Theoretical Investigation of the Inﬂuence of Different Heavy Metal Oxides Modiﬁers on ZnO-Bi 2 O 3 -B 2 O 3 -SiO 2 ’s Photon-and Neutron-Shielding Capabilities Using the Monte Carlo Method

: Radiation has become an essential part in medicine and researchers are constituently investigating radiation shielding materials that are suitable for different medical applications. Glass, due to its properties, has been considered an excellent radiation shield for such applications. One of the most common glasses used as a radiation shield is the ZnO-Bi 2 O 3 -B 2 O 3 -SiO 2 anti-radiation glass. Heavy metal oxides have many desirable properties such as high density, transparency to visible light, stability in air and water, high interaction cross section, high infrared transparency, and good absorption of radiation, which make them desirable to be used as modiﬁers with anti-radiation glass. Research has been focusing on environmentally friendly shielding material which leads to non-lead modiﬁers such as Na 2 O, Al 2 O 3 , MgO, TiO 2 , SrO, Sb 2 O 3 , and BaO, which have become more desired than PbO. So far, ZnO-Bi 2 O 3 -B 2 O 3 -SiO 2 ’s photon shielding properties have been studied experimentally with the addition of BaO at certain energies only. In this work, different heavy metal oxides are added as modiﬁers to ZnO-Bi 2 O 3 -B 2 O 3 -SiO 2 glass in order to investigate theoretically their effects on the shielding properties of the glass at a wide range of photon and neutron energies. Simulation is cost-and time-effective when it comes to investigating different compositions of glass and different modiﬁers with different weight percentages at any energy range for any type of radiation. Simulation could be considered the ﬁrst step in order to identify the best mixture with the best weight fractions prior to any experimental investigations of other desired properties based on the needed application. In this work, the photon-and neutron-shielding capabilities of the ZnO-Bi 2 O 3 -B 2 O 3 -SiO 2 anti-radiation glass is investigated with different weight fractions of heavy metal oxides at wide photon and neutron energy ranges. Geant4, which is a Monte Carlo-based powerful toolkit, is used to ﬁnd the mass attenuation coefﬁcients ( µ m) of photons, as well as the effective removal cross sections ( Σ R) of neutrons, of all the investigated samples in the studied energy range.


Introduction
Radiation is an essential part of life and despite all its benefits; it can cause damage to humans either directly or indirectly through deformation and inheritance to future generations because of its ability to penetrate human bodies [1][2][3][4]. This is the reason why researchers are focusing on finding suitable materials that have the ability to shield radiation in order to reduce its damage on humans. Radiation materials used in medical applications should be environmentally friendly, transparent, durable, and easy to shape and construct [5][6][7][8][9][10].
When photons enter a material with a certain intensity (I 0 ), it attenuates and its intensity after passing through a mass per unit area (x) layer of material is reduced to (I). The photon mass attenuation coefficient (µ m ) depends on the material and can be calculated using Equation (1) [49]: The influence of different modifiers on the mass attenuation coefficients of the investigated glass is evaluated in this work.

Neutron Attenuation
The probability of neutron reactions with any material is expressed by the neutron removing cross section (Σ R ), and is given by Equation (2) [50]: where (ρ R ) is the partial density, and (Σ R /ρ) is the mass removal cross section, which can be calculated using Equation (3) for any compound [51]: where (A) is the atomic weight, and (Z) is the atomic number. The influence of different modifiers on the effective removal cross sections of the investigated glass is evaluated in this work.

Methods
In this work, the powerful Monte Carlo-based toolkit, Geant4.11.02, which is utilized in nuclear physics, nuclear engineering, and medical physics, was used to evaluate the photon-and neutron-shielding properties of the investigated samples [52]. Geant4 is very reliable and has been used in many shielding assessment studies, has been compared to experimental results and other software, and has shown excellent agreement. Root (6.10/04) software was used to plot figures presented in this work [53].

Effect of Na 2 O Modifier
Na 2 O is one of the most commonly used materials in medical applications, when added to glass it decreases the crystallization rates, lowers the melting temperatures, and enhances the performance in the glass-forming zone [54]. Table 1 summarizes the mass attenuation coefficients of the studied glass with different fractions of Na 2 O at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 2 summarizes the neutron effective removal cross sections of the studied glass with different fractions of Na 2 O. It can be seen that the photon-shielding capabilities of glass have decreased with the addition of the Na 2 O modifier while the neutron-shielding capabilities are enhanced.

Effect of Al 2 O 3 Modifier
Al 2 O 3 enhances the long-time stability, chemical durability, melting properties, and opacity of glass and yet it is of low cost [54]. Table 3 summarizes the mass attenuation coefficients of the studied glass with different fractions of Al 2 O 3 at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 4 summarizes the neutron effective removal cross sections of the studied glass with different fractions of Al 2 O 3 . The photonshielding capabilities of glass have decreased with the addition of the Al 2 O 3 modifier while the neutron-shielding capabilities are enhanced.

Effect of MgO Modifier
MgO is one of the most commonly used materials in medical applications, when added to glass it decreases the crystallization rates, lowers the melting temperatures, and enhances the performance in the glass-forming zone [54]. Table 5 summarizes the mass attenuation coefficients of the studied glass with different fractions of MgO at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 6 summarizes the neutron effective removal cross sections of the studied glass with different fractions of MgO. MgO decreased the photon-shielding capabilities of glass while it enhanced the neutron-shielding capabilities.

Effect of TiO 2 Modifier
TiO 2 when added to glass protects its optical efficiency [55]. Table 7 summarizes the mass attenuation coefficients of the studied glass with different fractions of TiO 2 at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 8 summarizes the neutron effective removal cross sections of the studied glass with different fractions of TiO 2 . It can be seen that the photon-shielding capabilities of glass have decreased with the addition of the TiO 2 modifier while the neutron-shielding capabilities are enhanced.

Effect of SrO Modifier
SrO raises the characteristic temperature of glasses and resistance to crystallization [56]. Table 9 summarizes the mass attenuation coefficients of the studied glass with different fractions of SrO at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 10 summarizes the neutron effective removal cross sections of the studied glass with different fractions of SrO. The photon-shielding capabilities of glass have been enhanced with the addition of the SrO modifier while the neutron-shielding capabilities are decreased.

Effect of Sb 2 O 3 Modifier
Sb 2 O 3 when added to glass enhances its structural, thermal, and optical properties [57]. Table 11 summarizes the mass attenuation coefficients of the studied glass with different fractions of Sb 2 O 3 at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 12 summarizes the neutron effective removal cross sections of the studied glass with different fractions of Sb 2 O 3 . The photon-shielding capabilities of glass have been enhanced with the addition of the Sb 2 O 3 modifier while the neutron-shielding capabilities are decreased.

Effect of BaO Modifier
BaO when added to glass improves its density and stability [55]. Table 13 summarizes the mass attenuation coefficients of the studied glass with different fractions of BaO at a wide photon energy range from 10 keV to 20 MeV. On the other hand, Table 14 summarizes the neutron effective removal cross sections of the studied glass with different fractions of BaO. The photon-shielding capabilities of glass have been enhanced with the addition of the Sb 2 O 3 modifier while the neutron-shielding capabilities are decreased.

Comparison between the Influence of All Investigated Modifiers on the Shielding Properties of the Studied Glass
In order to clearly compare the influence of the investigated modifiers on the performance of the studied glass as a radiation shield, the photon attenuation coefficients and the neutron removal cross sections were plotted for the pure glass against the glass with 1% fraction of the different modifiers studied in this work as shown in Figures 1 and 2. The glasses with 20% fraction of modifiers were compared and plotted as well in Figures 3 and 4. The average percentage differences between the coefficients and cross sections in the case of glass with modifiers are tabulated in Table 15 for easier comparison among the effects of the different modifiers.
As can be seen from Figures 5 and 6, the results show that BaO enhances the photonshielding properties of ZnO-Bi 2 O 3 -B 2 O 3 -SiO 2 the most among all compared metal oxides with an average between 0.95% and 18.94%, but on the other hand it decreases the neutronshielding by an average ranging from −0.49% to −10.71%. The Sb 2 O 3 performed nearly the same with average percentage differences between 0.61% and 12.16% for photon-shielding abilities and between −0.61% and −8.74% for neutron-shielding abilities. The SrO also increased the ability of glass to shield against photons and reduced its ability against neutrons. The MgO modifier, on the one hand, enhanced the neuron-shielding capabilities of the studied glass the most with average percentage differences ranging from 0.56% to 10.43%, while it decreased the photon-shielding properties by, on average, between −0.39% to −7.89%. The Na 2 O, Al 2 O 3 , and TiO 2 increased the ability of the studied glass to shield against neutrons as well and reduced the ability to shield against photons. In general, the effects of modifiers on photon shielding-properties are higher than on neutron-shielding properties. From a practical point of view, the neutron activation of elements and the formation of point defects must be considered when choosing the best modifier and this can be evaluated experimentally, as some studies have reported [58][59][60].
mance of the studied glass as a radiation shield, the photon attenuation coefficients and the neutron removal cross sections were plotted for the pure glass against the glass with 1% fraction of the different modifiers studied in this work as shown in Figures 1 and 2. The glasses with 20% fraction of modifiers were compared and plotted as well in Figures  3 and 4. The average percentage differences between the coefficients and cross sections in the case of glass with modifiers are tabulated in Table 15 for easier comparison among the effects of the different modifiers.          It is essential to choose the right modifiers to be added to anti-radiation glasses based on the required applications while taking into account the effects on the physical and chemical properties.

Conclusions
The performance of ZnO-Bi2O3-B2O3-SiO2 anti-radiation glass as a photon and neutron shield was investigated at a wide energy range and the effect of some selected heavy metal oxides modifiers on the shielding properties were studied at chosen fractions. The results indicate that some modifiers enhance the photon-shielding ability of the studied  It is essential to choose the right modifiers to be added to anti-radiation glasses based on the required applications while taking into account the effects on the physical and chemical properties.

Conclusions
The performance of ZnO-Bi2O3-B2O3-SiO2 anti-radiation glass as a photon and neutron shield was investigated at a wide energy range and the effect of some selected heavy metal oxides modifiers on the shielding properties were studied at chosen fractions. The results indicate that some modifiers enhance the photon-shielding ability of the studied  It is essential to choose the right modifiers to be added to anti-radiation glasses based on the required applications while taking into account the effects on the physical and chemical properties.

Conclusions
The performance of ZnO-Bi 2 O3-B 2 O3-SiO 2 anti-radiation glass as a photon and neutron shield was investigated at a wide energy range and the effect of some selected heavy metal oxides modifiers on the shielding properties were studied at chosen fractions. The results indicate that some modifiers enhance the photon-shielding ability of the studied glass but at the same time reduces its ability to shield against neutrons and vice versa. Choosing the preferable modifier should be influenced by the desired application and by the effects on the other chemical and physical properties of glass.
Future studies should focus on choosing the right modifier with the right percentage in order to fit a certain application and maybe even mixing different modifiers to get the right combination of features. Simulation is the most effective way to evaluate different mixtures without wasting time, money, and effort. However, future experimental detailed studies of the defect formation mechanism and the radiation-induced variation of optical and structural properties of the chosen glasses are important along with investigation of any defects, crystallization, or bubble formation which must be completed before using the best configuration for any desired application [58]. This is especially the case when considering the long-term use of such shields; lattice oxygen vacancy defects created by radiation and their effects on transparency and shielding effectiveness should be evaluated [59,60].