## 3 Result and Discussion  
### Material Features Study  
The application of glassy complexes for radiation shielding purposes is a function of its composition, which accordingly impacts the material properties of the system. Following the proposed glass's compositional layout, some physical and mechanical attributes were computed to depict the effect of various heavy metal ion modifiers incorporated in the system. From Tables 1 and 2, the variation in the measured density and molar volume values validate the effect of modifiers, and it is graphically signified in Figure 2. The figure indicates the compositional variation in density and molar volume as the additive is varied in each system and the values follow the order SBT-Pb > SBT-Ba > SBT-Zn > SBT-Ti and SBT-Ti > SBT-SbT-Pb > SBT-Ba > SBT-Zn, respectively. The behavior of molar volume is contrary to that of density in the general case. However, in the current investigation, it is unnoticed due to the formation of various structural units due to additives inclusion and non-bridging oxygens (NBOs) creation in the modifier reliant multi-component glass matrices [29]. \begin{table}
\begin{tabular}{c c c c c} \hline  & **SBT-Ti** & **SBT-Zn** & **SBT-Ba** & **SBT-Pb** \\ \hline MW & 106.561 & 106.864 & 121.253 & 135.228 \\ Molar volume & 26.252 & 24.871 & 25.584 & 25.681 \\ \(V_{i}\) & 16.405 & 15.065 & 15.285 & 15.825 \\ \(G_{t}\) & 72.660 & 62.400 & 60.320 & 57.480 \\ \(V_{t}\) & 0.625 & 0.606 & 0.597 & 0.616 \\ Young & 90.810 & 75.596 & 72.077 & 70.840 \\ Bulk & 68.096 & 54.949 & 51.675 & 52.384 \\ Shear & 35.535 & 29.746 & 28.432 & 27.789 \\ Poisson & 0.278 & 0.271 & 0.268 & 0.275 \\ micro-hardness & 5.265 & 4.547 & 4.406 & 4.176 \\ Longitudinal & 115.476 & 94.610 & 89.585 & 89.436 \\ longitudinal velocity & 5333.739 & 4692.414 & 4347.607 & 4121.235 \\ Shear velocity & 2958.797 & 2631.106 & 2449.274 & 2297.251 \\ Softining temperature & 452.948 & 339.322 & 302.472 & 267.102 \\ Bond fractal conductivity & 2.087 & 2.165 & 2.201 & 2.122 \\ \hline \end{tabular}
\end{table} 
Table 2: Physical and mechanical attributes of the prepared glasses. Figure 1: The created geometry describes the Monte Carlo simulation input file. In the case of multi constituent glasses, each element applies its effect so that any change in the mechanical attribute can be considered as a combination of the impact of all the individual constituents. With this context, the mechanical moduli (including young, bulk, shear, and longitudinal moduli) along with Poisson's ratio, microhardness, and more features were calculated for the as-prepared glass specimens with the formulae specified in the literature [26; 30] and gathered in Table 2. The correlation between dissociation energy and packing density is illustrated in Figure 3, which depicts the fact that among all the proposed glasses, SBT-Ti is noticed to own greater volume density of binding energy and reduced ionic volume that are essential for better radiation attenuation. The structural compactness and alteration in the geometrical arrangement in the glass complexes due to additives inclusion are apparent from the estimated elastic constants, which are graphically correlated in Figure 4. The change in the elastic moduli denotes the distinction in the nature and strength of the chemical bonds, cross-link density, which describes the glass configuration and is also related to the dissociation energy of the system. Figure 4 proves that the tightly packed structure with better cross-linkage density is possessed by the SBT-Ti glass system among the titled glass batch. The elastic moduli also rely on the shear and longitudinal velocities of the complex, which are also high for the SBT-Ti glass system, as observed in Table 2. The gradual reduction in both the velocities in the systems with different additives results from the rise in the molar volume, which leads to a loosened structure [31]. Commonly, the Poisson's ratio of glassy complexes is affected by the alteration in its cross-link density which arises from the structural modification [20; 32].