Fabrication, physical, structure characteristics, neutron and radiation shielding capacity high density neodymio-cadmium lead borate glasses: Nd2O3/CdO/PbO/B2O3/Na2O

doi:10.21203/rs.3.rs-1559498/v1

High density glasses of neodymio-cadmium lead borate of chemical composition xNd₂O₃/20CdO/20PbO/(57-x)B₂O₃/3Na₂O, where (0 (0Nd) ≤ x ≤ 5 (5Nd) wt%) have been fabricated by a melt quenching process. Physical, structure properties as well as gamma-radiation and neutron shielding effectiveness in wide photon energy range 0.015-15 MeV have been examined. The amorphous nature of xNd-glasses was confirmed, where there was a lack of their crystallinity. Density was gradually increased from 5.006 g/cm³ for 0Nd-glass sample to 5.245 g/cm³ for 5Nd-glass sample. In terms of the MAC, introducing Nd³⁺ ions in the glass matrix has a direct constructive influence on the obtained values of MAC. Generally, the MAC trend follows the order (MAC)_5Nd > (MAC)_4Nd > (MAC)_3Nd > (MAC)_2Nd > (MAC)_1Nd > (MAC)_0Nd. The LAC has a similar trend as MAC for all xNd-glasses. In terms of the T_1/2, the 5Nd-glasses possessed the minimum T_1/2 values (0.004 cm at 15 keV to 4.301 cm at 15 MeV). Therefore, the T_1/2 of the fabricated xNd-glasses has an inverse behavior of the MAC and LAC. Thus, (T_1/2)_0Nd > (T_1/2)_1Nd > (T_1/2)_2Nd > (T_1/2)_3Nd > (T_1/2)_4Nd > (T_1/2)_5Nd. the Z_eff parameter follows the order (Z_eff)_5Nd > (Z_eff)_4Nd > (Z_eff)_3Nd > (Z_eff)_2Nd > (Z_eff)_1Nd > (Z_eff)_0Nd. In the energies preferred for radiation applications, 5Nd-glasses possess very low EBF and EABF values. The FNRC of the fabricated glasses is improved as the Nd³⁺ content increases in the glass matrix.

Glasses

Photon

Neutron

Mass attenuation coefficient

Radiation shielding

Due to the fact that glasses are transparent materials, low in price, ease in fabrication, light in weight, tough, non-toxic, and radiation resistant, the use of different glasses for radiation shielding applications has more attention from several researchers and engineers [1–4]. In addition, the interesting physical, mechanical, thermal characteristics of glasses, several glass compositions have been suggested and investigated for their optical, mechanical and radiation shielding capacity through different experimental and theoretical treatments [5–8].

The most common oxide that can act as a glass base is boron oxide (B₂O₃). Borate-based glasses are particularly advantageous due to their physical and chemical properties, which include a low melting point and good transparency [9, 10]. To make a series of glasses with promising optical and radiation shielding properties, the chemical structure of the glasses must be flexible, allowing for doping with new elements or radicals, and changing the stoichiometry of atomic components of glasses. This has necessitated a large number of glass series, each with its own set of properties. A large number of studies have investigated the ability of various metal oxides (B, Li, Cd, Zn, Ca, and others) and rare earth elements (Gd₂O₃, Sm₂O₃, Y₂O₃, La₂O₃, Nd₂O₃ and others) in the glass matrix, such as, to improve photon and charged particle radiation shielding coefficients [11, 12]. Kilic [13] studied the influence of Nd³⁺ ions on structural, optical, and thermal characterization of V₂O₅–TeO₂- (B₂O₃/Nd₂O₃) glasses and concluded that Nd³⁺ ions makes changing in the glass network and acts as a modifier leads to improve the optical and thermal properties. Rammah et al. [14] investigated the optical features of the prepared bismuth boro-tellurite glasses doped with NdCl₃. They reported that the optical properties were enhanced as NdCl₃ content increases. Abdel-Aziz et al. [15] reported that Nd³⁺ and Er³⁺ ions enhanced the physical, structure, mechanical, and dielectric characteristics of calcium lead-borate glasses. In terms of radiation shielding field, Mahmoud et al. [16] investigated the gamma-ray shielding capacity of glasses doped with Nd³⁺ ions rare earth using MCNP-5 code, they claimed that the insertion of Nd³⁺ ions in the glass matrix leads to enrich their radiation shielding capacity. Hegazy et al. [17] studied the nuclear shielding properties of borate glasses modified with Nd³⁺ ions; they reported that increasing Nd³⁺ ions content in the glass matrix helps to enhance the radiation attenuation capacity. Recently, Rammah et al. [18] reported that the insertion of Nd³⁺ ions in the fabricated cadmium lead-borate glasses has a direct improvement in their physical, structural, and optical features.

This paper reports about:

Fabrication of high density neodymio-cadmium leads borate glasses.
XRD patterns and physical properties of the fabricated glasses have been measured.
Investigating the role of neodymium (Nd³⁺) ions content in the fabricated glasses on the photon and neutron shielding efficacy.

2.1 Preparation of xNd-glasses

A series of high density neodymio-cadmium lead borate glasses of chemical composition xNd₂O₃/20CdO/20PbO/(57-x)B₂O₃/3Na₂O, where (0 ≤ x ≤ 5 wt%) have been fabricated by a melt quenching process. The fabricated process was achieved using high purity (99 %) for all oxides which supplied from Strem chemicals and Riedel-De Haën company. Precursors were weighed and thoroughly mixed to obtain a homogeneous composite mixture and finely divided additions, which were then placed in porcelain crucibles and stored inside an electric melting furnace at temperature 1050^oC for about 25 min. Then, the prepared glasses quickly pressed with a steel plate to place in a preheated oven at 250°C and leave to cool to room temperature inside the oven. The code of the fabricated glasses is abbreviated as xNd-glasses: 0 (0Nd), 1 (1Nd), 2 (2Nd), 3 (3Nd), 4 (4Nd), and 5 (5Nd). A photo of the fabricated glasses is shown in Figure 1.

The amorphous state of the fabricated xNd-glasses was examined using X-ray diffraction (XRD) technique with Cu K_α radiation source (λ=1.54nm), Philips model (PW-1729) step size 0.02^oC; time per step: 21 sec.

Density (ρ_glass) of the fabricated xNd-glasses was measured experimentally by Archimedes' principle with (Xylene) as an immersion liquid medium with density (ρ_Xylene =0.863 g/cm³). Weigh each glass sample in air (W_Air) and in Xylene (W_Xylene) and the density of every xNd-glass samples was calculated using the next relation:

Table 1 shows codes, chemical compositions, density of the xNd- glasses.

2.2 XCOM software and FLUKA code for γ-photons

In the current work, FLUKA simulation code was used to examine the gamma-ray shielding characteristics of the prepared xNd-glasses [19]. Figure 2 displays the needed geometry for investigating γ-ray transmission via the prepared glasses. A mono-energetic gamma source emits an initial number of γ-photons about 10⁶ photons to incident directly on the glass sample. The ratio of initial and passed photons used to evaluate the linear attenuation coefficient (LAC = µ) for each glass sample. Then, the mass attenuation coefficients (MAC = µ/ρ=µ_m: ρ is the glass density) based on the following expression [20-25]:

The obtained results of FLUKA code were compared with the theoretical values obtained via XCOM platform [26]. Furthermore, the values µ and µ/ρ were used to examine the half value layer (HVL, T_1/2), mean free path (MFP, λ), and effective atomic number (Z_eff) as follows [20-25,27]:

where A_i and f_i are the atomic mass and molar fraction of ith constituent pure element in the glass. The exposure buildup factor (EBF) and energy absorption buildup factor (EABF) of the fabricated xNd-glasses also examined using the G–P fitting coefficients (b, c, a, Xk and d) as in Ref. [28].

2.3 Calculation of fast neutron removal cross section

Inelastic collisions occur when a fissile/fast neutron collides with any non-hydrogenous material. The fast neutron removal cross section is the statistical probability that a fast neutron interacts in such a way that it is no longer categorized as fast ($FNRC-{{\Sigma }}_{R}$). For fast neutrons with energy ranging from 2 to 12 MeV, this is the macroscopic cross section. The ($FNRC$) may be calculated for materials (xNd-glasses) according to the following expression [29]:

$${{\Sigma }}_{R}=\rho \sum {w}_{i}{\left(MRCS\right)}_{i}$$

4

where, $\rho ,$ ${\left(MRCS\right)}_{i}$, and ${w}_{i}$ are the mass density of the interacting medium, mass removal cross section, and weight fraction of the i^th element.

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=µ_m). The LAC and MACmainly 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 [26] and simulated via FLUKA code [19]. 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=µ_m) 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 T_1/2 in cm with photon energy (E) of the fabricated xNd-glasses is depicted in Figure 6. The variation of T_1/2 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 T_1/2 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 T_1/2 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 T_1/2 values changes from 0.005 cm at 15 keV to 4.719 cm at 15 MeV. Therefore, the T_1/2 of the fabricated xNd-glasses has an inverse behavior of the MAC and LAC. Thus, (T_1/2)_0Nd > (T_1/2)_1Nd > (T_1/2)_2Nd > (T_1/2)_3Nd > (T_1/2)_4Nd > (T_1/2)_5Nd. Regarding to the obtained results of MAC, LAC, and T_1/2, 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) [30], Hematite-Serpentine concrete (HSO) [30], (ILmenite-Limonite concrete (ILC) [30], Basalt-Magnitite concrete (BMC) [30], Imenite concrete (IC) [30], Steel-Scrap concrete (SSC) [30], and glasses [31]. 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 (Z_eff)on photon energy (E) for all xNd-glasses. According to Figure 9, the increasing of the Nd₂O₃content in the fabricated glass matrix has a positive influence for enriching the Z_eff. The Z_effis strongly dependent on the glass density. Results confirm that the Z_eff parameter follows the order (Z_eff)_5Nd > (Z_eff)_4Nd > (Z_eff)_3Nd > (Z_eff)₂_Nd > (Z_eff)_1Nd > (Z_eff)_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, X_k 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) [2], and OC (FNRC= 0.094 cm^-1) [12], the fast neutron absorbing capacity of xNd-glasses is superior to that of other materials.

A series of six samples with high density of neodymio-cadmium lead borate glasses of chemical composition xNd₂O₃/20CdO/20PbO/(57-x)B₂O₃/3Na₂O, where (0 (0Nd) ≤ x ≤ 5 (5Nd) wt%) have been fabricated by a melt quenching process. Physical, structure characteristics as well as gamma-radiation and neutron shielding effectiveness in wide photon energy range 0.015-15 MeV have been examined. The amorphous nature of xNd-glasses was confirmed, where there was a lack of their crystallinity. Density of the fabricated xNd-glasses was gradually increased from 5.006 g/cm³ for 0Nd-glass sample with free of Nd³⁺ ions to 5.245 g/cm³ for 5Nd-glass sample enrich with Nd³⁺ ions. In terms of the MAC, introducing Nd³⁺ ions in the glass matrix has a direct constructive influence on the obtained values of MAC 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. The LAC has a similar trend as MAC for all xNd-glasses. In terms of the T_1/2, the 5Nd-glasses with high density (5.245 g/cm³) possessed the minimum T_1/2 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 T_1/2 values changes from 0.005 cm at 15 keV to 4.719 cm at 15 MeV. Therefore, the T_1/2 of the fabricated xNd-glasses has an inverse behavior of the MAC and LAC. Thus, (T_1/2)_0Nd > (T_1/2)_1Nd > (T_1/2)_2Nd > (T_1/2)_3Nd > (T_1/2)_4Nd > (T_1/2)_5Nd. the Z_eff parameter follows the order (Z_eff)_5Nd > (Z_eff)_4Nd > (Z_eff)_3Nd > (Z_eff)_2Nd > (Z_eff)_1Nd > (Z_eff)_0Nd. 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. The FNRC of the fabricated glasses is improved as the Nd³⁺ content increases in the glass matrix. The obtained results confirm that the 5Nd-glasses have more capacity compared to other proposed glasses in absorbing photons.

Acknowledgments

The authors express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project (Grant No. PNURSP2022R60), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Compliance with Ethical Standards

Authors declare that this manuscript is original, has not been published before, and is not currently being considered for publication elsewhere.

Data Availability Statements and Author Contribution

All authors contribute in Conceptualization, Methodology, Software, Validation, Investigation, Data Curation, Writing-Review and Editing, Visualization

Conflict of interest

The authors declare that they have no conflict of interest.

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Table 1: Codes, chemical compositions, and density of the xNd- glasses.

Code	Chemical compositions (Wt %)	Density, ρ_glass (g/cm³)±0.001
0Nd	0Nd₂O₃/20CdO/20PbO/57B₂O₃/3Na₂O	5.006
1Nd	1Nd₂O₃/20CdO/20PbO/56B₂O₃/3Na₂O	5.054
2Nd	2Nd₂O₃/20CdO/20PbO/55B₂O₃/3Na₂O	5.101
3Nd	3Nd₂O₃/20CdO/20PbO/54B₂O₃/3Na₂O	5.150
4Nd	4Nd₂O₃/20CdO/20PbO/53B₂O₃/3Na₂O	5.200
5Nd	5Nd₂O₃/20CdO/20PbO/52B₂O₃/3Na₂O	5.245

Table 2: Mass attenuation coefficient (MAC,μ_m) values as a function of photon energy of 0Nd, 1Nd, and 3Nd glass samples.

ENERGY	0Nd			1Nd			2Nd
E (MeV)	µm FLUKA	µm XCOM	∆	µm FLUKA	µm XCOM	∆	µm FLUKA	µm XCOM	∆
0.015	25.78	27.96	-0.08	26.05	28.61	-0.09	26.18	29.26	-0.11
0.02	18.16	19.15	-0.05	18.85	19.45	-0.03	18.81	19.75	-0.05
0.03	11.15	12.03	-0.07	11.64	12.13	-0.04	11.60	12.22	-0.05
0.04	6.00	5.67	0.06	5.81	5.71	0.02	5.88	5.75	0.02
0.05	3.33	3.15	0.06	3.47	3.28	0.06	3.61	3.42	0.06
0.06	2.09	1.96	0.07	2.18	2.04	0.07	2.27	2.12	0.07
0.07	1.42	1.32	0.08	1.47	1.38	0.07	1.54	1.43	0.07
0.08	1.02	0.95	0.08	1.07	0.99	0.08	1.11	1.03	0.08
0.09	1.78	1.73	0.03	1.81	1.76	0.03	1.84	1.78	0.03
0.10	1.39	1.33	0.04	1.41	1.36	0.04	1.44	1.38	0.04
0.15	0.55	0.53	0.05	0.56	0.53	0.05	0.57	0.54	0.05
0.20	0.31	0.30	0.05	0.32	0.30	0.05	0.32	0.30	0.05
0.30	0.17	0.16	0.04	0.17	0.16	0.04	0.17	0.16	0.05
0.40	0.12	0.12	0.03	0.12	0.12	0.03	0.12	0.12	0.03
0.50	0.10	0.10	0.02	0.10	0.10	0.02	0.10	0.10	0.02
0.60	0.09	0.09	0.01	0.09	0.09	0.02	0.09	0.09	0.02
0.70	0.08	0.08	0.01	0.08	0.08	0.01	0.08	0.08	0.01
0.80	0.07	0.07	0.01	0.07	0.07	0.01	0.07	0.07	0.01
0.90	0.07	0.07	0.01	0.07	0.07	0.01	0.07	0.07	0.00
1.00	0.06	0.06	0.00	0.06	0.06	0.00	0.06	0.06	0.01
1.02	0.06	0.06	0.00	0.06	0.06	0.00	0.06	0.06	0.00
1.50	0.05	0.05	-0.01	0.05	0.05	0.00	0.05	0.05	0.00
2.00	0.04	0.04	-0.01	0.04	0.04	-0.01	0.04	0.04	0.00
2.04	0.04	0.04	-0.01	0.04	0.04	-0.01	0.04	0.04	0.00
3.00	0.04	0.04	0.00	0.04	0.04	-0.01	0.04	0.04	0.00
4.00	0.03	0.03	-0.01	0.03	0.03	0.00	0.03	0.03	0.00
5.00	0.03	0.03	-0.01	0.03	0.03	0.00	0.03	0.03	0.00
6.00	0.03	0.03	-0.01	0.03	0.03	-0.01	0.03	0.03	-0.02
7.00	0.03	0.03	-0.01	0.03	0.03	-0.01	0.03	0.03	0.00
8.00	0.03	0.03	0.01	0.03	0.03	0.00	0.03	0.03	0.00
9.00	0.03	0.03	-0.06	0.03	0.03	-0.07	0.03	0.03	-0.01
10.00	0.03	0.03	-0.06	0.03	0.03	-0.07	0.03	0.03	0.00
11.00	0.03	0.03	-0.06	0.03	0.03	-0.07	0.03	0.03	0.00
12.00	0.03	0.03	-0.06	0.03	0.03	-0.07	0.03	0.03	0.00
13.00	0.03	0.03	-0.07	0.03	0.03	-0.07	0.03	0.03	0.00
14.00	0.03	0.03	-0.07	0.03	0.03	-0.08	0.03	0.03	0.00
15.00	0.03	0.03	-0.08	0.03	0.03	-0.08	0.03	0.03	0.00

Table 3: Mass attenuation coefficient (MAC,μ_m) values as a function of photon energy of 3Nd, 4Nd, and 5Nd glass samples.

ENERGY	3Nd			4Nd			5Nd
E (MeV)	µm FLUKA	µm XCOM	∆	µm FLUKA	µm XCOM	∆	µm FLUKA	µm XCOM	∆
0.015	26.74	29.91	-0.11	27.96	30.56	-0.08	30.32	31.21	-0.03
0.02	18.49	20.05	-0.08	20.03	20.34	-0.02	19.17	20.64	-0.07
0.03	11.43	12.32	-0.07	12.08	12.42	-0.03	12.09	12.51	-0.03
0.04	6.00	5.79	0.04	6.06	5.84	0.04	6.15	5.88	0.05
0.05	3.77	3.56	0.06	3.91	3.69	0.06	4.09	3.83	0.07
0.06	2.35	2.21	0.06	2.44	2.29	0.06	2.52	2.38	0.06
0.07	1.59	1.49	0.07	1.65	1.54	0.07	1.71	1.60	0.07
0.08	1.14	1.06	0.08	1.19	1.10	0.08	1.23	1.14	0.08
0.09	1.87	1.81	0.03	1.90	1.84	0.03	1.93	1.87	0.04
0.10	1.46	1.40	0.04	1.48	1.42	0.04	1.50	1.44	0.05
0.15	0.57	0.55	0.05	0.58	0.55	0.05	0.59	0.56	0.05
0.20	0.32	0.31	0.05	0.33	0.31	0.05	0.33	0.31	0.06
0.30	0.17	0.16	0.04	0.17	0.16	0.04	0.17	0.17	0.05
0.40	0.12	0.12	0.03	0.12	0.12	0.03	0.12	0.12	0.04
0.50	0.10	0.10	0.02	0.10	0.10	0.03	0.10	0.10	0.02
0.60	0.09	0.09	0.02	0.09	0.09	0.02	0.09	0.09	0.01
0.70	0.08	0.08	0.02	0.08	0.08	0.01	0.08	0.08	0.02
0.80	0.07	0.07	0.00	0.07	0.07	0.00	0.07	0.07	0.01
0.90	0.07	0.07	0.01	0.07	0.07	0.00	0.07	0.07	0.00
1.00	0.06	0.06	-0.01	0.06	0.06	0.01	0.06	0.06	0.00
1.02	0.06	0.06	0.00	0.06	0.06	0.01	0.06	0.06	0.00
1.50	0.05	0.05	0.00	0.05	0.05	0.01	0.05	0.05	0.00
2.00	0.04	0.04	-0.01	0.04	0.04	0.00	0.04	0.04	0.00
2.04	0.04	0.04	0.00	0.04	0.04	0.01	0.04	0.04	0.00
3.00	0.04	0.04	-0.01	0.04	0.04	-0.01	0.04	0.04	0.00
4.00	0.03	0.03	-0.01	0.03	0.03	0.00	0.03	0.03	0.01
5.00	0.03	0.03	-0.01	0.03	0.03	0.00	0.03	0.03	0.00
6.00	0.03	0.03	0.00	0.03	0.03	-0.01	0.03	0.03	0.00
7.00	0.03	0.03	-0.01	0.03	0.03	0.00	0.03	0.03	0.00
8.00	0.03	0.03	0.00	0.03	0.03	0.00	0.03	0.03	-0.01
9.00	0.03	0.03	0.00	0.03	0.03	0.00	0.03	0.03	-0.01
10.00	0.03	0.03	0.00	0.03	0.03	-0.01	0.03	0.03	-0.01
11.00	0.03	0.03	0.00	0.03	0.03	-0.01	0.03	0.03	-0.01
12.00	0.03	0.03	-0.01	0.03	0.03	0.00	0.03	0.03	0.00
13.00	0.03	0.03	0.00	0.03	0.03	-0.01	0.03	0.03	-0.01
14.00	0.03	0.03	0.00	0.03	0.03	0.00	0.03	0.03	-0.01
15.00	0.03	0.03	0.00	0.03	0.03	-0.01	0.03	0.03	-0.01

Table 4: (EBF and EABF) G–P fitting coefficients (b, c, a, Xk and d) of 0Nd sample.

Energy (MeV)	Z_eq	G-P Fitting Parameters for EBF					G-P Fitting Parameters for EABF
Energy (MeV)	Z_eq	a	b	c	d	X_k	a	b	c	d	X_k
0.015	5.86	0.140	1.429	0.557	-0.069	14.399	0.146	1.442	0.545	-0.074	14.495
0.020	5.89	0.073	1.955	0.756	-0.037	16.275	0.070	1.983	0.761	-0.035	16.318
0.030	5.91	-0.034	3.609	1.195	0.012	12.957	-0.034	3.807	1.192	0.011	12.758
0.040	5.92	-0.133	5.375	1.780	0.059	13.959	-0.131	5.101	1.769	0.057	14.116
0.050	5.93	-0.173	6.800	2.142	0.075	14.348	-0.166	5.602	2.092	0.070	14.497
0.060	5.94	-0.201	7.285	2.414	0.089	14.521	-0.188	5.419	2.308	0.079	14.670
0.080	5.95	-0.229	6.828	2.714	0.100	14.450	-0.205	4.848	2.502	0.083	14.819
0.100	5.95	-0.239	5.991	2.829	0.104	14.470	-0.210	4.294	2.558	0.083	14.901
0.150	5.96	-0.246	4.438	2.874	0.107	14.186	-0.204	3.528	2.489	0.079	15.041
0.200	5.96	-0.235	3.756	2.715	0.107	15.049	-0.196	3.176	2.364	0.075	14.875
0.300	5.97	-0.213	3.147	2.428	0.095	14.398	-0.175	2.795	2.131	0.069	14.965
0.400	5.97	-0.193	2.844	2.208	0.081	13.447	-0.153	2.626	1.928	0.063	14.827
0.500	5.97	-0.172	2.658	2.020	0.080	14.152	-0.138	2.455	1.802	0.062	16.012
0.600	5.97	-0.152	2.543	1.858	0.062	13.602	-0.119	2.398	1.664	0.046	14.974
0.800	5.97	-0.134	2.313	1.696	0.065	13.790	-0.109	2.198	1.564	0.046	14.091
1.000	5.97	-0.111	2.194	1.547	0.054	13.774	-0.093	2.087	1.461	0.041	14.194
1.500	5.17	-0.080	2.063	1.361	0.044	13.763	-0.062	1.936	1.283	0.028	14.339
2.000	5.15	-0.049	1.946	1.210	0.027	14.367	-0.041	1.835	1.180	0.018	14.195
3.000	5.14	-0.017	1.780	1.067	0.010	12.621	-0.013	1.715	1.053	0.005	13.162
4.000	5.14	0.006	1.679	0.979	-0.005	18.417	0.004	1.629	0.987	-0.003	14.634
5.000	5.14	0.018	1.595	0.934	-0.010	14.881	0.017	1.570	0.939	-0.010	14.016
6.000	5.14	0.026	1.539	0.905	-0.014	14.835	0.027	1.524	0.903	-0.015	13.046
8.000	5.14	0.035	1.446	0.872	-0.022	14.594	0.042	1.448	0.860	-0.022	11.293
10.000	5.14	0.041	1.382	0.853	-0.018	13.269	0.040	1.387	0.856	-0.021	14.482
15.000	5.13	0.048	1.285	0.832	-0.025	14.183	0.047	1.293	0.835	-0.027	14.318

Table 5: (EBF and EABF) G–P fitting coefficients (b, c, a, Xk and d) of 1Nd sample.

Energy (MeV)	Z_eq	G-P Fitting Parameters for EBF					G-P Fitting Parameters for EABF
Energy (MeV)	Z_eq	a	b	c	d	X_k	a	b	c	d	X_k
0.015	6.47	0.158	1.312	0.508	-0.079	14.290	0.158	1.319	0.506	-0.078	14.493
0.020	6.49	0.105	1.708	0.658	-0.051	15.775	0.105	1.727	0.658	-0.051	15.670
0.030	6.49	0.014	3.054	0.993	-0.016	14.305	0.014	3.205	0.994	-0.015	14.358
0.040	6.50	-0.090	4.580	1.504	0.037	13.739	-0.088	4.507	1.495	0.036	13.945
0.050	6.50	-0.140	5.838	1.864	0.061	14.085	-0.136	5.229	1.839	0.058	14.209
0.060	6.51	-0.175	6.318	2.149	0.079	14.084	-0.168	5.277	2.094	0.074	14.193
0.080	6.51	-0.210	6.058	2.475	0.094	13.836	-0.194	4.889	2.349	0.083	14.078
0.100	6.52	-0.213	5.525	2.550	0.093	14.395	-0.195	4.495	2.388	0.080	14.666
0.150	6.52	-0.226	4.159	2.643	0.100	14.124	-0.196	3.645	2.387	0.078	14.663
0.200	6.52	-0.219	3.558	2.541	0.097	14.126	-0.187	3.277	2.273	0.076	14.786
0.300	6.53	-0.194	3.046	2.265	0.084	14.219	-0.171	2.821	2.089	0.068	14.550
0.400	6.53	-0.176	2.765	2.076	0.074	13.788	-0.152	2.624	1.910	0.062	14.494
0.500	6.53	-0.157	2.592	1.914	0.069	14.157	-0.138	2.459	1.792	0.058	14.989
0.600	6.53	-0.142	2.468	1.788	0.059	13.881	-0.122	2.379	1.672	0.048	14.573
0.800	6.53	-0.121	2.273	1.630	0.056	13.927	-0.107	2.200	1.553	0.045	14.151
1.000	6.53	-0.102	2.154	1.505	0.047	13.885	-0.089	2.099	1.443	0.038	14.486
1.500	5.79	-0.072	2.023	1.323	0.036	13.707	-0.060	1.940	1.277	0.027	14.302
2.000	5.76	-0.045	1.911	1.197	0.022	14.089	-0.038	1.841	1.171	0.015	14.442
3.000	5.76	-0.015	1.760	1.061	0.007	12.153	-0.011	1.715	1.051	0.003	14.154
4.000	5.75	0.004	1.660	0.984	-0.007	23.669	0.003	1.627	0.989	-0.002	13.315
5.000	5.75	0.017	1.581	0.938	-0.011	14.604	0.015	1.566	0.945	-0.008	14.767
6.000	5.75	0.026	1.529	0.907	-0.015	14.490	0.029	1.520	0.901	-0.018	12.541
8.000	5.75	0.037	1.442	0.869	-0.032	16.393	0.035	1.435	0.877	-0.017	11.884
10.000	5.75	0.042	1.375	0.855	-0.020	12.606	0.040	1.381	0.858	-0.022	14.365
15.000	5.75	0.046	1.278	0.838	-0.028	14.969	0.047	1.286	0.837	-0.031	15.470

Table 6: (EBF and EABF) G–P fitting coefficients (b, c, a, Xk and d) of 2Nd sample.

Energy (MeV)	Z_eq	G-P Fitting Parameters for EBF					G-P Fitting Parameters for EABF
Energy (MeV)	Z_eq	a	b	c	d	X_k	a	b	c	d	X_k
0.015	6.25	0.153	1.346	0.522	-0.075	14.299	0.156	1.355	0.515	-0.078	14.459
0.020	6.26	0.093	1.784	0.692	-0.046	16.135	0.092	1.805	0.694	-0.045	16.027
0.030	6.27	-0.004	3.260	1.065	-0.005	13.637	-0.005	3.439	1.065	-0.004	13.553
0.040	6.27	-0.107	4.886	1.612	0.046	13.816	-0.105	4.759	1.603	0.044	14.015
0.050	6.27	-0.154	6.227	1.974	0.066	14.199	-0.149	5.393	1.941	0.063	14.331
0.060	6.27	-0.185	6.717	2.254	0.083	14.284	-0.176	5.343	2.180	0.076	14.402
0.080	6.28	-0.217	6.373	2.571	0.097	14.105	-0.199	4.877	2.411	0.083	14.404
0.100	6.28	-0.225	5.687	2.671	0.098	14.397	-0.201	4.411	2.459	0.081	14.761
0.150	6.29	-0.235	4.257	2.741	0.103	14.131	-0.200	3.591	2.433	0.079	14.794
0.200	6.29	-0.225	3.642	2.610	0.101	14.547	-0.191	3.231	2.313	0.076	14.779
0.300	6.29	-0.201	3.090	2.330	0.089	14.303	-0.173	2.811	2.107	0.069	14.730
0.400	6.29	-0.183	2.799	2.129	0.077	13.649	-0.152	2.626	1.917	0.062	14.646
0.500	6.29	-0.163	2.620	1.957	0.074	14.171	-0.138	2.458	1.796	0.060	15.453
0.600	6.29	-0.146	2.501	1.816	0.060	13.758	-0.121	2.388	1.668	0.047	14.751
0.800	6.29	-0.126	2.290	1.657	0.059	13.871	-0.108	2.199	1.557	0.045	14.124
1.000	6.29	-0.106	2.171	1.522	0.050	13.839	-0.091	2.094	1.451	0.039	14.361
1.500	5.71	-0.073	2.028	1.328	0.037	13.714	-0.061	1.939	1.278	0.027	14.306
2.000	5.69	-0.046	1.915	1.198	0.023	14.120	-0.038	1.840	1.172	0.016	14.414
3.000	5.69	-0.015	1.762	1.061	0.007	12.204	-0.012	1.715	1.051	0.003	14.046
4.000	5.68	0.005	1.662	0.984	-0.007	23.109	0.003	1.627	0.989	-0.002	13.456
5.000	5.68	0.017	1.582	0.937	-0.011	14.634	0.015	1.566	0.944	-0.008	14.687
6.000	5.68	0.026	1.530	0.907	-0.015	14.527	0.029	1.521	0.901	-0.017	12.594
8.000	5.68	0.037	1.442	0.869	-0.031	16.206	0.036	1.436	0.876	-0.018	11.823
10.000	5.68	0.042	1.376	0.854	-0.020	12.674	0.040	1.381	0.858	-0.022	14.377
15.000	5.68	0.047	1.279	0.838	-0.028	14.889	0.047	1.287	0.837	-0.031	15.352

Table 7: (EBF and EABF) G–P fitting coefficients (b, c, a, Xk and d) of 3Nd sample.

Energy (MeV)	Z_eq	G-P Fitting Parameters for EBF					G-P Fitting Parameters for EABF
Energy (MeV)	Z_eq	a	b	c	d	X_k	a	b	c	d	X_k
0.015	6.57	0.161	1.297	0.502	-0.080	14.287	0.159	1.303	0.502	-0.078	14.508
0.020	6.57	0.109	1.679	0.645	-0.054	15.639	0.110	1.698	0.644	-0.054	15.535
0.030	6.57	0.020	2.984	0.969	-0.020	14.532	0.020	3.125	0.969	-0.019	14.632
0.040	6.57	-0.084	4.481	1.469	0.035	13.715	-0.082	4.426	1.461	0.033	13.922
0.050	6.57	-0.136	5.716	1.830	0.059	14.049	-0.133	5.178	1.807	0.056	14.171
0.060	6.58	-0.172	6.197	2.117	0.078	14.024	-0.165	5.257	2.068	0.073	14.130
0.080	6.58	-0.207	5.966	2.446	0.093	13.757	-0.193	4.893	2.330	0.083	13.983
0.100	6.58	-0.210	5.479	2.515	0.091	14.394	-0.193	4.519	2.367	0.080	14.639
0.150	6.59	-0.224	4.132	2.615	0.099	14.122	-0.195	3.660	2.374	0.078	14.626
0.200	6.59	-0.218	3.534	2.522	0.096	14.010	-0.186	3.290	2.262	0.076	14.788
0.300	6.59	-0.192	3.034	2.247	0.083	14.196	-0.171	2.824	2.084	0.068	14.501
0.400	6.59	-0.174	2.755	2.062	0.073	13.825	-0.152	2.623	1.908	0.061	14.454
0.500	6.60	-0.156	2.584	1.903	0.068	14.153	-0.138	2.460	1.791	0.058	14.866
0.600	6.60	-0.141	2.459	1.781	0.059	13.913	-0.122	2.377	1.673	0.048	14.526
0.800	6.60	-0.120	2.268	1.623	0.055	13.941	-0.107	2.200	1.551	0.044	14.158
1.000	6.60	-0.101	2.150	1.501	0.047	13.897	-0.089	2.100	1.441	0.037	14.519
1.500	6.08	-0.068	2.007	1.307	0.032	13.790	-0.060	1.940	1.275	0.027	14.298
2.000	6.06	-0.044	1.895	1.191	0.020	13.987	-0.037	1.842	1.168	0.014	14.492
3.000	6.05	-0.014	1.750	1.058	0.006	12.096	-0.011	1.715	1.050	0.003	14.401
4.000	6.05	0.004	1.652	0.986	-0.008	25.086	0.003	1.626	0.989	-0.002	12.903
5.000	6.05	0.017	1.574	0.939	-0.011	14.450	0.014	1.564	0.946	-0.007	14.966
6.000	6.05	0.026	1.525	0.908	-0.015	14.258	0.029	1.518	0.902	-0.018	12.607
8.000	6.05	0.038	1.439	0.869	-0.034	16.805	0.033	1.430	0.883	-0.016	12.106
10.000	6.04	0.042	1.372	0.856	-0.021	12.440	0.040	1.377	0.860	-0.022	14.320
15.000	6.05	0.046	1.276	0.841	-0.030	15.259	0.047	1.282	0.838	-0.033	15.865

Table 8: (EBF and EABF) G–P fitting coefficients (b, c, a, Xk and d) of 4Nd sample.

Energy (MeV)	Z_eq	G-P Fitting Parameters for EBF					G-P Fitting Parameters for EABF
Energy (MeV)	Z_eq	a	b	c	d	X_k	a	b	c	d	X_k
0.015	10.03	0.213	1.081	0.394	-0.109	12.501	0.197	1.081	0.414	-0.095	11.935
0.020	10.15	0.199	1.181	0.425	-0.106	13.820	0.192	1.181	0.433	-0.104	14.530
0.030	10.30	0.157	1.526	0.529	-0.082	14.966	0.167	1.561	0.510	-0.085	14.039
0.040	10.39	0.083	2.024	0.721	-0.042	15.877	0.096	2.096	0.694	-0.051	15.640
0.050	10.44	0.064	2.666	0.832	-0.043	14.185	0.064	2.801	0.831	-0.049	14.724
0.060	10.48	0.017	3.103	1.008	-0.023	13.342	0.012	3.407	1.021	-0.019	14.281
0.080	10.54	-0.044	3.497	1.277	0.006	13.591	-0.053	4.272	1.312	0.015	11.932
0.100	10.58	-0.074	3.522	1.450	0.019	14.290	-0.090	4.523	1.521	0.032	13.402
0.150	10.65	-0.102	3.260	1.625	0.030	14.687	-0.129	4.032	1.770	0.051	13.619
0.200	10.68	-0.109	3.000	1.669	0.032	14.575	-0.135	3.591	1.815	0.052	13.798
0.300	10.73	-0.110	2.675	1.658	0.030	14.126	-0.132	3.014	1.785	0.049	13.888
0.400	10.75	-0.104	2.492	1.605	0.030	15.024	-0.124	2.716	1.713	0.045	14.146
0.500	10.76	-0.100	2.359	1.560	0.032	14.814	-0.115	2.534	1.643	0.042	14.252
0.600	10.77	-0.092	2.260	1.507	0.028	15.346	-0.105	2.400	1.575	0.037	14.543
0.800	10.77	-0.082	2.121	1.428	0.026	15.119	-0.091	2.226	1.472	0.033	14.829
1.000	10.77	-0.071	2.028	1.360	0.024	15.612	-0.078	2.111	1.390	0.029	14.808
1.500	8.43	-0.056	1.921	1.260	0.022	14.575	-0.056	1.942	1.260	0.022	14.305
2.000	8.15	-0.036	1.835	1.163	0.014	15.343	-0.037	1.839	1.166	0.014	14.628
3.000	8.09	-0.011	1.710	1.052	0.002	12.796	-0.011	1.710	1.052	0.002	14.231
4.000	8.07	0.004	1.624	0.990	-0.007	20.281	0.006	1.621	0.986	-0.007	12.975
5.000	8.06	0.016	1.553	0.947	-0.011	14.438	0.018	1.556	0.942	-0.013	13.266
6.000	8.05	0.025	1.505	0.917	-0.023	15.551	0.029	1.505	0.906	-0.026	15.099
8.000	8.05	0.033	1.417	0.891	-0.020	12.324	0.031	1.411	0.896	-0.017	12.329
10.000	8.05	0.039	1.358	0.872	-0.025	13.975	0.041	1.355	0.867	-0.027	13.901
15.000	8.04	0.050	1.265	0.842	-0.039	15.020	0.048	1.259	0.849	-0.036	14.750

Table 9: (EBF and EABF) G–P fitting coefficients (b, c, a, Xk and d) of 5Nd sample.

Energy (MeV)	Z_eq	G-P Fitting Parameters for EBF					G-P Fitting Parameters for EABF
Energy (MeV)	Z_eq	a	b	c	d	X_k	a	b	c	d	X_k
0.015	6.61	0.162	1.290	0.499	-0.081	14.285	0.159	1.296	0.500	-0.078	14.515
0.020	6.62	0.111	1.665	0.640	-0.055	15.576	0.113	1.684	0.637	-0.055	15.472
0.030	6.61	0.023	2.951	0.957	-0.022	14.639	0.023	3.087	0.958	-0.020	14.761
0.040	6.61	-0.081	4.434	1.452	0.033	13.703	-0.079	4.387	1.444	0.031	13.911
0.050	6.61	-0.134	5.657	1.814	0.058	14.032	-0.131	5.154	1.792	0.055	14.153
0.060	6.61	-0.170	6.137	2.102	0.077	13.994	-0.164	5.247	2.055	0.073	14.098
0.080	6.62	-0.206	5.920	2.432	0.093	13.717	-0.193	4.894	2.321	0.083	13.935
0.100	6.62	-0.208	5.455	2.497	0.091	14.394	-0.192	4.532	2.357	0.079	14.625
0.150	6.62	-0.222	4.117	2.601	0.099	14.121	-0.195	3.668	2.368	0.078	14.607
0.200	6.62	-0.217	3.522	2.512	0.095	13.950	-0.185	3.296	2.256	0.076	14.789
0.300	6.63	-0.191	3.027	2.238	0.082	14.184	-0.170	2.825	2.082	0.068	14.475
0.400	6.63	-0.173	2.750	2.054	0.073	13.846	-0.152	2.623	1.908	0.061	14.432
0.500	6.63	-0.155	2.580	1.897	0.068	14.151	-0.138	2.460	1.791	0.058	14.798
0.600	6.63	-0.140	2.454	1.777	0.059	13.931	-0.122	2.376	1.674	0.048	14.500
0.800	6.63	-0.119	2.266	1.619	0.054	13.949	-0.106	2.201	1.551	0.044	14.161
1.000	6.63	-0.101	2.147	1.499	0.046	13.903	-0.088	2.101	1.440	0.037	14.538
1.500	6.24	-0.066	2.000	1.301	0.031	13.971	-0.060	1.938	1.276	0.026	14.313
2.000	6.22	-0.043	1.889	1.188	0.020	13.981	-0.038	1.841	1.169	0.015	14.394
3.000	6.22	-0.014	1.744	1.059	0.006	12.436	-0.011	1.713	1.052	0.003	14.052
4.000	6.22	0.004	1.648	0.987	-0.007	23.349	0.004	1.627	0.988	-0.003	13.164
5.000	6.22	0.017	1.572	0.939	-0.011	14.289	0.016	1.565	0.943	-0.009	14.697
6.000	6.21	0.027	1.523	0.906	-0.016	13.926	0.027	1.514	0.908	-0.018	13.443
8.000	6.21	0.037	1.436	0.872	-0.031	15.853	0.035	1.430	0.881	-0.018	12.094
10.000	6.21	0.041	1.370	0.859	-0.021	12.770	0.040	1.375	0.861	-0.022	14.322
15.000	6.21	0.046	1.275	0.841	-0.031	15.218	0.047	1.281	0.838	-0.033	15.705

Fabrication, physical, structure characteristics, neutron and radiation shielding capacity high density neodymio-cadmium lead borate glasses: Nd2O3/CdO/PbO/B2O3/Na2O

Status:

Version 1

Abstract

Figures

1. Introduction

2. Materials And Methods

3. Results And Discussion

4. Conclusion

Declarations

References

Tables

Status:

Version 1