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Article

Theoretical Investigation of the Influence of Different Heavy Metal Oxides Modifiers on ZnO-Bi2O3-B2O3-SiO2’s Photon- and Neutron-Shielding Capabilities Using the Monte Carlo Method

by
Hanan Akhdar
Department of Physics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
Appl. Sci. 2023, 13(16), 9332; https://doi.org/10.3390/app13169332
Submission received: 27 July 2023 / Revised: 9 August 2023 / Accepted: 16 August 2023 / Published: 17 August 2023
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Abstract

:
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-Bi2O3-B2O3-SiO2 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 Na2O, Al2O3, MgO, TiO2, SrO, Sb2O3, and BaO, which have become more desired than PbO. So far, ZnO-Bi2O3-B2O3-SiO2’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-Bi2O3-B2O3-SiO2 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-Bi2O3-B2O3-SiO2 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 (µm) of photons, as well as the effective removal cross sections (ΣR) of neutrons, of all the investigated samples in the studied energy range.

1. 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].
Researchers have been focusing on studies related to radiation shielding material, as radiation plays an essential part in medicine, for the sake of finding the most suitable materials for different applications. Glass has been considered an excellent radiation shield due to its properties [1,8,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. Many studies focused on investigating the capabilities of glass to shield against different radiation for many industrial and medical applications [1,8,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. Glass offers excellent shielding properties as well as good transparency to visible light which is important in many medical-related applications [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28].
The ZnO-Bi2O3-B2O3-SiO2 anti-radiation glass is one of the most commonly used lead-free glasses in radiation protection [28]. Heavy metal oxide modifiers such as PbO enhance the shielding properties of glass when added at certain percentages [29,30,31,32,33,34,35,36]. However, research interest has shifted towards environmentally friendly materials such as Na2O, Al2O3, MgO, TiO2, SrO, Sb2O3, and BaO instead of PbO. Those modifiers influence 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 [37,38,39]. Glasses with heavy metal oxide modifiers can shield against both photons and neutrons since they are of high content of both heavy and light elements [40]. However, the neutron-induced damage to these heavy metal oxide modifiers due to the transfer of incident neutrons energy via elastic collision with the primary knock-on atoms, should be considered [41,42,43,44,45,46,47,48].
In this work, the photon- and neutron-shielding capabilities of the ZnO-Bi2O3-B2O3-SiO2 anti-radiation glass are 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 (µm) of photons, as well as the effective removal cross sections (ΣR) of neutrons, of all the investigated samples in the studied energy range.

2. Materials

The samples investigated in this work are composed of (wt%) HMO (100—wt%) [0.3 ZnO 0.2 Bi2O3 0.2 B2O3 0.3 SiO2] (where wt% is 0%, 1%, 5%, 10%, 15%, and 20%) and the used heavy metal oxides are Na2O, Al2O3, MgO, TiO2, SrO, Sb2O3, and BaO.

3. Theory

3.1. Photon Attenuation

When photons enter a material with a certain intensity (I0), 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 (μm) depends on the material and can be calculated using Equation (1) [49]:
I = I 0 e − μ m x
The influence of different modifiers on the mass attenuation coefficients of the investigated glass is evaluated in this work.

3.2. Neutron Attenuation

The probability of neutron reactions with any material is expressed by the neutron removing cross section (ΣR), and is given by Equation (2) [50]:
Σ R = ∑ i ρ i Σ R / ρ i
where (ρR) is the partial density, and (ΣR/ρ) is the mass removal cross section, which can be calculated using Equation (3) for any compound [51]:
Σ R ρ = 0.206 A − 1 3 Z − 0.294
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.

4. 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].

5. Effect of Na2O Modifier

Na2O 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 Na2O 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 Na2O. It can be seen that the photon-shielding capabilities of glass have decreased with the addition of the Na2O modifier while the neutron-shielding capabilities are enhanced.

6. Effect of Al2O3 Modifier

Al2O3 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 Al2O3 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 Al2O3. The photon-shielding capabilities of glass have decreased with the addition of the Al2O3 modifier while the neutron-shielding capabilities are enhanced.

7. 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.

8. Effect of TiO2 Modifier

TiO2 when added to glass protects its optical efficiency [55]. Table 7 summarizes the mass attenuation coefficients of the studied glass with different fractions of TiO2 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 TiO2. It can be seen that the photon-shielding capabilities of glass have decreased with the addition of the TiO2 modifier while the neutron-shielding capabilities are enhanced.

9. 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.

10. Effect of Sb2O3 Modifier

Sb2O3 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 Sb2O3 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 Sb2O3. The photon-shielding capabilities of glass have been enhanced with the addition of the Sb2O3 modifier while the neutron-shielding capabilities are decreased.

11. 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 Sb2O3 modifier while the neutron-shielding capabilities are decreased.

12. 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 Figure 1 and Figure 2. The glasses with 20% fraction of modifiers were compared and plotted as well in Figure 3 and Figure 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 Figure 5 and Figure 6, the results show that BaO enhances the photon-shielding properties of ZnO-Bi2O3-B2O3-SiO2 the most among all compared metal oxides with an average between 0.95% and 18.94%, but on the other hand it decreases the neutron-shielding by an average ranging from −0.49% to −10.71%. The Sb2O3 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 Na2O, Al2O3, and TiO2 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].
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.

13. 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 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].

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The author declares no conflict of interest.

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Applsci 13 09332 g001
Figure 1. The effect of 1% of different modifiers on the photon mass attenuation coefficients of the studied glass.
Figure 1. The effect of 1% of different modifiers on the photon mass attenuation coefficients of the studied glass.
Applsci 13 09332 g001
Applsci 13 09332 g002
Figure 2. The effect of 20% of different modifiers on the photon mass attenuation coefficients of the studied glass.
Figure 2. The effect of 20% of different modifiers on the photon mass attenuation coefficients of the studied glass.
Applsci 13 09332 g002
Applsci 13 09332 g003
Figure 3. The effect of 1% of different modifiers on the neutron removal cross sections of the studied glass.
Figure 3. The effect of 1% of different modifiers on the neutron removal cross sections of the studied glass.
Applsci 13 09332 g003
Applsci 13 09332 g004
Figure 4. The effect of 20% of different modifiers on the neutron removal cross sections of the studied glass.
Figure 4. The effect of 20% of different modifiers on the neutron removal cross sections of the studied glass.
Applsci 13 09332 g004
Applsci 13 09332 g005
Figure 5. Comparison between the effects of all investigated modifiers on the photon-shielding abilities of the studied glass.
Figure 5. Comparison between the effects of all investigated modifiers on the photon-shielding abilities of the studied glass.
Applsci 13 09332 g005
Applsci 13 09332 g006
Figure 6. Comparison between the effects of all investigated modifiers on the neutron-shielding abilities of the studied glass.
Figure 6. Comparison between the effects of all investigated modifiers on the neutron-shielding abilities of the studied glass.
Applsci 13 09332 g006
Table 1. The photon mass attenuation coefficients of the studied glass with Na2O modifier.
Table 1. The photon mass attenuation coefficients of the studied glass with Na2O modifier.
Photon Energy (keV)Pure GlassGlass with Na2O Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508587.2008584.2008580.4506876.7005172.95034
2025.8958525.6545824.6894923.4832222.2768621.07059
308.960428.877208.544418.128357.712317.29628
404.197274.158934.005573.813873.622183.43047
502.345782.324962.241672.137572.033471.92936
601.479641.467031.416571.353491.290421.22734
701.019401.011140.978090.936800.895490.85419
800.746520.740820.718040.689570.661090.63261
900.569170.565130.548990.528820.508650.48848
1001.237921.227121.183901.129861.075841.02181
2000.295510.293760.286730.277960.269180.26040
3000.163530.162930.160540.157540.154550.15155
4000.121140.120860.119730.118320.116910.11550
5000.100670.100520.099890.099100.098320.09753
6000.088370.088270.087890.087400.086920.08643
7000.079910.079840.079590.079270.078950.07863
8000.073540.073500.073320.073100.072880.07266
9000.068500.068470.068340.068180.068030.06787
10000.064340.064320.064230.064110.064000.06389
20000.044210.044200.044160.044120.044070.04402
30000.037060.037040.036960.036860.036750.03665
40000.033570.033540.033410.033250.033090.03293
50000.031630.031590.031420.031220.031010.03080
60000.030500.030450.030250.030000.029740.02949
70000.029830.029770.029540.029250.028950.02866
80000.029440.029370.029110.028790.028460.02814
90000.029220.029150.028870.028510.028160.02781
10,0000.029130.029060.028750.028370.027990.02761
20,0000.030410.030300.029850.029290.028730.02817
Table 2. The neutron effective removal cross sections of the studied glass with Na2O modifier.
Table 2. The neutron effective removal cross sections of the studied glass with Na2O modifier.
Neutron Energy (keV)Pure GlassGlass with Na2O Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.76048.96429.21799.47229.7254
2030.958031.342032.171029.097029.484028.3910
308.93078.95869.06509.19799.33309.4645
408.97738.99859.09339.21139.33039.4500
508.57188.61468.77818.98209.18509.3901
609.16669.18929.27879.38999.50239.6138
709.25699.27229.33479.41479.49419.5725
808.61958.63818.71738.81728.91369.0093
909.45119.46759.50379.55559.60729.6546
1009.70329.72349.74229.76839.79459.8461
20011.929011.982012.244012.549012.849013.1560
30010.491010.584010.741010.975011.229011.4480
40013.889013.914014.018014.147014.274014.4030
50010.400010.383010.317010.238010.154010.0800
6007.86047.91288.12278.38508.64768.9098
7007.04237.15847.62298.20338.78359.3645
8007.44067.50917.78378.12708.47198.8161
9007.37457.43277.66587.95698.24818.5393
100014.718014.711014.681014.645014.608014.5720
20004.82764.85044.93945.05495.17275.2828
30004.14364.16484.24924.35484.46024.5657
40005.28605.29655.33835.39065.44275.4952
50004.00224.01074.04564.08904.13234.1756
60004.64484.64964.67014.69874.72514.7520
70003.50663.51413.54443.58193.61963.6571
80003.50543.51163.53633.56713.59823.6289
90003.91563.92063.93963.96353.98754.0115
10,0003.96633.97143.99204.01774.04334.0690
20,0004.26354.27224.30694.35044.39384.4372
Table 3. The photon mass attenuation coefficients of the studied glass with Al2O3 modifier.
Table 3. The photon mass attenuation coefficients of the studied glass with Al2O3 modifier.
Photon Energy (keV)Pure GlassGlass with Al2O3 Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508587.1576383.9841580.0172076.0502572.08331
2025.8958525.6489824.6617823.4278022.1938120.95975
308.960428.875598.536448.112507.688537.26458
404.197274.158314.002453.807633.612813.41798
502.345782.324662.240212.134652.029081.92353
601.479641.466871.415811.351981.288161.22433
701.019401.011050.977690.935970.894260.85255
800.746520.740780.717830.689150.660470.63179
900.569170.565110.548910.528650.508390.48813
1001.237921.227121.183881.129831.075791.02175
2000.295510.293780.286870.278230.269590.26094
3000.163530.162960.160670.157810.154960.15210
4000.121140.120880.119860.118570.117290.11601
5000.100670.100540.100010.099340.098670.09801
6000.088370.088290.088000.087620.087250.08687
7000.079910.079860.079690.079470.079260.07904
8000.073540.073520.073420.073300.073180.07305
9000.068500.068480.068430.068370.068310.06824
10000.064340.064330.064310.064290.064270.06424
20000.044210.044210.044220.044230.044240.04425
30000.037060.037050.037000.036940.036870.03681
40000.033570.033540.033440.033300.033170.03304
50000.031630.031600.031440.031250.031060.03087
60000.030500.030450.030260.030020.029770.02953
70000.029830.029770.029540.029250.028970.02868
80000.029440.029370.029110.028780.028460.02813
90000.029220.029150.028860.028500.028140.02778
10,0000.029130.029060.028740.028350.027960.02757
20,0000.030410.030290.029820.029220.028630.02803
Table 4. The neutron effective removal cross sections of the studied glass with Al2O3 modifier.
Table 4. The neutron effective removal cross sections of the studied glass with Al2O3 modifier.
Neutron Energy (keV)Pure GlassGlass with Al2O3 Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.73688.84458.97839.11199.2463
2030.958031.722031.202027.459028.366027.3610
308.93078.95629.04979.16449.27899.3984
408.97738.99709.08689.19939.31139.4229
508.57188.60048.70058.83298.96419.0933
609.16669.18529.26399.36119.45879.5574
709.25699.27409.34629.43639.52679.6170
808.61958.64258.73998.85468.97419.0924
909.45119.47109.52459.59829.66769.7456
1009.70329.71949.76109.80959.86659.9317
20011.929011.904011.824011.717011.613011.4960
30010.491010.539010.415010.364010.288010.2380
40013.889013.888013.914013.938013.957013.9940
50010.400010.462010.702011.009011.313011.6230
6007.86047.90818.09928.33818.57708.8160
7007.04237.08177.23947.43667.63377.8308
8007.44067.46797.57697.71497.85207.9894
9007.37457.42277.61597.85768.09838.3405
100014.718014.778015.024015.331015.638015.9440
20004.82764.85444.96415.10075.23675.3728
30004.14364.15794.21494.28604.35744.4288
40005.28605.30125.36315.43975.51685.5937
50004.00224.00824.03154.06094.09004.1193
60004.64484.65634.69954.75694.81334.8701
70003.50663.51373.54133.57613.61113.6457
80003.50543.51103.53353.56143.58963.6176
90003.91563.92403.95753.99944.04124.0830
10,0003.96633.97604.01504.06374.11244.1611
20,0004.26354.27814.33634.40914.48194.5547
Table 5. The photon mass attenuation coefficients of the studied glass with MgO modifier.
Table 5. The photon mass attenuation coefficients of the studied glass with MgO modifier.
Photon Energy (keV)Pure GlassGlass with MgO Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508587.2203484.2978080.6445876.9912773.33805
2025.8958525.6572024.7027123.5096622.3165321.12339
308.960428.878058.548398.136427.724437.31243
404.197274.159294.007363.817433.627523.43760
502.345782.325152.242662.139552.036441.93333
601.479641.467151.417221.354801.292371.22995
701.019401.011240.978580.937760.896950.85613
800.746520.740900.718420.690330.662240.63415
900.569170.565200.549320.529470.509620.48977
1001.237921.227181.184181.130421.076681.02293
2000.295510.293790.286900.278280.269660.26105
3000.163530.162960.160670.157810.154950.15209
4000.121140.120880.119850.118560.117260.11597
5000.100670.100540.100000.099320.098640.09797
6000.088370.088290.087990.087600.087220.08683
7000.079910.079860.079680.079450.079230.07900
8000.073540.073520.073410.073280.073150.07301
9000.068500.068480.068420.068350.068280.06820
10000.064340.064330.064300.064270.064240.06420
20000.044210.044210.044220.044230.044230.04424
30000.037060.037050.037010.036950.036890.03683
40000.033570.033550.033450.033330.033210.03309
50000.031630.031600.031460.031290.031120.03095
60000.030500.030460.030280.030070.029850.02963
70000.029830.029780.029570.029320.029060.02880
80000.029440.029380.029140.028850.028560.02827
90000.029220.029160.028900.028580.028260.02794
10,0000.029130.029070.028790.028440.028090.02774
20,0000.030410.030310.029880.029360.028830.02830
Table 6. The neutron effective removal cross sections of the studied glass with MgO modifier.
Table 6. The neutron effective removal cross sections of the studied glass with MgO modifier.
Neutron Energy (keV)Pure GlassGlass with MgO Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.73298.82598.94219.05859.1745
2030.958031.250030.549029.757029.738029.9910
308.93078.95339.03399.13499.23509.3364
408.97738.99419.07079.16699.26309.3582
508.57188.59918.69598.81778.94129.0611
609.16669.19059.28789.40959.53169.6529
709.25699.31869.56649.876910.186010.4960
808.61959.083710.926013.229015.535017.8370
909.45119.698610.670011.889013.112014.3270
1009.70329.777610.035010.384010.728011.0790
20011.929011.937011.961011.991012.031012.0570
30010.491010.567010.917011.383011.803012.1840
40013.889013.932014.081014.266014.462014.6540
50010.400010.460010.711011.027011.345011.6600
6007.86047.89388.02788.19518.36268.5299
7007.04237.08297.24537.44827.65157.8545
8007.44067.46177.55087.66527.77707.8879
9007.37457.39687.48527.59557.70607.8163
100014.718014.731014.786014.854014.922014.9900
20004.82764.83734.87554.92364.97115.0190
30004.14364.15464.19794.25274.30674.3612
40005.28605.29085.31105.33645.36175.3868
50004.00224.00664.02424.04614.06824.0900
60004.64484.64534.65044.65644.66194.6677
70003.50663.51003.52263.53893.55523.5713
80003.50543.50843.51993.53463.54923.5638
90003.91563.91883.93113.94633.96173.9772
10,0003.96633.97123.99054.01464.03884.0629
20,0004.26354.27264.30894.35424.39964.4450
Table 7. The photon mass attenuation coefficients of the studied glass with TiO2 modifier.
Table 7. The photon mass attenuation coefficients of the studied glass with TiO2 modifier.
Photon Energy (keV)Pure GlassGlass with TiO2 Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508587.7500086.9474685.9449284.9415383.93814
2025.8958525.7365325.0995824.3033123.5070322.71076
308.960428.902638.671368.382238.093147.80404
404.197274.169594.058893.920503.782123.64374
502.345782.330362.268652.191532.114402.03726
601.479641.470141.432181.384711.337251.28978
701.019401.013140.988130.956860.925580.89431
800.746520.742150.724680.702840.681010.65917
900.569170.566060.553640.538120.522600.50708
1001.237921.227801.187281.136641.085991.03535
2000.295510.293830.287100.278690.270290.26188
3000.163530.162950.160610.157680.154750.15182
4000.121140.120860.119720.118310.116890.11548
5000.100670.100510.099860.099050.098230.09742
6000.088370.088270.087850.087330.086800.08628
7000.079910.079830.079540.079180.078820.07846
8000.073540.073490.073280.073020.072760.07249
9000.068500.068460.068300.068100.067900.06770
10000.064340.064310.064180.064030.063870.06372
20000.044210.044200.044150.044080.044020.04395
30000.037060.037050.036980.036890.036800.03671
40000.033570.033550.033450.033340.033220.03311
50000.031630.031610.031500.031360.031220.03108
60000.030500.030470.030340.030180.030020.02986
70000.029830.029790.029650.029470.029290.02911
80000.029440.029400.029240.029040.028840.02864
90000.029220.029180.029010.028800.028590.02837
10,0000.029130.029090.028910.028680.028450.02823
20,0000.030410.030350.030090.029780.029460.02914
Table 8. The neutron effective removal cross sections of the studied glass with TiO2 modifier.
Table 8. The neutron effective removal cross sections of the studied glass with TiO2 modifier.
Neutron Energy (keV)Pure GlassGlass with TiO2 Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.88169.567510.427011.285012.1430
2030.958031.347033.491034.865036.735038.8290
308.93079.00249.28629.63839.988710.3420
408.97739.08869.544310.114010.684011.2540
508.57188.58318.61688.65878.70088.7421
609.16669.23299.50029.834010.168010.5020
709.25699.28419.39529.53559.67499.8123
808.61958.64388.72538.83128.93269.0352
909.45119.46059.46799.47939.49039.5033
1009.70329.74429.859910.006010.162010.3190
20011.929011.890011.737011.550011.359011.1690
30010.491010.499010.328010.09209.88509.6833
40013.889013.862013.753013.624013.483013.3460
50010.400010.389010.350010.297010.246010.1940
6007.86047.83527.73437.60857.48197.3547
7007.04237.04907.07627.11017.14407.1778
8007.44067.42017.34137.23897.13877.0393
9007.37457.36677.33547.29657.25687.2166
100014.718014.714014.700014.683014.666014.6490
20004.82764.83074.84324.85884.87454.8903
30004.14364.14794.16474.18524.20594.2265
40005.28605.28915.30145.31695.33255.3482
50004.00224.00394.01094.02004.02874.0376
60004.64484.64874.66344.68134.69964.7187
70003.50663.50923.51973.53253.54573.5588
80003.50543.50613.50933.51343.51723.5213
90003.91563.91643.91953.92343.92743.9312
10,0003.96633.96693.96923.97213.97493.9778
20,0004.26354.26194.25554.24754.23954.2315
Table 9. The photon mass attenuation coefficients of the studied glass with SrO modifier.
Table 9. The photon mass attenuation coefficients of the studied glass with SrO modifier.
Photon Energy (keV)Pure GlassGlass with SrO Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508587.6101786.2457684.5399282.8343281.12873
2025.8958526.1782227.3079728.7201730.1322931.54449
308.960429.053479.425689.8909310.3561910.82144
404.197274.239304.407414.617554.827695.03784
502.345782.367812.455902.566022.676142.78625
601.479641.492341.543141.606651.670161.73367
701.019401.027321.059011.098621.138241.17785
800.746520.751870.773270.800020.826780.85353
900.569170.572910.587880.606600.625320.64404
1001.237921.232841.212501.187071.161641.13622
2000.295510.294470.290310.285100.279900.27469
3000.163530.163120.161440.159340.157250.15516
4000.121140.120910.119980.118810.117650.11648
5000.100670.100520.099900.099130.098370.09760
6000.088370.088260.087800.087230.086670.08610
7000.079910.079820.079450.079000.078550.07810
8000.073540.073470.073170.072790.072420.07204
9000.068500.068430.068170.067850.067530.06721
10000.064340.064280.064050.063770.063490.06320
20000.044210.044190.044080.043940.043810.04367
30000.037060.037050.037000.036930.036860.03679
40000.033570.033560.033550.033530.033510.03349
50000.031630.031640.031650.031670.031690.03170
60000.030500.030540.030550.030600.030650.03070
70000.029830.029870.029900.029980.030050.03013
80000.029440.029490.029530.029630.029730.02983
90000.029220.029290.029340.029460.029580.02970
10,0000.029130.029200.029270.029410.029550.02969
20,0000.030410.030530.030670.030930.031190.03145
Table 10. The neutron effective removal cross sections of the studied glass with SrO modifier.
Table 10. The neutron effective removal cross sections of the studied glass with SrO modifier.
Neutron Energy (keV)Pure GlassGlass with SrO Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.67158.51968.32798.13857.9538
2030.958030.659030.314029.044027.305027.0660
308.93078.90638.80378.67538.54548.4192
408.97738.94688.83038.68548.54108.3976
508.57188.57158.55888.54398.53438.5141
609.16669.13419.00818.84578.68548.5232
709.25699.22289.08868.92088.75328.5852
808.61958.58418.44268.25878.07987.9004
909.45119.40419.16408.87758.58868.3006
1009.70329.66309.52009.36259.18008.9981
20011.929011.861011.626011.328011.023010.7170
30010.491010.453010.249010.03109.79129.5296
40013.889013.822013.582013.266012.959012.6420
50010.400010.360010.208010.01909.82989.6396
6007.86047.85477.83227.80417.77577.7481
7007.04237.07597.21077.37637.54737.7155
8007.44067.50397.76828.09458.42028.7511
9007.37457.42647.63667.89908.15938.4244
100014.718014.681014.534014.350014.166013.9810
20004.82764.81584.76884.70984.65084.5921
30004.14364.13264.08894.03393.97873.9237
40005.28605.26655.18835.09124.99334.8957
50004.00223.98963.93943.87643.81373.7506
60004.64484.63024.57374.50204.42994.3593
70003.50663.50033.47533.44383.41273.3814
80003.50543.49903.47383.44233.41063.3790
90003.91563.90743.87463.83353.79243.7513
10,0003.96633.95833.92643.88663.84673.8068
20,0004.26354.24944.19284.12214.05143.9808
Table 11. The photon mass attenuation coefficients of the studied glass with Sb2O3 modifier.
Table 11. The photon mass attenuation coefficients of the studied glass with Sb2O3 modifier.
Photon Energy (keV)Pure GlassGlass with Sb2O3 Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508588.3008589.6983191.4457693.1932294.94068
2025.8958525.8269525.5516925.2074624.8633124.51915
308.960428.932978.823318.686198.549158.41201
404.197274.324644.834085.470916.107726.74454
502.345782.416362.698693.051623.404543.75746
601.479641.522801.695431.911222.127022.34281
701.019401.047581.160291.301181.442081.58297
800.746520.765900.843450.940371.037311.13424
900.569170.583150.639090.709010.778930.84886
1001.237921.240451.250571.263211.275861.28851
2000.295510.295590.295890.296270.296650.29703
3000.163530.163470.163230.162920.162610.16230
4000.121140.121070.120770.120400.120030.11966
5000.100670.100600.100320.099980.099630.09928
6000.088370.088310.088050.087730.087410.08708
7000.079910.079850.079610.079310.079010.07871
8000.073540.073490.073270.072990.072710.07244
9000.068500.068440.068240.067980.067720.06746
10000.064340.064290.064090.063850.063600.06336
20000.044210.044190.044090.043970.043850.04373
30000.037060.037060.037050.037030.037010.03699
40000.033570.033580.033630.033690.033760.03382
50000.031630.031660.031760.031890.032020.03215
60000.030500.030540.030690.030870.031060.03124
70000.029830.029870.030060.030290.030530.03076
80000.029440.029490.029710.029990.030260.03054
90000.029220.029290.029540.029850.030160.03048
10,0000.029130.029200.029480.029830.030170.03052
20,0000.030410.030530.030980.031540.032100.03267
Table 12. The neutron effective removal cross sections of the studied glass with Sb2O3 modifier.
Table 12. The neutron effective removal cross sections of the studied glass with Sb2O3 modifier.
Neutron Energy (keV)Pure GlassGlass with Sb2O3 Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.67208.51988.32938.13947.9488
2030.958030.719029.287025.923027.037025.7530
308.93078.88988.72848.52118.31588.1122
408.97738.93438.76868.56388.35728.1520
508.57188.53578.38988.20638.02547.8407
609.16669.12448.95448.74168.52918.3167
709.25699.21319.03948.82268.60568.3893
808.61958.58478.43608.25038.06517.8797
909.45119.41109.22919.00468.76908.5529
1009.70329.65199.45879.22478.98038.7515
20011.929011.855011.570011.216010.861010.5030
30010.491010.426010.24309.96879.60369.3798
40013.889013.814013.535013.183012.833012.4760
50010.400010.351010.15409.90719.66179.4152
6007.86047.82767.69687.53367.37037.2067
7007.04237.01646.91296.78356.65416.5247
8007.44067.40977.28827.13656.98346.8317
9007.37457.34827.24327.11146.97926.8474
100014.718014.648014.369014.020013.671013.3230
20004.82764.81354.75674.68554.61474.5435
30004.14364.81354.07434.00553.93633.8670
40005.28604.13015.17415.06214.95024.8383
50004.00223.98563.91883.83553.75223.6688
60004.64484.62534.54804.45134.35474.2577
70003.50663.49453.44533.38403.32283.2612
80003.50543.49343.44483.38423.32383.2634
90003.91563.90243.84933.78273.71653.6499
10,0003.96633.95363.90253.83873.77493.7111
20,0004.26354.24854.18864.11374.03883.9639
Table 13. The photon mass attenuation coefficients of the studied glass with BaO modifier.
Table 13. The photon mass attenuation coefficients of the studied glass with BaO modifier.
Photon Energy (keV)Pure GlassGlass with BaO Modifier
1%5%10%15%20%
Mass Attenuation Coefficients (cm2/g)
1087.9508588.7466191.9279795.9050899.88305103.86017
2025.8958525.9005125.9190725.9423725.9656825.98898
308.960428.958818.952298.944158.936108.92797
404.197274.375155.086695.976126.865547.75497
502.345782.445902.846393.347013.847624.34824
601.479641.541511.789002.098362.407732.71709
701.019401.060261.223721.428051.632371.83670
800.746520.774880.888361.030191.172031.31387
900.569170.589700.671840.774510.877190.97986
1001.237921.245441.275531.313131.350731.38833
2000.295510.296330.299580.303650.307720.31179
3000.163530.163700.164380.165230.166080.16693
4000.121140.121160.121260.121380.121490.12161
5000.100670.100650.100560.100450.100330.10022
6000.088370.088330.088170.087960.087760.08756
7000.079910.079860.079660.079420.079180.07894
8000.073540.073490.073290.073030.072780.07252
9000.068500.068440.068240.067980.067720.06746
10000.064340.064290.064080.063820.063560.06330
20000.044210.044180.044070.043930.043790.04365
30000.037060.037060.037050.037040.037020.03701
40000.033570.033590.033660.033750.033840.03393
50000.031630.031670.031810.031990.032170.03235
60000.030500.030550.030750.031000.031250.03150
70000.029830.029890.030140.030450.030770.03108
80000.029440.029510.029800.030170.030540.03090
90000.029220.029310.029640.030050.030470.03089
10,0000.029130.029230.029590.030050.030510.03097
20,0000.030410.030560.031150.031890.032630.03337
Table 14. The neutron effective removal cross sections of the studied glass with BaO modifier.
Table 14. The neutron effective removal cross sections of the studied glass with BaO modifier.
Neutron Energy (keV)Pure GlassGlass with BaO Modifier
1%5%10%15%20%
Removal Cross Section (mm2/g)
108.71008.66008.46398.21757.97267.7255
2030.958030.894030.198028.052026.901025.5530
308.93078.86548.60718.28267.95647.6300
408.97738.90708.63808.30137.96527.6280
508.57188.51068.25167.92537.60117.2800
609.16669.10308.84618.52518.20407.8825
709.25699.21179.03368.81168.58718.3657
808.61958.62348.63238.63368.65488.6638
909.45119.38909.13248.81268.49308.1752
1009.70329.64629.35119.00778.65218.3051
20011.929011.844011.495011.068010.624010.1970
30010.491010.478010.12109.79819.46599.1192
40013.889013.798013.433012.981012.529012.0720
50010.400010.337010.08009.76589.44669.1292
6007.86047.81767.64717.43407.22047.0074
7007.04237.00806.87106.69986.52856.3573
8007.44067.40267.25127.06236.87286.6835
9007.37457.34027.20287.03036.85826.6861
100014.718014.629014.276013.835013.394012.9530
20004.82764.81334.75644.68534.61434.5433
30004.14364.13074.07954.01533.95123.8869
40005.28605.26095.16105.03554.91024.7849
50004.00223.98403.91083.81933.72793.6364
60004.64484.62164.53004.41404.29854.1848
70003.50663.49243.43503.36353.29193.2205
80003.50543.49133.43463.36343.29263.2216
90003.91563.89913.83333.75093.66853.5862
10,0003.96633.95023.88553.80463.72383.6430
20,0004.26354.24704.18094.09824.01553.9329
Table 15. Average percentage difference between the shielding abilities of the studies glass with different modifiers.
Table 15. Average percentage difference between the shielding abilities of the studies glass with different modifiers.
Photon Mass Attenuation Coefficients Percentage DifferenceNeutron Effective Removal Cross Section Percentage Difference
1%5%10%15%20%1%5%10%15%20%
Na2O modifier−0.41%−2.06%−4.13%−6.19%−8.25%0.40%1.83%3.17%4.90%6.46%
Al2O3 modifier−0.41%−2.04%−4.09%−6.13%−8.17%0.37%1.36%2.28%3.71%4.95%
MgO modifier−0.39%−1.97%−3.94%−5.92%−7.89%0.56%2.58%5.15%7.78%10.43%
TiO2 modifier−0.30%−1.52%−3.04%−4.56%−6.08%0.22%1.09%2.01%3.00%4.02%
SrO modifier0.21%0.90%1.79%2.69%3.59%−0.23%−1.07%−2.21%−3.41%−4.44%
Sb2O3 modifier0.61%3.04%6.08%9.12%12.16%−0.61%−2.22%−4.63%−6.58%−8.74%
BaO modifier0.95%4.74%9.47%14.21%18.94%−0.49%−2.62%−5.38%−8.04%−10.71%
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Akhdar, H. Theoretical Investigation of the Influence of Different Heavy Metal Oxides Modifiers on ZnO-Bi2O3-B2O3-SiO2’s Photon- and Neutron-Shielding Capabilities Using the Monte Carlo Method. Appl. Sci. 2023, 13, 9332. https://doi.org/10.3390/app13169332

AMA Style

Akhdar H. Theoretical Investigation of the Influence of Different Heavy Metal Oxides Modifiers on ZnO-Bi2O3-B2O3-SiO2’s Photon- and Neutron-Shielding Capabilities Using the Monte Carlo Method. Applied Sciences. 2023; 13(16):9332. https://doi.org/10.3390/app13169332

Chicago/Turabian Style

Akhdar, Hanan. 2023. "Theoretical Investigation of the Influence of Different Heavy Metal Oxides Modifiers on ZnO-Bi2O3-B2O3-SiO2’s Photon- and Neutron-Shielding Capabilities Using the Monte Carlo Method" Applied Sciences 13, no. 16: 9332. https://doi.org/10.3390/app13169332

APA Style

Akhdar, H. (2023). Theoretical Investigation of the Influence of Different Heavy Metal Oxides Modifiers on ZnO-Bi2O3-B2O3-SiO2’s Photon- and Neutron-Shielding Capabilities Using the Monte Carlo Method. Applied Sciences, 13(16), 9332. https://doi.org/10.3390/app13169332

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