The Impact of PbF2-Based Glasses on Radiation Shielding and Mechanical Concepts: An Extensive Theoretical and Monte Carlo Simulation Study

This work aimed to investigate the impact of Lead-fluoride based glasses via theoretical and simulation techniques on mechanical and radiation shielding parameters. Accordingly, Bi2O3 was blended with TeO2–B2O3–PbF2 glasses by using melt-quenching method. Using Fluka Monte Carlo code, the radiation shielding properties have measured. Moreover, Comparatively higher density PbF80 = 6.163 g/cm3 with 80 mol % Bi2O3, greater µ, µm and Zeff and lower T1/2, λ, tenth value layer values achieved for TeO2–B2O3– PbF2/Bi2O3 glass pointed it out as the best shield of gamma. Besides, the computed effective removal cross-sections against fast neutrons (ΣR) observed that the PbF80 sample has commensurately greater with a value 5.2954 (cm−1). The results observed that the variation PbF2/Bi2O3 improves the gamma protection ability of Lead-fluoride based glasses. The incremental of Bi2O3 at the expense of PbF2 increases the density and the packing density of the glasses and hence increase the longitudinal modulus-L, shear modulus-S, bulk modulus-K, and Young's modulus-Y from 15.89 to 25.9 GPa, from 8.49 to 12.09 -GPa, from 4.58 to 9.77 GPa, and from 15.74 to 25.69 GPa, respectively. The increase of the elastic moduli can be attrinuted to the glass former role of Bi2O3. The results indicate that the highest PbF2/Bi2O3 ratio encoded PbF00 has the best shielding and mechanical competence with measurable physical properties.


Introduction
It is well-known that various kinds of radiation such as gamma and x-ray emission from natural background radiation sources and human-made synthetic radiation sources such as medical equipment, nuclear reactors, and nuclear weapons [1]. Depending on the type and energy of radiation, possible adverse effects are detected. Special precautions can be taken, when it comes to natural radiation. These precautions can be listed to quantify natural radioactivity and properly design living spaces. These precautions could be listed as defining the amount of natural radioactivity and designing living spaces properly. However, the case may be totally different in artificial radiation sources and their facilities. According to the well-known ALARA principle, it is highly wanted to save living tissues and the environment from the ionising radiation. This protection proceeding is predominantly performed by decreasing the radiation to the safe level by utilising convenient shielding materials. Manufactured glass plays an essential role in shielding against ionizing radiation, such as X-and gamma rays [2]. It is used in many medical applications, such as radiation protection windows and radiation-protective suit glasses. While the new trend recently in glass is used in immobilization Radionuclide [3] and in storing and burying radioactive waste. This study is concerned with highlighting the importance of a new type of Bi 2 O 3 blended with TeO 2 -B 2 O 3 -PbF 2 glasses in its ability to block and absorb radiation and highlight its mechanical properties. Traditionally, concrete and lead are known as the most used shielding materials due to their superior attenuation properties against gamma-ray and x-ray [4]. Their employment could be performed not only in radiation staff equipment but also in shielding radiation facilities and radioactive sources. In addition to mentioned shield kinds, different materials like ceramics, polymers, concrete, and alloys have been proposed as radiation shielding materials in previous studies [5][6][7]. Among the alternative shielding materials, glasses are utilised as radiation protection substances instead of traditional materials [8]. This is because glasses are reputed by high-level optical clarity and can be produced in varied sizes and shapes.
Heavy metal fluoride-based glasses (HMF) had favorable potentials in optical applications, specifically in the field of non-radiative loss infrared transmission and low phonon energy [9,10]. These features enable these glasses to achieve strong upconversion luminescence [11], i.e., these glasses can be considered as promising hosts for luminescent ions, solid-state batteries [12], electrochemical applications [11], laser windows [13], and optical components with multiple functions [14]. However, although HMF had interesting characteristics, these glasses had low corrosion durability, chemical and thermal stability that restricted their synthesis and use. Therefore, the oxyfluoride-based glasses will be more suitable for updated use because these glasses consolidate the high phonon energies, the high chemical and thermal stability of oxide glasses with the interesting optical properties of fluoride-based glasses [15][16][17][18]. However, the TeO2-based glasses (TG) are the most suitable oxide glasses for consolidation with HMF because tellurite glasses had remarkable characteristics such as relatively low-phonon energy [19,20]. Also, TG had distinct refractive indices, high corrosion durability, thermal and chemical stability. Thus, blending TG with HMF is expected to give interesting features such as a wide range of optical transmittance with low optical losses, enhanced mechanical, chemical, and thermal stability. Also, the new glasses can be considered as a good host for rare earth oxides to enhance their upconversion luminescence [21]. Among HMF, PbF 2 had a dual glass role, i.e., like Bi 2 O 3 , it had a glass former or modifier role. So, blending PbF 2 and Bi 2 O 3 into a tellurite-based glasses network can form a wide range of stable glasses [22]. In continuation of other works [22][23][24], this study aims to evaluate the mechanical and radiation shielding parameters of a wide range of Bi 2 O 3 blended with TeO 2 -B 2 O 3 -PbF 2 glasses. A wide range of binary PbF 2 -TeO 2 [23] and extended TeO 2 -B 2 O 3 -Bi 2 O 3 [22] were studied with several characterization techniques. So, the findings of this research will be valuable in the subject of glass literature, particularly in radiation shielding. As a result of the conclusion of this investigation, researchers will be able to learn more about the usefulness of Bi 2 O 3 blended with TeO 2 -B 2 O 3 -PbF 2 glasses as nuclear shielding materials.

Shielding Properties
It is well-known that if an attenuator specimen as shield located between the detector and the source, the intensity of incident gamma-ray reduces exponentially due to Beer-Lambert law [25]: where the intensity of primary gamma is I o , and the intensity of transmitted gamma through the glass is I. Besides, μ indicates the linear attenuation coefficient of the energy of interest. The term x is the thickness of the attenuator sample. The MAC, in the case of a compound, of glasses are estimated [26]: where the weight fraction of the ith constitute elements is w i .
The effective atomic number and effective electron density, depending on the total molecular cross_section (σ t ); total atomic cross-section (σ a ), and total electronic cross_ section (σ e ); was used to measure the total effective atomic cross-section [27].
The terms n i , A i , Z i , f i, and N A are the number of atoms, atomic weight, atomic number, a fractional abundance of the ith element, and Avogadro number. It's worth mentioning that a certain attenuator thickness can decrease the absorbed gamma intensity to 1/2 of the premier radiation: this is called the half-value layer (HVL), and are acquired using the following equations [28,29]: An absorption of 0.368 of the incident gamma radiation observed by materials that have a thickness of one mean free path (MFP) [30]: The exposure buildup factor (EBF) and energy absorption buildup factor (EABF) terms are also key parameters for seeing overall contributions to gamma rays' attenuation in material. G-P suitable approach was used to evaluate exposure buildup factor (EBF) and energy absorption buildup factor (EABF), in the analysis. The specifics of our previous study can be found in literature elsewhere [31][32][33][34].

Simulation Studies Using FLUKA Code
Nine samples of glass were simulated using the FLUKA Monte Carlo code [32,35,36]. The FLUKA is a simulation program used to estimate the Mass Attenuation Coefficient by obtaining photons passing through materials and an initial number of photons in the detector's volume. Besides, the USRBIN was used as a detector map to predict the photon flux inside the detector (Fig. 1). During the current simulation, the required card MATERIAL was attached to the COMPOUND card for sample identification. Composition, name, density, material number, etc. of the Complex were selected as a MATERIAL CARD. Three inches of × and three inches of a cylindrical NaI(Tl) detector was placed in a Pb-cylindrical collimator with these dimensions (12, 0.2, 15) cm outer, inner, length respectively. A USRTRACK scorecard (metric) described the NaI region as a fluctuation in the path length according to statistical error (< 0.1%), The total of elementary photons for simulation is about 10 million. LOW-BIAS card requires asymmetric absorption and/or an energy cutoff during low energy neutron transport on a regional basis. A BEAM card determined particle's shape and energy; although, it produced to set a monoenergetic (0.2 cm size) photon with energies between 0.015 and 15 MeV to determine the source beam. The BEAMPOS card made to adjust this beam source's orientation and position on the positive z‫ـ‬axis. The photon transmission power cut adjusted to an energy level of 10 -7 GeV using the EMFCUT card at low levels of energy. For modelling all glass samples, a cylindrical geometry with a 1.0 cm diameter and a thickness varying between 0.1 and 0.5 cm (based on the primary photon energy) was used. In all samples encoded PbF00, PbF10, PbF20, PbF30, PbF40, PbF50, PbF60, PbF70 and PbF80, a cylindrical geometry with a diameter of 1.0 cm and a thickness of 0.1 to 0.5 cm (depending on the energy of the primary photon) was used. The glass samples were formalised with a RPP body. It was denoted by minX − maxX, minY − maxY and minZ − maxZ, and boundaries parallel to the coordinate axis. In this geometry, the maxX value (maxY value) and the minX value (minY value) were chosen as + 5 cm and − 5 cm, respectively [37]. The target material is selected with a length of 15 cm and a width of various thicknesses with the obtained max Z and min z. After interacting with the sample, the photons were located in the detector volume. The size of a detector is covered with a lead collimator to prevent the identification of scattered photons.

Elastic Parameters
The studied glass samples' density values were in good agreement with those obtained earlier [22][23][24]. The rigidity of radiation shielding materials had a special interest, so, the structure of a shielding can be correlated to the rigidity. This correlation can determine the use of such shielding. The rigidity of the glass shielding can be evaluated by determining the elastic moduli of such shielding. The elastic moduli can be evaluated according to Makishima -Mackenzie model [38,39]. The bulk modulus (K mac ) and Young's modulus (Y mac ) in terms of the dissociation energy (Gt i ), the mole fraction of the ith oxide (A m O n ) in the glass sample (x i ), and the ionic radii according to Pauling of the ith cation (R A ) and oxygen (R O ) respectively as: where N A is Avogadro's number and ρ is the density of the glass sample. The packing density and the dissociation energy are decisive parameters in determining the elastic moduli of the glasses according to Makishima -Mackenzie model. Table 1 presents the values of the density and the former physical parameters.
On the other hand, El Agammy et al. [23] reported, with several characterization techniques, on the dual role of PbF 2 in tellurite-based glasses. At high concentrations of PbF 2 constructed its network and behaved as a glass former. At these ratios of PbF 2 , the network of PbF 2 -TeO 2 will be composed of Pb 2+ 1∕2 [TeO 3+1 ] − and TeO 3/2 F structural units with two-non bridging oxygens. These arguments agree with studies on the role of PbO [40]. The incremental of Bi 2 O 3 at the expense of PbF 2 increases the density of the explored glasses as there is a difference between the atomic mass of Bi 2 O 3 (465.959 g/mol) and atomic mass of PbF 2 (245.197 g/ mol). Saddeek et al. [22] reported on the formation of the concentrations of [BiO 6 ] and [BiO 3 ] structural units as the Bi2O3 content increases. In the explored glasses, as the Bi 2 O 3 content increases, the glass former role of Bi 2 O 3 manifests itself in the presence of two formers glass with high field strength cations, namely, TeO 2 and B 2 O 3 . This procedure will affect the elastic moduli of the explored glasses. According to the literature, the packing density and the dissociation energy of Bi2O3 are 26.1 × 10 -6 m 3 mol −1 and 31.6 × 10 9 J m −3 , respectively [41], while those of PbF 2 are 10.21 × 10 -6 m 3 mol −1 and 23.21 × 10 9 J m −3 , respectively [42][43][44], i.e., the bond strength of Bi-O is larger than that of the Pb-F. Thus, the increase of Bi 2 O 3 will strengthen the lead telluro-borate network [45]. The strength will be achieved by creating bridging oxygens provided from the structural units of Bi 2 O 3 . These oxygens converted Pb 2+ 1∕2 [TeO 3+1 ] − into TeO 4 structural units. This process will compact the glass network, increase the density, and increase the packing density and dissociation energy of the explored network as tabulated in Table 1. Therefore, the elastic moduli of the lead telluro-bortae network will increase and such an increment was stem from the former role of Bi 2 O 3 .

Shielding Parameters
In this study, different types of glasses encoded PbF00, PbF10, PbF20, PbF30, PbF40, PbF50, PbF60, PbF70, and PbF80 were evaluated by using Monte Carlo simulation methods in terms of gamma-ray attenuation competencies. The efficiency of a substance while subjected to gamma radiation is based on its elemental structure and density. For simulation studies, material properties of the examined sample should be taken into account. Recently, the shielding efficiency of glass shield samples was examined using Monte Carlo simulation. Figure 1 demonstrates the general setup for evaluating the attenuation properties of glass shielding products. The isotropic point source was mounted within a Lead (Pb) plating shield. In addition to installing a collimator into the Pb block, the main gamma-ray beam was also used. For calculation of certain important parameters such as the linear attenuation coefficients (µ), mass attenuation coefficients (µ m ), half-value layer (T 1/2 ), and mean free path (λ), primary and secondary gamma-ray intensities, which are obtained from FLUKA output file were used. The Fig. 2 shows the variance of linear attenuation coefficients of PbF00, PbF10, PbF20, PbF30, PbF40, PbF50, PbF60, PbF70, and PbF80 samples at various photon energies from 0.015 to 15 MeV. The three most dominant interaction mechanisms explored in the figure are the Photoelectric Effect (PE), Compton Scattering (CS), and Pair Production (PP). In low-energy zones, PE was shown to be the primary factor for the absorption of gamma-rays [46]. The reduction was recorded in the same area. However, comparatively smooth functional decrements existed at mid and high frequency, gamma-band frequencies. CS and PP were strongest in the mid-level and high-level photon energy zones, respectively [47]. The effect being observed is characteristic of attenuators and is based on the association of incident photons with the substance's atomic structure. However, the results showed that PBF00 sample has the highest linear attenuation coefficient (µ) values at all photon energies. This can be explained by the elemental composition and materials characteristic of PBF00 sample that caused superior shielding competencies among the investigated glass shields. The term of mass attenuation coefficients (µ m ) of an attenuator is a particular quantity that may be used for classification purposes of shields depending on the LAC value. Figure 3a-i is a comprehensive demonstration between FLUKA general-purpose Monte Carlo code and XCOM software. The figure depicts the variation of mass attenuation coefficient (µ m ) values versus photon energy (E) for glass samples, respectively. It is seen from the Fig. 3a-i that obtained µm values are in high accordance. Figure 4 was added into results to demonstrate the quantitative differences between the FLUKA and XCOM for Pb80 and Pb00 glass samples. It is seen from Fig. 4 that the variation trend of µ m values is in a similar attitude. This is clear evidence for the reliability of utilised Monte Carlo simulations considering the standard NIST data. However, some slight differences were also reported at some specific energies. The smooth differences are expected deviations since the FLUKA and XCOM database uses different approaches during the determination of mass attenuation coefficients. On the other hand, this behavior can be attributed to way of data providing since FLUKA uses individual simulation techniques, where the primary and secondary gamma-ray intensities are main quantities for the calculation of coefficient, whereas XCOM provides direct results from the NIST database [48]. By utilisation of linear attenuation coefficients, half value layer (T 1/2 ) values of studied glass samples were determined. There is an inverse relationship between the T 1/2 and µ values. It means that the materials with higher µ values will have lower T 1/2 values at related energy values. In other words, one can say that the materials with higher µ values require lower thicknesses to reduce the incident gamma-ray to its half. Figure 5 represents the variation of half-value layer (T 1/2 ) values with photon energy for glass samples. It can be observed from the figure that half value layers increased with increasing photon energy. This can be explained with gamma-ray material interaction facts that higher energy gamma-rays require higher material thicknesses to be reduced to their half intensity. However, half value layer values are also critical parameters to distinguish the competencies of shielding materials. As previously discussed, PBF00 sample was reported with the highest linear attenuation coefficients. Therefore, one can expect that this sample will require the lowest thicknesses among the studied samples. This is clear in Fig. 5 that the PBF00 sample has the lowest half value layer values at used photon energy values, whereas PBF80 has the highest. The aforementioned situation can also be linked with their sharp chemical compositions as well as material densities (i.e., the highest and the lowest). The HVL values for PbF00 and PbF80 samples were compared with the values for various concretes [49] and the ZBV4 model [50]. The lowest and highest HVL values were obtained for comparable materials in the photon energy range of 0.015-15 MeV, as in Fig. 6.  Our results show that the superior PbF00 sample has lower HVL values than conventional concrete at the photon energies investigated. Thus, it can be argued that the PbF00 sample is a suitable candidate for use in radiation installations, where ordinary concrete serves as the week shield that protects public-health. Regarding basalt-magnetite concrete and hematite serpentine concrete had higher HVL values than both PbF00 and PbF80 samples. It can be concluded that these additional improvements can be made to the current gamma attenuation capabilities of the PbF00 sample to reduce the HVL values further. Increasing the PbF 2 /Bi 2 O 3 gain can be considered as an approach to gain for this purpose. However, it is vital to study the effect of additional gain values on mechanical characteristics on behavioral assessment. Figure 7 shows another vital shielding parameter variation, namely mean free path (λ) values with photon energy for glass samples. The mean free part is an essential parameter to define the average distance of gamma-rays that they can travel through the material. The superior shielding materials can be expected to have lower distances that gamma-ray can travel through the attenuator. The aforementioned situation is clearly seen in Fig. 7 that PBF00 was noted with the lowest mean free path values. This can also be considered evidence for its superior gamma-ray shielding competencies among the all-studied glass shields. Figure 8  shows the variation of Z eff values with photon energy for glass samples. Z eff is a handy parameter to assess the attenuation competencies of mixtures considering their substance elements with their individual atomic numbers (Z). It is well-known that the elements with higher Z numbers have a remarkable advantage during the attenuation process of ionising gamma-rays. In parallel, it can be said that mixtures, which consist of substances with higher Z numbers, can attenuate the gamma-rays in a better way. Considering the elemental compositions of studied glasses, it can be noted that the amount of high Z substances in PBF00 sample has caused the existing situation, which can be clearly observed from Fig. 8. It can be said that the PbF00 sample has the highest Z eff values at all photon energy values. Finally, it's worth mentioning that effective removal cross-sections against fast neutrons (Σ R ) were also theoretically calculated for all glasses. This is a theoretical parameter that indicates the resistance potential of studied compositions against fast neutrons, which is directly dependent on partial density and removal cross-sections of substance elements in a composition. The results showed a synergistic relationship between the gamma-ray shielding competencies and effective removal cross-sections of PbF00 sample (Fig. 9). It can be noted that superior gamma-ray attenuator encoded PbF00 is also a potential neutron shield against fast neutrons.

Conclusion
this study aims to evaluate the mechanical and radiation shielding parameters of a wide range of Bi 2 O 3 blended with TeO 2 -B 2 O 3 -PbF 2 glasses. The different types of glasses encoded PbF00, PbF10, PbF20, PbF30, PbF40, PbF50, PbF60, PbF70, and PbF80 were evaluated by using Monte Carlo simulation methods in terms of gamma-ray attenuation competencies. The efficiency of a substance while subjected to gamma radiation is based on its elemental structure and density. Computational methods had computed the mass attenuation coefficients (MAC). The MAC values at 0.015 MeV increase from 85.16 to 96.92 (cm 2 g −1 ) as the PbF 2 /Bi 2 O 3 ratio changed from 0 to 80 mol_%, and the HVL values decrease from 1.93 to 1.66 (cm) at 1 MeV. The results indicate that the PbF00 glass sample with 80% mol Bi 2 O 3 has the best mechanical competence and best in blocking ionising radiation. In this study, we gave thorough findings based on a variety of factors. However, given the substantial material qualities of glass, it may be argued that continued work is necessary to optimize and enhance the suggested glassy system.