Effects of reducing PbO content on the elastic and radiation attenuation properties of germanate glasses: a new non‐toxic candidate for shielding applications

This work presents a detailed study on the effects of reducing PbO content on the elastic and radiation shielding properties of germanate glasses described by the chemical formula 50GeO2-(50-x)PbO-xZnO, where x between 0 and 50 mol % with step of 10. A theoretical analysis based on Makishima-Mackenzie’s theory (MM-theory) was employed to obtain the elastic moduli of the studied glass specimens. Moreover, the Monte Carlo simulations were applied via Geant4 platform to assess the radiation shielding ability of the GeO2-PbO-ZnO glass system by evaluating several fundamental properties such as gamma and neutron transmission factors, total cross sections, effective atomic numbers, 1/e penetration depths, and exposure buildup factors. We found that the bulk elastic modulus increased from 50.751 GPa to 85.389 GPa as the PbO content decreased from 50 mol% to 0. The results of the linear attenuation coefficient show that the cross sections of σPE,σCS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left(\sigma \right)}_{PE}, {\left(\sigma \right)}_{CS}$$\end{document}, and σPP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\left(\sigma \right)}_{PP}$$\end{document} dominates the photon attenuation at 0.15 ≤ E ≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\le$$\end{document}0.08; 0.8 < E < 8, and 8 < E < 15 MeV, respectively. Moreover, the present glasses have superior photon absorbing capacity compared to ordinary and barite concrete; RS-253-G18 and RS-360 commercial glass shields. This suggests that the GeO2-PbO-ZnO glass system can be used as a non-toxic shielding material in the nuclear facilities.


Introduction
Nuclear radiation has become an essential tool in many applications to ensure the high quality of our daily lives. For examples, nuclear radiation plays a main role in medicine for diagnostic and treatment complicated diseases such as cancer [1]. Moreover, radiation (e.g. X-rays) is used in security devices to detect weapons in luggage as well as to warn us of fire (smoke detectors) [2]. However, there are catastrophic health risks associated with frequently exposure to nuclear radiation [3][4][5]. Therefore, the radiation shielding is a considerable technology in the nuclear facilities to protect the workers and public from exposure to the damaging radiation [6,7]. Over the years, lead (Pb) and its products are used as reliable shielding materials due to their scientifically known ability to block radiation [8][9][10][11]. Nevertheless, there are also serious concerns related to the toxicity of Pb and its harmful effects on human and environment [12][13][14].
At present, several glass systems are being considered as advanced radiation shielding technologies in dental and medical applications. Stalin et al. reported on a new LBWB glass system containing Bi 2 O 3 as a heavy metal oxide to modify the shielding ability of the system [15]. The highest density was recorded for the LBWB0 sample with the value of 3.969 g/cm 3 [15]. Moreover, the best shielding ability was also for the LBWB0 sample with the mass attenuation value of 69.367 cm 2 /g at the low energy region (15 keV). Boukhris et al. investigated the impact of PbO addition on the optical features and gamma shielding efficiency of four glass samples containing Na 2 O, Sb 2 O 3 ,WO 3 , and PbO [16]. The obtained results show that the highest optical transmission was recorded for SbNaWPb1 sample (lowest PbO content) with the value 0.7916, and the maximum of the mass attenuation coefficient (MAC) is found at 0.284 MeV with the value of 0.2750 cm 2 /g for the SbNaWPb4 sample (highest PbO content). Olarinoye et al. studied the impact of La 2 O 3 content on the mechanical features (elastic moduli) and radiation shielding ability of ZnO-based glasses [17]. The bulk modulus and the other elastic moduli were found in a decrease trend as the La 2 O 3 content increased up to 10 mol %. Moreover, the maximum MAC occurred at 15 keV with the value of 43.019 cm 2 g -1 for LZB4 sample (highest La 2 O 3 content). Recently, germanate glass systems attract a tremendous scientific attention due to their unique physical, optical, and structural properties [18][19][20][21]. For example, these glass systems have high solubility, high density, low melting points, wide light transmittance, high immunity, and high refractive indices [19][20][21][22]. Such promising properties of germanate glass systems encouraged us to investigate their fundamental radiation shielding features.
In the present research article, the effects of reducing PbO content on the elastic and radiation shielding properties of the GeO 2 -PbO-ZnO glass system. A theoretical analysis based on MM-theory was employed to obtain the elastic moduli of the studied glass specimens. Furthermore, the Monte Carlo simulation was applied via Geant4 platform to assess the radiation shielding ability of the GeO 2 -PbO-ZnO glass system by evaluating several fundamental properties such as gamma and neutron transmission factors, total cross sections, effective atomic numbers, 1/e penetration depths, and exposure buildup factors.

Glass preparation
The glass specimens described by the chemical form of 50GeO 2 -(50-x)PbO-xZnO, where x between 0 and 50 mol% with step of 10, were prepared by melting the amounts of GeO 2 , PbO, and ZnO at temperature of 1000-1560°C, as reported in Ref. [23]. The detailed chemical constituent and density for each studied glass samples can be found in Table 1.

Theoretical analysis
A theoretical analysis based on Makishima-Mackenzie's theory (MM-theory) was employed to obtain the elastic moduli of the studied glass specimens. The full description of MM-theory can be found in Refs [25,26]. Briefly, it depends on some compositional factors such as M w and V m and several parameters like packing factor (V t ) and dissociation energy (G t ). All the mathematical relations of MM-theory are summarized in Table 2. More details about the elastic properties of different glass systems are reported by El-Moneim et al. [27][28][29].
On the hand, the theoretical analysis of the radiation shielding study was employed using Phy-X J Mater Sci: Mater Electron (2021) 32:15080-15094 software over a wide energy range varying between 15 keV and 15 MeV [30]. This software offers more than 15 parameters to investigate the radiation shielding competence of any composite materials.

Simulation method
Monte Carlo is a promising method to deal with the scientific problems in the software environment by eliminating all the difficulties of experiments like the high cost and exposure risks in radiation studies. By applying Monte Carlo method, several simulations were carried out using Geant4 toolkit over a wide energy range reaching 15 MeV [24]. The present simulation geometry contains a vacuum system as a main part where all the simulation setup was placed there. Such that gamma source, sample, and the detector were placed in the designed vacuum system, as shown in Fig. 1. Table 3 summarizes the elastic features such as packing density (or packing factor), dissociation energy, and the four elastic moduli (E th , K th , S th , and L th ) of the present GeO 2 -PbO-ZnO glass samples. From this table, it is clear that all the elastic features strongly relate with the glass composition. Such that the molar volume (see Table 1) of the present glasses is similar to the behavior for the density. With reducing PbO content from 50 mol % to 0, the molar volume decreased from 30.129 to 20.575, and all of E th , K th , S th , and L th increased from 101.857 to 149.797, from 50.751 to 85.389, from 46.865 to 66.351, and from 113.238 to 173.857 for E th , K th , S th , and L th , respectively. Therefore, the interesting observation is that the elastic moduli of pure GeO 2 -ZnO (G50 glass sample with the lowest density) are much greater than those of pure GeO 2 -PbO (G00 glass sample with the highest density). The obtained results are attributed to the structural role of PbO and ZnO in the germanate glasses network [27][28][29]. Such that it is well known from the molar volume of the studied glasses, which being larger in the order pure GeO 2 -PbO [ pure GeO 2 -ZnO (See Table 1).

Results and discussion
Photon transmission (T) in the narrow beam approximation is predicted by the Beer-Lambert The linear attenuation coefficient (lÞ of a photon absorbing medium can be obtained via the transmission experiment or simulation using the equation. Using the Geant4 simulation tool and Phy-X free web-based software, l was obtained for the glasses for photon energies (E) in the range 0.015 B E B 15 MeV and presented in Tables 4  and 5. Also, presented in the tables is the deviation (Dev. in %) between the l value obtained via the two Packing factor (V t , cm 3 /mol) Young's modulus (E th , GPa) Bulk modulus (K th , GPa) Shear modulus (S th , GPa) Longitudinal modulus (L th , GPa) methods. The Dev. is calculated according to the expression [31,32]: Values of l presented in Tables 4 and 5 show that the simulation results agree well with the direct calculation with Phy-X tool. Quantitatively, the agreement is showcased in the value of Dev. which varies between 0.50 and 1.54, 0.55-1.86, 0.51-1.96, 0.52-1.86, 0.63-1.73, and 0.63-1.94 % for G00 -G50, respectively. Clearly the simulation result is reliable and accurate. Generally, l decreases in value with photon energy for all the glasses, hence, the maximum value was obtained at the least energy while the least l value was gotten between 6 and 8 MeV depending on the chemical content of the glasses. For the energy range given in the table, three basic photon interaction processes and their gross section dictate the value l and its variation with E. These are photoelectric effect (PE), Compton scattering (CS), and pair production (PP) absorption processes. Their respective cross section (r) depends on E according to: r ð Þ PE / E À3:5 , r ð Þ CS / E À1 , and r ð Þ PP / E. The result  of the linear attenuation coefficient of the glasses as presented in Table 2 shows that r ð Þ PE ; r ð Þ CS , and r ð Þ PP dominates the photon interaction cross section at 0.15 B E 0.08; 0.8 \ E \ 8, and 8 \ E \ 15 MeV, respectively. Also, the l data revealed that r ð Þ PE ; r ð Þ CS , and r ð Þ PP is maximum at 15 keV, 6-8 MeV and 15 MeV in the glasses, respectively. The position of the peak of r ð Þ CS changes as the atomic number of the glasses changes [31]. Hence, minimum l value was obtained at different energies depending on the glass' effective atomic number.
In order to clearly present the variation of photon attenuation capacity of the G00 -G50 glasses with respect to photon energy and chemical content, the mass attenuation coefficient ( l = q at selected energies (0.015, 0.03, 0.05, 0.1, 0.2, 0.5, 1, and 2 MeV) is presented in Fig. 2. According to the figure l = q diminishes with E in a similar way as l. The gradual decline of l = q is due to the decay in photon interaction cross section as photon energy grows. Furthermore, at equal energy, l = q increases as PbO (ZnO) Thus, G00 with maximum PbO concentration produced the highest l = q throughout the energy spectrum. This trend can be attributed to the relative higher atomic number, density, and hence photon absorption cross section of Pb/PbO compared to other chemical species in the glass system. This also explains the increase in the mass density of the glasses as PbO increases.
The effect of the glasses' composition on photon absorption competence may be quantitatively assessed and compared via the effective atomic number, Z eff . The variation of Z eff with E is presented in Fig. 3. The value of Z eff initially increases with E and latter declines at E [ 0.1 MeV for G00-G40, while for G50, the effective atomic number declines continuously with photon energy. The initial increase observed for G00 -G40 is attributed to an increase in photon for G00 -G50. The peak of Z eff for G50 which contains no PbO content was at the least energy (15 keV) due to photoelectric absorption cross section and its dependence on chemical content of the glass. The behavior of Z eff with respect to E is attributed to the dependence of the partial photon interaction cross sections ( r ð Þ PE ; r ð Þ CS , and r ð Þ PP Þ on chemical content and their variation with E. On the other hand, the range of Z eff is influenced by the range of atomic number of the atoms present in the glass system [32][33][34]. One practical parameter for the comparison and recommending photon shields is the half value layer (HVL). It is the thickness of the shield needed to reduce photon dose by one-half. Figure 4 shows the pictorial relationship between HVL and E of the glasses. Clearly, HVL increases in value with E; an indication that more glass thickness is required to achieve same level of gamma radiation protection at higher energies. The figure also shows that HVL increases as ZnO content of the glasses increases relative to PbO. At equal energy, HVL follows the   In many practical situations, the narrow beam approximation adopted for the evaluation l, l = q , Z eff , and HVL may not be accurate. In the broad beam approximation, transmitted photons include secondary photons generated via the interaction of primary incident photons with the attenuating medium. Such secondary photons buildup creates the error in the previously estimated parameters. Figure 5 shows the exposure buildup factor (EBF) obtained at four selected energies and for glass thickness of 0.1-1 cm via the GP fitting parameter procedure. The GP fitting procedure have been clearly explained in previous publication [35][36][37]. Across the considered energies, EBF increases with glass thickness. At low energy (50 and 100 keV): (EBF) G50 \ (EBF) G40 \ (EBF) G30 \ (EBF) G20 \ (EBF) G10 \ (EBF) G00 . However, at higher energies, the trend is reversed. Photon buildup is proportional to absorber's thickness [35][36][37][38], CS cross section, and other photon interaction cross sections. In the low energy region, the EBF is higher for higher Z eff absorber due to photoelectric process, while at higher energies, CS dictates scattering and the scattering cross section higher for lower Z eff glasses. Due to the high mass attenuation coefficient and Z eff value of the glasses, EBF is Photon transmission T (in %) calculated vis the adjusted Beer Lambert equation: T ¼ EBFe Àlx for the four photon energies are given in Fig. 6. As expected, photon transmission decreases with glass thickness (x) due to increasing photon interaction and absorption. At E = 0.05 MeV, a thickness of 0.5 cm or more is enough to absorbs nearly all incident photons in all the glasses. on the other hand, a glass thickness of 0.1 cm reduces photon to less than 40% in all the glasses. as predicted by the photon attenuation parameters, photon transmission increases as Pb content of the glasses increases. Generally, the photon absorbing capacity of the glasses increases according to the order of increasing PbO content as observed in other glass systems involving PbO [39][40][41][42].  To establish the position of the present glass samples among conventional photon shields, the MFP (mean free path) of G00 and G50 were compared with those of conventional gamma radiation shields (ordinary and barite concretes, RS-360, RS-520, and RS-253-G18 glass shields; and a recently studied glass shield TVM60 [32]) at photon energies 0.015 B E B 10 MeV (Fig. 7). Obviously, the present glasses have superior photon absorbing capacity compared to ordinary and barite concrete; RS-253-G18 and RS- Table 6 Comparison of the G00 (present work) with other previous works such as P2 polymer [43], VR3 volcanic rock [44], FBCSP-E alloy [45], and BBSN5.7 [17]   360 commercial glass shields. although TVM60 absorbs photon better than G50, G00, however, possess a better shielding ability compared to the other shields except RS-520 whose photon shielding ability is comparable to G00 glass sample at all considered energies. The present glass (G00) thus possess tremendous photon protection capacity which is superior to many conventional ionizing radiation shields. Finally, Table 6 shows a comparison of the G00 (the present work) with other previous works such as P2 polymer [43], VR3 volcanic rock [44], FBCSP-E alloy [45], and BBSN5.7 [17] glassy systems. Clearly, the G00 glass sample (the present work) possesses the lowest MFP values (the best shielding ability) among the other samples such as P2 polymer, VR3 volcanic rock, FBCSP-E alloy, and BBSN5.7 glassy systems which are recently studied and published elsewhere [43][44][45]17]. Neutron absorption also follows a form of Beer Lambert: T ¼ e ÀR T x . The parameter R T , represents the linear attenuation coefficient of the neutron flux incident on an absorber of thickness x. R T depends directly on atomic density and total microscopic cross section (r T ) of neutrons of certain materials in the absorber. R T and by extension r T depends on the interacting nuclide and neutron energy. On the other hand, r T ¼ r c þ r i þ r a where the subscript c, i, and a represents coherent scattering, incoherent scattering and absorption, respectively. For the present glass samples, r c and r a have constant value for cold neutrons of energies within 0.01-2 meV and glass thickness between 0.1 and 1 cm for each glass. However, r i changes in value with respect to neutron energy but remain unchanged with thickness. The variation of r c and r a with to glass sample is displayed on Fig. 8a. The differences in the chemical content of the glasses as it affects the atomic densities of each of the atomic species contained in the glasses is responsible for this observation. The gradual reduction/increase of Pb/Zn in the glasses increase/ decreases r c and r a of the neutron in the glasses. The moderation of neutrons depends mostly on r i and hence atomic density of the glasses. As the neutron energy grows, r i drops as shown in Fig. 8b in all the glasses. The changes in the atomic density of the glasses due to differences in glass chemical composition is responsible for the trend of r i and total cross section, r T (Fig. 9) at a particular neutron energy. r T is higher for glasses with higher ZnO content due to the higher r T of Zn ?O compared to Pb and Ge.  Hence, neutron transmission increases with energy and glass composition as predicted by r T as shown in Fig. 10. Since transmission a 1 = r T , G50 thus show the best potential for neutron absorption among the glasses and neutron included in the study. This is further buttressed by Fig. 11 which shows the variation of MFP of neutrons with respect to glass composition and neutron energy. Obviously, glasses with higher transmission value at a particular energy is required to be thicker to provide the same level of neutron attenuation. Figure 12 depicts the effect of glass thickness on neutron transmission for glass thicknesses between 0.1 and 1 cm and selected neutron energies. increase in glass thickness increase the atomic density and R T which results in high absorption and low transmission. Based on the presented data, neutron absorbing capacity in the glasses follows the trend: The findings of the present study support all the recent results published elsewhere [46][47][48][49].

Conclusions
This work reported on the effects of reducing PbO content on the elastic and radiation shielding properties of germanate glasses described by the chemical formula 50GeO 2 -(50-x)PbO-xZnO, where x between 0 and 50 mol% with step of 10. A MM-theory was employed to obtain the elastic moduli of the studied glass specimens. Moreover, the Monte Carlo simulations were applied via Geant4 platform to assess the radiation shielding ability of the GeO 2 -PbO-ZnO glass system. With reducing PbO content from 50 mol% to 0, we found that the molar volume decreased from 30.129 to 20.575, and all of E th , K th , S th , and L th increased from 101.857 to 149.797, from 50.751 to 85.389, from 46.865 to 66.351, and from 113.238 to 173.857 for E th , K th , S th , and L th , respectively. The value of Z eff increases throughout the considered energy spectrum as the Pb content of the glasses increases; Z eff falls within the range of 30  gamma rays and neutrons, it is clear that the glass composition strongly influenced the ability of a glass for shielding purposes. The optimum composition which gives the best neutron absorption produced the worst gamma ray shielding efficacy. However, analyzed data proved that the glass system can be used as an effective photon and neutron shields.