3.1 Density property and XRD analysis
Through relation (1), the densities of the fabricated xNd-glasses were measured and listed in Table 1. Results of densities showed a gradual slightly increase in the sample’s density with Nd2O3 addition. This trend may be attributed to the systematic increase in the molecular mass of the glass samples due to the addition of the higher molecular weight Nd2O3 (336.48 g/mol) at the expense of the lighter molecular weight B2O3 (69.6 g/mol). Another equally valid interpretation is that the density of xNd-glasses increased as the gradual replacement of the lower density B2O3 (2.46 g/cm3) by the higher density Nd2O3 (7.24 g/cm3).
Figure 1 illustrates the XRD patterns of the fabricated xNd-glasses. As shown in Figure 1, the XRD patterns confirm the amorphous phase for all fabricated glasses. Furthermore, the characteristic diffraction peak was defined and sharp at around 29°, confirming the amorphous state. In addition, the absence of strong diffraction peaks and the presence of hump can be seen in all XRD patterns for all samples.
3.2 γ-radiation shielding characteristics
The ionizing radiation shielding effectiveness of the fabricated xNd-glasses is controlled, governed, and examined using the linear (LAC=µ) and mass attenuation coefficient (MAC=µm). The LAC and MAC mainly depends on both the nature of glasses (compositions) and incident photon energy and not depends on thickness of glasses. Physically, the MAC is considered as the sum of the probability of photons interaction mechanism with the material (i.e. photoelectric effect (PE), Compton scattering (CS), and pair production (PP) processes).
In the current work, the MAC of the fabricated xNd-glasses with their elemental compositions and density is estimated as a function of the photon energy (E) in the range 0.015-15 MeV via XCOM programs  and simulated via FLUKA code . The obtained values of 0Nd, 1Nd, and 2Nd glasses are listed in Table 2 and for 3Nd, 4Nd, and 5Nd glasses are listed in Table 3. The variation of mass attenuation coefficient (MAC=µm) values as a function of photon energy (E) of xNd-glasses is illustrated in Figure 3. The relative deviation between the computed and simulated values has been calculated and depicted in Figure 4, it was in the range from -8% to 8% for 0Nd-glasses, while in the range of -7% to 8% for 5Nd-glasses. Therefore, the simulated and computed values were in well agreement.
As shown in Figure 3, introducing Nd3+ ions in the glass matrix has a direct constructive influence on the obtained values of MAC. It is observed that the MAC enriched with the increase of the Nd3+ ions content in the fabricated glasses. Therefore, the 5Nd-glasses possess the highest MAC and the 0Nd-glasses possess the lowest values. The minimum MAC at 15 MeV were 0.027 cm2/g, 0.027 cm2/g, 0.030 cm2/g, 0.030 cm2/g, and 0.030 cm2/g for 0Nd, 1Nd, 2Nd, 3Nd, 4Nd, and 5Nd glasses, respectively. The maximum of MAC at 0.015 MeV were 25.780 cm2/g, 26.051 cm2/g, 26.177 cm2/g, 26.737 cm2/g, 26.963 cm2/g, and 30.322 cm2/g for 0Nd, 1Nd, 2Nd, 3Nd, 4Nd, and 5Nd glasses, respectively. Generally, the MAC trend follows the order (MAC)5Nd > (MAC)4Nd > (MAC)3Nd > (MAC)2Nd > (MAC)1Nd > (MAC)0Nd which confirms the influence of Nd3+ ions in glass matrix. The obtained trend of the MAC explained as: In the lowest photon energy, the behavior of the MAC exhibits due to the photoelectric effect (PE) that variation is directly with Z4 of absorbing material and inversely with the E3 of the photon energy. In the intermediate region, the Compton Scattering (CS) varies directly with (Z/A) and inversely with energy (E). In the highest energy region, pair production (PP) interaction changes with the second power of Z. In conclusion, the MAC has the highest values depending on the higher (Z) and density of the absorber. Thus, in terms of the MAC parameter, the 5Nd-glasses (5 wt% of Nd3+ ions) with high density (5.245 g/cm3) possessed the greatest MAC values, while 0Nd-glasses (free of Nd3+ ions) with low density (5.006 g/cm3) possessed the minimum MAC values.
Dependence of linear attenuation coefficient (LAC=µ) in cm-1 versus photon energy (E) for the fabricated xNd-glasses is shown in Figure 5. As it was observed in Figure 5, the LAC has a similar trend of MAC, i.e. the 5Nd-glasses possessed the highest LAC values, while 0Nd-glasses possessed the lowest LAC values. Therefore, the LAC trend follows the order (LAC)5Nd > (LAC)4Nd > (LAC)3Nd > (LAC)2Nd > (LAC)1Nd > (LAC)0Nd.
Dependence of the half-value layer T1/2 in cm with photon energy (E) of the fabricated xNd-glasses is depicted in Figure 6. The variation of T1/2 with low energy region is small and their values tend close together, because of the (PE) cross section dominance in this region. By increasing of (E), the T1/2 improved and values more differ from sample to another due to the dominance of both (CS) and (PP) interactions processes. As 5Nd-glasses with high density (5.245 g/cm3) possessed the minimum T1/2 values and it varied from 0.004 cm at 15 keV to 4.301 cm at 15 MeV. Furthermore, 0Nd-glasses with low density (5.006 g/cm3) possessed the maximum T1/2 values changes from 0.005 cm at 15 keV to 4.719 cm at 15 MeV. Therefore, the T1/2 of the fabricated xNd-glasses has an inverse behavior of the MAC and LAC. Thus, (T1/2)0Nd > (T1/2)1Nd > (T1/2)2Nd > (T1/2)3Nd > (T1/2)4Nd > (T1/2)5Nd. Regarding to the obtained results of MAC, LAC, and T1/2, one can conclude that 5Nd-glasses can be considered as superior in radiation shielding capacity among all fabricated glasses.
Figure 7 shows a comparison of the HVL of 5Nd sample with some commercial radiation shielding materials such as Ordinary concrete (OC) , Hematite-Serpentine concrete (HSO) , (ILmenite-Limonite concrete (ILC) , Basalt-Magnitite concrete (BMC) , Imenite concrete (IC) , Steel-Scrap concrete (SSC) , and glasses . From Figure 7, it was observed that the currently fabricated 5Nd-glasses is superior as radiation shielding material than several commercial ones.
In terms of mean free path (λ), the variations of λ with the incident photon (E) for xNd-samples is depicted in Figure 8. As shown in Figure 8, there was negative effect of Nd3+ ions content on the trend of λ. Consequently, 5Nd- glass has the lowest values of λ = 0.006 cm at photon energy 15 keV and 6.205 cm at photon energy 15 MeV, while the 0Nd-glass has the highest values of λ= 0.007 cm and 6.808 cm at photon energy 0.015 MeV and 15 MeV, respectively. Therefore, (λ)0Nd > (λ)1Nd > (λ)2Nd > (λ)3Nd > (λ)4Nd > (λ)5Nd. Results of the λ confirm that the 5Nd-glasses have the best shielding capacity among all xNd-glasses.
Figure 9 depicts the dependence of the effective atomic number (Zeff) on photon energy (E) for all xNd-glasses. According to Figure 9, the increasing of the Nd2O3 content in the fabricated glass matrix has a positive influence for enriching the Zeff. The Zeff is strongly dependent on the glass density. Results confirm that the Zeff parameter follows the order (Zeff)5Nd > (Zeff)4Nd > (Zeff)3Nd > (Zeff)2Nd > (Zeff)1Nd > (Zeff)0Nd.
For radiation shielding evaluating, buildup factors (EBF and EABF) are urgent. They are considered as parameters to study the effect of multiple scatterings in the construction of new shielding glasses. Figure 10 (a-f) and Figure 11 (a-f) present the variation of the EBF and EABF as a function of photon energy (E) at distinct mean free paths (0.5-40 mfp) for xNd-glasses, respectively. The EBF and EABF G–P fitting coefficients (b, c, a, Xk and d) of the fabricated 0Nd, 1Nd, 2Nd, 3Nd, 4Nd, and 5Nd glasses are tabulated in Tables 4-9. As shown in Figures 11 and 12, at low penetration depths, EBFs and EABFs are small. Secondary scatterings take place as the depth of penetration increases, thus the photon buildup becomes greater at 10-40 mfp. At higher energies, both EBFs and EABFs begin to enhance due to the possibility of photons interacting with the glasses in this energy region changes with Z2 (where PP interaction is dominant in this energy zone). In the energies preferred for radiation applications, 5Nd-glasses possess very low EBF and EABF values. This ensures that 5Nd-glasses have more effectiveness among all other glasses in absorbing photons.
3.3 Fast neutron removal cross section (FNRC)
The fast neutron shielding capacity of the fabricated xNd-glasses is evaluated by their fast neutron removal cross section (FNRC). The obtained values of FNRC of the xNd-glasses are presented in Figure 12. Values of the FNRC were 0.1684, 0.1686, 0.1687, 0.1688, 0.1689, and 0.1690 cm-1 for 0Nd, 1Nd, 2Nd, 3Nd, 4Nd, and 5Nd glasses, respectively. The result reveals that 0Nd-glasses (free with Nd3+ ions) include the optimum content of glass constituents that achieves the best neutron shielding ability. Compared to recently studied glass, graphite (FNRC=0.077 cm-1), S30 (FNRC=0.0506) , and OC (FNRC= 0.094 cm-1) , the fast neutron absorbing capacity of xNd-glasses is superior to that of other materials.