## 3 Result and Discussion
### Radiation Attenuation Studies  
The mass attenuation coefficient (\(\mu\)m, cm\({}^{2}\)/g) of the fabricated SBT-n glasses was calculated in an energy range varied between 0.015 and 15 MeV using the Monte Carlo simulation with a narrow beam transmission method. The achieved results were affirmed using the XCOM theoretical program [34] calculated data for the fabricated sample. Figure 6 shows an agreement between the simulated \(\mu\)m using MC simulation and the calculated data by the XCOM program, along with the studied energy range. Also, Figure 6 shows that the highest \(\mu\)m values achieved at gamma-ray energy 0.015 due to the photoelectric interaction, which has a cross-section of interaction that varies inversely with the third power of energy (\(\sigma_{\rm pe}\)\(\alpha\)E\({}^{-3.5}\)). The represented values in Figure 6 showed that the \(\mu\)m at 0.015 MeV varied in the order of 26.836, 33.419, 35.071, and 52.658 cm\({}^{2}\)/g for glasses SBT-Ti, SBT-Zn, SBT-Ba, SBT-Pb, respectively. The high variation in the \(\mu\)m values is related to the significant variation which occurred in the glass samples with the addition of the dopant compounds where the addition of the PbO to SBT glass causes a higher increase in the molecular weight of the fabricated glass, which has a positive effect on the density and atomic weight of the fabricated glasses. Thus, the linear and mass attenuation coefficients are highly increased compared to those glasses doped with TiO\({}_{2}\), ZnO, and BaO. The effect of glasses' atomic weight and density appears in the low energy region (photoelectric region) because the cross-section varies directly with the fourth power of the effective atomic number of the glass sample (\(\sigma_{\rm pe}\)\(\alpha\)\(Z^{4-5}\)) [35; 36]. According to the data presented in Figure 6, another interaction region (Compton scattering) began from 0.15 MeV and extended to lower than 5 MeV. In the mentioned region, the variation of the \(\mu\)m reduced linearly with energy. It linearly increased with the Z. The \(\mu\)m values varied between 0.3709-0.0311, 0.3853-0.0314, 0.04784-0.0324, and 0.8982-0.0348 cm\({}^{2}\)/g with an average of 0.1040, 0.1060, 0.1198, 1855 cm\({}^{2}\)/g for samples SBT-Ti, SBT-Zn, SBT-Ba, SBT-Pb, respectively. Also, the effect of the doping compounds in this energy hasn't a significant  
Figure 5: The correlation between Poisson ratio (\(\mu\)) and micro-hardness (H) of the fabricated SBT glasses. effect compared to the photoelectric region. In the mentioned intermediate region, the linear variation of the \(\upmu\)m values is related to the Compton scattering cross-section where CS \(\alpha\) Z/E. In the high energy region (E\(\geq\) 5 MeV), according to data presented in Figure 6, the \(\upmu\)m values began to increase with energy increase slightly. This behavior is due to the pair production interaction (PP) in which the cross-section varied with log E and \(Z^{2}\). Thus, the \(\upmu\)m values are close together for all fabricated samples and they are independent on the incident gamma-ray energy. In this energy region the \(\upmu\)m values have a slight increase between 0.0296-0.0308, 0.0302-0.0318, 0.0319-0.0346, 0.0351-0.0392 cm\({}^{2}\)/g for the fabricated samples SBT-Ti, SBT-Zn, SBT-Ba, SBT-Pb, respectively. The relation between the half-value layer (HVL, cm) (the thickness required to reduce the incident gamma flux to half of its initial value [37]) and the incident gamma-ray photons was illustrated in Figure 7. The thinner HVL achieved at the lowest gamma-ray energy among the studied energy range (i.e., 0.015 MeV) takes values 0.006, 0.005, 0.004, and 0.002 for samples SBT-Ti, SBT-Zn, SBT-Ba, and SBT-Pb, respectively. This law value is due to the predominant of the PE interaction at the mentioned energy. Thus, the photon energy is absorbed in one collision with a boundary electron. Also, it is clear that the SBT-Pb has a thinner HVL compared to other fabricated glass samples.