 and Ta 2 O 5 have empty D-orbitals increases the nonlinear optical response [32][33][34][35][36]. Finally, the ZrO 2 modifier raises the thermal and chemical stability of glass while also increasing viscosity, melting temperature, and glass transition temperature [37][38][39].
Although several studies have shown the effect of glassforming oxides and modifier oxides on the structure and properties of telluride glass, their radiation-shielding properties remain a subject of research. e literature review showed that no previous research has examined the impact of Nb 2 O 5 on borotellurite glasses' absorption capacities using Monte Carlo simulations for gamma rays. Consequently, in this study, we present an analysis of the gammaray radiation protection properties of Nb 2 O 5 added to borotellurite glass [40]   Gamma radiation attenuation parameters like mass attenuation coefficients, effective atomic numbers, and halfvalue relay (HVL) were calculated using the MCNPX [41] simulation code and the Phy-X/PSD program [42] with varying photon energies in the current work. In subsequent sections of this paper, the technical aspects as well as the theoretical underpinnings of the current investigation will be discussed in detail. is work's findings may be useful for future uses of the glass types investigated for radiation shielding in nuclear reactors. In addition, the findings may be useful for a better understanding of borotellurite glasses in the gamma-ray-shielding applications.

Glass Samples.
In this study, the nuclear radiationshielding properties of Ta 2 O 5 -and ZrO 2 -doped niobiumborotellurite glasses [40] were characterized in a wide energy S3 S1 Glass Type      Figure 4: Variations of the mass attenuation coefficient (cm 2 /g) with photon energy (MeV) for all S1-S3 glasses. 4 Science and Technology of Nuclear Installations     Science and Technology of Nuclear Installations 7 range (i.e., from 0.015 MeV to 15 MeV). Nb 2 O 5 was replaced with 1 mol % Ta 2 O 5 and 1 mol % ZrO 2 to evaluate the influence of modifier oxides. As a result, we examined this substitution as a possible monotonic influence on the gamma-ray-shielding behaviors of the analyzed glasses, as well as the effect of the alterations on the gamma-rayshielding characteristics.

Determination of Gamma-Ray-Shielding Properties Using the MCNPX Monte Carlo
Code. e attenuation coefficients of the glasses under examination were calculated using MCNPX (Monte Carlo N-Particle eXtended) version 2.6.0. MCNPX is a fully three-dimensional (three-dimensional) general-purpose application that utilizes upgraded nuclear cross-section libraries and physics models. e shape of the entire gamma-ray transmission setup was modelled using the MCNPX code's INPUT file as a first step in the simulation technique. e INPUT file of MCNPX is composed of three major components: a CELL card, a SURFACE card, and a DATA card. To start, we determined the CELL structures of the simulation equipment by defining their covering surfaces and densities. Additionally, the CELL card component has been defined for each glass sample considering their elemental compositions, which are already described in the material IDs (Mn) section taking into account their elemental mass fractions (see Table 1). Following that, the geometrical alignments of the surfaces for the glass attenuator material, as well as the geometrical structures of the surfaces, which may be planar, spherical, or cone, were entered. We included the radioisotope energies (from 0.015 MeV to 15 MeV, respectively) as well as the source geometry as point isotropic to the DATA card area. Figure 1 depicts the overall geometry of the successfully designed simulation setup. Additionally, we added a critical specification to the DATA card for the data gathering mechanism, which is stated as TALLY MESH. e outcome function of the modelled gamma-ray transmission setup was constructed in this work utilizing the MCNPX`s F4 TALLY MESH. F4 tally is used to record the average flux in a point.
ereafter, attenuation coefficients of the glasses under investigation were determined using the well-known equation, namely the Beer-Lambert law.
where μ (cm −1 ) is the linear attenuation coefficient of the sample and t is the physical thickness (cm) of the shielding material. To understand gamma energy loss as it passes through the shielding material, the mass attenuation coefficients (μ/ρ) can be used for the shielding materials [40]. e mass attenuation coefficient of a compound or mixture is calculated by summing the individual contributions of each of the elements that make up the mixture or compound (see for detailed calculation [43][44][45]. e obtained attenuation coefficients are then used for other critical shielding parameters, namely the tenth value layer (TVL), the half-value layer (HVL), and the mean free path (MFP).

Results and Discussions
e influence of Ta 2 O 5 and ZrO 2 on the gamma-ray attenuation capacities of three niobium-doped borotellurite glasses was examined in this work. e aim of the current investigation was to investigate the monotonic effect of varying molar contributions of Ta 2 O 5 and % ZrO 2 on niobium-doped borotellurite glass. It's well known that the material density has a great impact on the shielding properties of the materials. Comparing the three glass samples' densities showed that the S3 sample had the highest density value at 4.94 g/cm 3 followed by S2 at 4.93 g/cm 3 , and then the S1 sample marking the lowest density at 4.88 g/cm 3 (see Figure 2). e variances between the glasses were not as high due to their comparable chemical compositions and a small number of molar changes across the replacements. However, it is seen that the replacement of 2% moles Nb 2 O 3 with 1% mole Ta 2 O 5 + 1% mole ZrO 2 caused an increment in the glass density as 0.06 g/cm 3 . Along with the elemental alterations and their effect on gamma-ray-shielding behaviors, the given findings may be interpreted in terms of the 0.06 g/cm 3 density difference between the S1, S2, and S3 samples. Calculations for the overall study were conducted in two distinct phases. In the first phase, we utilized the MCNPX algorithm to determine the attenuation coefficients of the glass samples under investigation. To validate our findings, we compared them to those obtained using the Phy-X/PSD tool (see Table 2). Finally, since we verified two approaches, we utilized the Phy-X/PSD code to retrieve the remaining critical values. Figures 3 and 4 depict the numerical variations of the linear (µ) and mass (µ m )attenuation coefficients of the glasses. As it is seen, both figures share almost identical trends that exhibit a sharp decrease followed by a sharp increase in mass and linear attenuation coefficients at 0.03 and 0.04 MeV energies with gradual decreasing afterwards. e sharp changes in the linear and mass attenuation coefficients of the glasses can be explained by the photon-matter interactions in different energy zones such as low, middle and high energy, where the photoelectric effect, Compton scattering, and pair production are dominant, respectively [46][47][48]. It is seen that the variations share almost the same pattern of difference among the S1, S2, and S3 glass types, which is demonstrated in the zoomed-in graphs. As mentioned before, the linear attenuation of a material is density dependent, while the mass attenuation  Science and Technology of Nuclear Installations coefficient is not. As it is seen from Figure 3, there are slight variations between the linear attenuation coefficients of the three glasses.
is situation can be explained by similar density values of the glasses under investigation [49,50]. However, the similarity in the linear and mass attenuation coefficients (see Figure 4) among the three glasses may also be attributed to the similarities in the elemental compositions of the S1, S2, and S3 glasses since replacements have been used with 1% molar differences between the abovementioned structures. However, our findings showed that the S3 sample has the highest linear and mass attenuation coefficients at all the gamma-ray energies studied. Calculating the half-value layer (HVL) of a shielding material is a critical way for determining its effectiveness against the radiation being employed [51,52]. e half-value layer (HVL) is the thickness of a material required to reduce the air-kerma intensity of an X-ray or gamma-ray to half of its initial value. Variations of the half-value layer (cm) with photon energy (MeV) for all S1-S3 glasses are demonstrated in Figure 5. e variation trend of the reported HVL values starts with a gradual increase until 0.03 MeV, where a sharp decrease occurs which results in 0.010 cm value for all glasses; then, it returns to the same pattern of gradual increase in values. At 0.015 MeV, a zoom-in column graph clearly shows the difference among the glasses. Our finding revealed that the S3 sample has the minimum half-value layer thickness at all gamma-ray energies. One may conclude that the minimum material thickness necessary to halve the same amount of gamma-ray energy between the three glasses is the S3 sample, due to its better attenuation capabilities. Similar to the term high value layer (HVL), the tenth value layer (TVL) refers to a certain thickness value for a material necessary to reduce the initial gamma-ray intensity by one-tenth (1/10). Our findings showed that the tenth value layer (cm) graph (See Figure 6) exhibits the same trend behavior and the same difference among the glasses, where the S2 and S3 values are closer to each other, giving S3 the lowest rank in values and S1 the highest. One may conclude that the S3 sample is preferable not just for the HVL values but also for the TVL values in terms of lowering the initial gamma-ray intensity at the smallest material thicknesses. e term mean free path is very helpful in assessing the mean distance between two consecutive gamma-ray interactions in the attenuator material. Figure 7 describes the relationship of the mean free path variations (cm) with photon energy (MeV) for all S1-S3 glasses, which also demonstrates a very similar trend behavior to the HVL and TVL graphs, giving S1 the highest values followed by S2 and S3. As a result, the mean distance between two consecutive interactions in the S3 sample is the lowest among the glasses under consideration, due to its superiority in terms of the interaction frequency with the incoming  gamma-ray, and hence absorption. e relationship between the effective atomic number (Z eff ) and the effective electron density (N eff ) with the incident photon energy differs from previous trends, since they start at a higher value and increase at 0.04 MeV, and then decrease gradually until 1.0 MeV where the trends start increasing again. Both trends exhibit S1 values as the lowest followed by an increase in S2 and S3, giving S3 the highest rank of values (See Figures 8  and 9). erefore, it can be said that the replacement of 2% moles Nb 2 O 3 with 1% mole Ta 2 O 5 + 1% mole ZrO 2 caused an increment in the Z eff and N eff values of S1, S2, and S3 glasses. Figures 10-15 demonstrate the studied glasses' exposure build-up factor (EBF) and energy absorption build-up factor (EABF) values as a function of energy (MeV) at different mean free path (i.e., from 0.5 to 40) values. Similar behaviors are reported as a function of photon energy, with a substantial rise in these values at 0.04, 0.06, 0.08, 0.1, and 15 MeV energies, respectively (see . Variations in the EBF and EABF values are less at smaller penetration depths up to 15 MeV energy, yet they significantly increase with increasing mfp where the energy intensifies up to 15 MeV. e build-up of photons usually occurs at higher mfp values, particularly for thicker materials and a greater diversity of incoming X-rays or gamma rays [53][54][55][56][57]. Our findings clearly indicated that S1 ranks the highest followed by S2 with a slight decrease, and subsequently S3 ranks the lowest. In general, our findings for basic gamma-rayshielding qualities indicated that the S3 sample exhibits the greatest attenuation among the three glasses investigated. e final assessment step of this research compared the HVL values of the S3 sample, which demonstrated the best performances across all gamma-ray reduction parameters to those of many other glass-and concrete-shielding materials.
e compared materials and their codes are listed as follows.
To begin, all HVL values for the S3 sample were compared to those of other glassy shielding materials whose gamma-ray attenuation characteristics had been previously reported for the same gamma-ray energy range. As seen in Figure 16, the S3 sample's gamma-ray attenuation properties are much greater than those of the glass materials tested. e primary explanation for this condition is the disparity between the heavy element additions in the glass composition and the density increase caused indirectly by this additive. Additionally, the HVL values of the S3 sample were compared to those of many concrete-shielding materials functioning in the same energy range. ese concrete materials, including       Figure 17. As can be seen, especially at low energy levels, the HVL values of the S3 sample are much lower than those compared with the concrete samples. On the other hand, this advantageous situation in HVL values was also seen in all energy values studied. Although concrete is still the most effective and preferred shielding material for medical and industrial radiation fields, there are also disadvantages of this material. For this reason, the production and development of superior glassy shields such as the S3 sample, which can be an alternative to concrete and especially overcome the critical disadvantages of concrete, will make important contributions to the material literature, as well as enable the reshaping of the shielding materials recommended in radiation protection procedures.

Conclusion
e use of glass and glass-based materials for shielding in radiation fields has increased visibly in recent years. Some of the most main causes for this expansion are that glass constructions are incredibly adaptable to development and may be manufactured with a variety of components and their combinations in varying proportions. On the other hand, it is extremely important to understand the monotonic effect of certain types of additive ratios that increase or decrease in the glass composition during the production of glass series. e aim of this study was to examine the radiation attenuation difference occurring in the studied borotellurite glass structures according to the varying additive ratio and to discuss the rationale behind the positive change in the shielding ability. e glass samples that have been investigated in the current investigation were previously assessed in terms of their nonlinear refractive index. e initial outcome results indicate that while the modifier oxides have an effect on the structural units and polarizability of the glass, they are insufficient to alter the behavior of the nonlinear refractive index spectra, with the glass matrix being the primary source of optical nonlinearity in the system under study. As with prior results for other characteristics, our findings clearly demonstrate that although some behavioral changes occurred in the shielding qualities, modest improvements occurred in the attenuation properties depending on the modifier variation and its magnitude. However, the replacement of 2% moles of Nb 2 O 5 with 1% mole of Ta 2 O 5 and 1% mole of ZrO 2 provided significant improvements in both glass density and attenuation properties against gamma rays. While concrete remains the most efficient and favored shielding material in medical and industrial radiation sectors, it does have certain drawbacks. As a result, the production and development of superior glassy shields, such as the S3 sample that can be used in place of concrete and specifically overcome its critical disadvantages, will contribute significantly to the material literature, and enable the reshaping of shielding materials recommended in radiation protection procedures. As a consequence of this investigation, it can be concluded that the indicated type of additive to be added to borotellurite glasses will provide some advantages, particularly when used in radiation fields, by increasing the shielding qualities moderately. Additionally, supplementary material characterizations of the relevant glass types are recommended, and it would be beneficial to extend this follow-up research and provide additional data to the literature in order to fully understand and apply the relevant glass type's terms of use.

Data Availability
e data presented in this study are available on request from the corresponding author.

Conflicts of Interest
e authors declare that they have no conflicts of interest.