The effect of TeO2, ZnO, and NiO ratios in enhancing the radiation shielding, structural, and mechanical features of the provided glass sample

2.2. FLUKA simulation study

Different materials’ performance in terms of radiation shielding has garnered increasing attention in recent research. The high precision of the Monte Carlo (MC) methodology demonstrated in prior studies, especially concerning radiation shielding, highlights the necessity of applying the MC approach for further investigations. Consequently, this study evaluates the efficacy of a specific Te-enriched glass system using the MC technique FLUKA [24].

The simulation input file includes geometry details such as source, glass samples, lead collimator, NaI detector, and the compositions of each cell. The entire system is enclosed within a black-hole region, ensuring that no particles are tracked beyond this boundary. The study involved irradiating three provided glass specimens with several simulated mono-energetic photon sources. Key cards used in this study include BEAM, BEAMPOS, MATERIAL, COMPOUND, USRBDX, USRBIN scoring cards, and geometry cards. The BEAM and BEAMPOS cards define the characteristics of the radiation, while the geometry cards facilitate the simulation of complex geometries using the FLUKA code and Flair environment. Each cell in geometry is assigned specific materials through the MATERIAL and COMPOUND cards. The USRBDX and USRBIN scoring cards enable tracking and recording of particles when they reach the detector. The study defined 10⁷ primary events over five cycles to derive the data. Figure 2 (a, b) illustrates the 2-D and 3-D schematics of the MC simulation.

Figure 2. (a) 2-D and (b) 3-D FLUKA simulation of the provided ternary glass samples.

2.3. Radiation shielding features

The attenuation parameter, like the Half value layer (HVL), is extracted based on the Linear attenuation coefficient (LAC) and Beer-Lambert’s law by Equations 1-2 [25, 26]:

Where I₀ and I are unattenuated and attenuated gamma photons. x is the thickness of the samples.

The Effective atomic number (Z_eff) is crucial in assessing the shielding capabilities of selected samples, as determined using the Phy-X: PSD code. Phy-X: PSD is an accessible and user-friendly software that enables the analysis of attenuation properties in composites, glasses, and other materials. These factors can be evaluated by entering their weight percentage (wt.%), mole percentage (mol%), and density. This tool is readily available for researchers at  https://phy-x.net/ [27].

2.4. Structural and mechanical properties utilizing MM model

The MM model [28, 29] is a superior factor in estimating the mechanical features, which is our concern in this section. Accordingly, they were determined using the formulas provided in Equations 6-11 based on bond dissociation energy (G_t), packing factor (V_i), and packing density (V_t) (see Equations 3-5). These mechanical factors are Young’s (Y), bulk (B), shear (S), longitudinal (L) moduli, micro-hardness (H), and Poisson’s ratio (σ).

Where N_A, R³_A, R³_o, x, and y  represent Avogadro’s number, ionic radius of the metal, ionic radius of oxygen, the number of metal atoms, and the number of oxygen atoms, respectively [29-31].

3. Results and discussion

Figures 3 and 4 show the simulated gamma photon distributions as fluence for ¹³⁷Cs and ⁶⁰Co sources, respectively, highlighting distinct peaks at the corresponding energies of 0.662, 1.173, and 1.332 MeV. As anticipated, the gamma photon peaks were highest in the without sample case (in the air-unattenuated spectrum). However, in the presence of the 4:1-4NiO ternary sample (attenuated spectrum), the spectrum exhibited its lowest values, demonstrating the effectiveness of gamma photon shielding performance. Additionally, when samples are irradiated by ¹³⁷Cs and ⁶⁰Co, wider and broader peaks are observed in comparison to air case which is due to the gamma photon interactions with the glass samples.

The shielding performance of the glass samples can be gauged by HVL. Thus, the HVL values of the prepared novel glass have been extracted and revealed in Figure 5. Generally, the lower values of HVL typically translate to more effective radiation shielding.  As anticipated, increasing the NiO contents in the glass system increases the gamma photon shielding efficiency, likely due to the corresponding increase in density values.  All series exhibit a similar trend across wide energy ranges, with the dominance of PhotoElectric (P-E), Compton Scattering (C-S), and Pair Production (P-P) processes in various energy zones [17]. In the low energy region, the HVL values are relatively similar, whereas in the high energy range, they show greater divergence. For instance, HVL values for provided glasses vary between 0.002 and 3.284 cm, 0.002 and 3.274 cm, 0.002 and 3.266 cm, ranging from 0.015 to 10 MeV for 4:1-4, 4:1-8 4:1-12 specimens. Although HVL results show compliance specifically in low energy ranges, 4:1-12NiO has the lowest HVL and shows the best gamma photon shielding performance. Hence, there is a linear relationship between increased NiO content and HVL values. Since the energy and chemical composition of each glass sample are effective in the HVL behavior, in this specific glass sample, the chemical composition is less effective in comparison with the energy range.

Figure 6 graphically articulates the Z_eff values spanning from 0.015 to 15 MeV using the Phy-X: PSD software for Te novel glass system. A sharp fall and a smooth increase have been recorded for wide energy zones. A detailed analysis of the presented data shows that the Z_eff is proportional to Z^-1, Z, and Z² because of gamma photon interaction in different energy ranges [13]. A Z_eff profile reveals that this factor is energy dependent, specifically in low-energy regions, and only in certain high-energy ranges they show effectiveness against chemical compositions. Z_eff values show a graduation from 31.95 for 4:1-4NiO to 31.37 for 4:1-12NiO at 15 MeV energy range. Concurrently, a decrease in the contents of TeO₂ and ZnO indicates a complex interaction probability with radiation and highlights the attenuation concept. Hence, the 4:1-4NiO glass specimens, characterized by the highest concentrations of TeO₂ and ZnO and the lowest concentration of NiO, exhibit the highest Z_eff, particularly in high-energy regions.

The structural and mechanical parameters of the Te glass system have been obtained through MM model for oxide glasses using the analytical method (See Figures 7-9). The G_t and V_t against density have been represented for the provided glass specimens in Figure 7. Increasing the density, due to the increment of the NiO mol%, enhances the V_t, while the inverse trend is mirrored for G_t. The V_t values range from 2.93 cm³/mol to 3.0008  cm³/mol for 4 - 12 mol% NiO, respectively. Meanwhile, the G_t changes from 50.5 kJ/cm³ to 49.16 kJ/cm³ due to the substitution of the TeO₂ and ZnO with NiO. The Gt values for TeO₂ and ZnO are 54 kJ/cm³, 41.5 kJ/cm³ , while the value for NiO is 32kJ/cm³. Furthermore, as shown in Figure 8, increasing the NiO mol% will decrease the B and L moduli while giving rise to the E and S. For example, the E, B, S, and L for Te:Zn-4NiO are about 1236.987 GPa,4335.375 GPa, 450.257 GPa, and 4920.709 GPa, while these values for 12 mol.% NiO reach about 1233.262, 44426.76, 448.5345, 5009.855 GPa. The calculated H which defines the deformation of the glass network and σ in Figure 9 show a sharp rise for both parameters by increasing the NiO concentration. It weakens the stiffness of the glass network. In conclusion, our attempts to demonstrate enhancements in the mechanical characteristics of the novel Te glass were unsuccessful. The outcomes exhibited an unstable trend, with minor deviations in the measured properties. Furthermore, a detailed analysis revealed that density is not the sole factor influencing the mechanical characteristics as seen in Table 1. From Table 1 and the obtained results can be found that 4:1-12 NiO sample possesses the highest density and is not suitable for mechanical applications.

  Figure 8. Mechanical moduli for the provided ternary specimens.