Simulation of γ-Ray Radiation Shielding Utilizing Gd2O3/Bi2O3/Epoxy Resin

Simulation of γ-Ray Radiation Shielding Utilizing Gd2O3/Bi2O3/Epoxy Resin | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Simulation of γ-Ray Radiation Shielding Utilizing Gd 2 O 3 /Bi 2 O 3 /Epoxy Resin Rongxing Cao, Guangyao Li, Hongxia Li, Yuxiong Xue, Xianghua Zeng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4233481/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Jun, 2024 Read the published version in Journal of Inorganic and Organometallic Polymers and Materials → Version 1 posted 17 You are reading this latest preprint version Abstract In order to meet the requirement of radiation shielding materials for space nuclear reactors, gamma shielding effect of epoxy resin base added with Gd 2 O 3 /Bi 2 O 3 particles was studied by Monte Carlo simulation platform Geant4 in this paper. Firstly, the gamma ray shielding effects of functional filler with different ratios and content were simulated. Then, based on the gamma-ray energy range generated by space nuclear reactors, the γ-ray protection performance of epoxy resin composites under different energy ranges was studied. Finally, the effects of the particle size and arrangement of the fillers on the γ-ray shielding properties of the composites were presented, and the results showed that the smaller of the particle size, the better the shielding effect will be; for the same size of the filler, the arrangement of the filler with a larger projection area has a better γ-ray shielding performance. The effect of Gd 2 O 3 /Bi 2 O 3 added to epoxy resin base on low-energy gamma rays is obvious, but the effect on high-energy rays is less. Gamma ray shielding Gd2O3/Bi2O3 epoxy resin Geant4 simulation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 I. Introduction For γ-ray protection materials, bismuth oxide (Bi 2 O 3 ), gadolinium oxide (Gd 2 O 3 ) or other heavy metals and rare earth element oxides can effectively improve the γ-ray shielding ability. [1],[2],[3],[4] Different γ-ray irradiation sources were used to measure the γ-ray mass attenuation coefficient of the composites, and the results showed that the mass attenuation coefficient significantly increased with the increase of Bi 2 O 3 filler content in the composites.[ 5] Several different composites by adding Bi 2 O 3 content have be studied previously, including WO 3 /Bi 2 O 3 / waterborne polyurethane composites[ 6] , NaO/CdO/Bi 2 O 3 /B 2 O 3 glass material[ 7] , silicone rubber as matrix material with Bi 2 O 3 and hexagonal BN[ 8] , Bi 2 O 3 /polyvinyl alcohol composite[ 9] , Bi 2 O 3 /hydroxy-nitrile butadiene rubber[ 10] , and polyvinyl alcohol /polypyrrole /Bi 2 O 3 nanocomposites [ 11] , etc. On the other hand, Gd 2 O 3 was regarded as a good filler for γ-ray shielding. For example, Saenboonruang et al. [ 12] studied the γ-ray shielding effect of high density polyethylene (HDPE) composites containing rare earth oxides (Sm 2 O 3 , Eu 2 O 3 and Gd 2 O 3 ) and found that the γ-ray shielding performance is obviously improved with the increase of rare earth oxide content. Yu et al. [ 13] studied the γ-ray shielding effects with Gd 2 O 3 -BaO-P 2 O 5 glass samples and found that the addition of Gd 2 O 3 enhanced the material's tolerance to γ-rays. Ge et al. [ 14] studied the γ-ray shielding effects of Gd 2 O 3 /Al 2 O 3 ceramic composites and found that the shielding ratio of the composite against γ-rays increased with the increase of Gd 2 O 3 content and the composite still showed good mechanical stability when exposed to continuous γ-rays. Moreover, the epoxy-based shielding samples have significant capacities in the γ-ray and neutron radiation shielding, which has been proved experimentally and theoretically previously. And polymers used for radiation shielding will be reinforced by doping certain metals, metal oxides, or chemical compounds. For example, WO 3 /epoxy resin samples were prepared with nano and micro particles and found that nanoscale WO 3 /epoxy sample has the best γ-ray absorbing ability.[ 15] The studies of the epoxy resin matrix composites filled with dispersed Gd 2 O 3 particles revealed that nano-Gd 2 O 3 composites have better ability to shield X- and γ- ray than micro-Gd 2 O 3 composites.[ 16] The composites consisted with epoxy resin 60% and NiO 40% exhibited excellent shielding properties.[ 17] Actually, polymer-based samples will be good gamma-ray shielding materials used in space nuclear reactors due to lightweight and excellent properties in corrosion-resistance and mechanical strength, etc. In this paper, the shielding effects of the epoxy resin composites filled with dispersed Gd 2 O 3 and Bi 2 O 3 particles have been studied with Geant4 simulation and the optimum mixing ratios were determined. The results showed that Gd 2 O 3 and Bi 2 O 3 have the same shielding effect on γ- rays. With the increase of γ- ray energy, the shielding ratio of γ- ray of the composite materials showed a downward trend except for the energies at the absorption edge of Gd and Bi elements (50.5 and 91.0 keV). The effect of the particle size and arrangement of the filler on the shielding properties was studied, demonstrating that smaller particle size and larger projection area will bring better shielding performance. Those studies will be helpful for designing shielding materials for space nuclear reactors. II. Analog simulation 2.1 Simulation of gamma-ray shielding of functional fillers The gamma rays in space nuclear reactor are mainly produced by two parts, one is in the active region, which is mainly produced by fission reaction and neutron inelastic scattering. The other part is mainly the secondary gamma rays released after neutron absorption in the structural material, which is not considered in this paper. Herein, the gamma rays generated by fission reaction in the active region are mainly targeted. The gamma rays produced by the fission reaction have an energy of about 1~3 MeV and are mainly concentrated near 1 MeV. Therefore, the energy of gamma ray source was set to be 1 MeV. The simulated structure diagram is shown in Fig. 1(a) . Both the γ-ray source and the shielding material are placed in vacuum. The γ-ray is vertically incident on the shielding material along the positive direction of the Z axis. The radiation area of the ray surface source is consistent with the cross-section area of the shielding material which is 10×10 mm 2 , and the thickness of the shielding material is set to 1 cm. In order to study the shielding performance of different ratios of functional fillers, the content range of functional fillers Bi 2 O 3 and Gd 2 O 3 is set to 0%~50% respectively. The content range of functional fillers is set to 0%~60% in the research of different content of functional fillers. Geant4 program was used to simulate the shielding effect of composite materials with different functional filling ratios for 1 MeV gamma rays, and the simulation results were shown in Fig. 1(b) . In the figure, the X and Y axes represent the content of Gd 2 O 3 and Bi 2 O 3 respectively, and the Z axis represents the transmittance of gamma rays. It can be seen from Fig. 1(b) that the shielding effect of the composite materials with different Gd 2 O 3 and Bi 2 O 3 filler ratios on gamma rays is obvious, i.e., with the same content of Gd 2 O 3 , the transmission of gamma rays decreases with the increase of Bi 2 O 3 content, and vice versa. These results indicate that the functional fillers Gd 2 O 3 and Bi 2 O 3 have good shielding properties for 1 MeV γ-rays with almost the same improvement amplitude. Therefore, Gd 2 O 3 and Bi 2 O 3 are mixed in equal proportions. The shielding effects of the depth dependent γ-ray intensity are studied after adding equal Gd 2 O 3 and Bi 2 O 3 in epoxy resin, as shown in Fig. 2. It shows the γ-ray shielding performance of different functional fillers contents. Fig. 2(a) shows the attenuation of gamma rays entering epoxy resin composites with different functional fillers content. The horizontal and vertical coordinates are the depth and intensity of gamma rays entering the shielding material respectively. One can find that, after γ-rays enter the composite materials with different functional filler content, the γ-ray intensity declines with increasing incident depth. Without the filler in epoxy resin material, the attenuation amplitude of γ-ray intensity is the smallest, and when the filler content is 60%, the attenuation amplitude of γ-ray intensity is the largest. At the same incident depth, with the increasing of functional particle content, the intensity of gamma rays decreases significantly. Fig. 2(b) shows the effect of functional particle filling content on the γ-ray shielding ratio of the composite material. As can be seen from the figure, the gamma ray shielding ratio rises when the content increases from 0% to 60%. This is mainly because when the content of functional fillers is low, the collision probability of gamma rays entering the shielding material with Gd and Bi elements is small, so the shielding effect of the material for gamma rays is relatively weak. With the increase of the total content of functional fillers, Gd and Bi elements can form a network structure in the epoxy resin material. Therefore, the probability of collision of gamma ray with the effective element is greatly increased, so that the shielding performance of the composite material is significantly improved. 2.2 Gamma shielding in different energy regions Gamma rays produced by space nuclear reactors are concerned with energies ranging from a few keV to about 10 MeV. The γ-ray with low energies can be easily absorbed by the shielding material, so it does not need to be considered. The energies of gamma rays are divided into three regions, i.e., low-energy (10~100 keV), medium-energy (100 ~1000 keV), and high-energy (1~10 MeV). The simulated structure in this section is the same as that in Fig. 1(a) . According to the above calculation results, the mass ratio of Bi 2 O 3 and Gd 2 O 3 is set at 1:1, and the mass ratio of the functional filler and the base material is also set at 1:1. 2.2.1 Low energy gamma shielding Firstly, we considered the gamma rays with energies from 10 to ~100 keV, the attenuation of γ-ray intensity entering epoxy resin composites with different energy values is shown in Fig. 3 . In Fig. 3(a) where the γ-ray energy ranges from 10 to 51 keV, the γ-ray intensity presents a different decreasing trend with the increase of incident depth under different γ-ray energies. The gamma ray intensities with the energy of 10-50 keV have slower attenuation with the depth when the energy increasing, however, the attenuation suddenly gets faster when the energy increases to 50.5-51 keV. Similarly, in the range of 60-100 keV, the depth dependent attenuation of gamma ray intensities shows a sudden increment when the energy increases to 91 keV as shown in Fig. 3(b) . From the calculations, we found that the gamma-rays are almost completely absorbed after the 1cm shielding material, and the rapid reduction in gamma-rays density happens at the depths less than 0.1 cm for energies from 10 to 100 keV. Here, we present the gamma-ray shielding ratio at the depth of 0.1cm shielding material under different energies, as shown in Fig. 4(a) . It shows that, with the gamma ray energy less than 20 keV, the gamma ray is completely absorbed by the composite material. This is mainly because when the gamma ray energy is low, the composite material mainly reduces the gamma ray intensity through the photoelectric effect, and the probability of photoelectric effect is inversely proportional to the third power of the gamma ray energy. When the γ-ray energy is higher than 20 keV, the γ-ray shielding ratio of the composite decreases with the increase of γ-ray energy. At 50.5 and 91keV, the γ-ray shielding ratio increases abruptly, and then continues to decline with the increase of γ-ray energy. The sudden increase in the shielding ratio of gamma rays is due to the Gd element and Bi element contained in the composite material, and the K absorption edge of Gd element and Bi element is 50.2 and 90.7 keV respectively, as shown in Fig. 4(b) . When the energy of gamma rays is exactly equal to the K absorption edge of Gd element or Bi element, the gamma ray energy will be completely absorbed by electrons. Moreover, γ-rays are also prone to photoelectric effects, so the shielding ratio of γ-rays of composite materials is significantly increased. Subsequently, with the increase of γ-ray energy, the γ-ray shielding ratio of the material decreases significantly with the increase of γ-ray energy, which is because the probability of photoelectric effect is inversely proportional to the third power of the γ-ray energy. 2.2.2 Medium energy gamma shielding The medium energy of the gamma-ray is selected from 100 to 1000 keV, and the attenuation of γ ray intensity entering epoxy resin composite materials is shown in Fig. 5. It shows that the γ-ray intensity with different energies incident on the composite material presents a different decreasing trend with the increase of incident depth. The attenuation amplitude and rate of γ-ray intensity both decreases with the increase of γ-ray energy. When the γ-ray energy is 100 keV, the γ-ray intensity decreases quickly and almost all the gamma rays are absorbed by the composite at 0.5 cm. When the gamma ray energy is 1 MeV, the gamma ray intensity only attenuates to 80% after passing through the 1cm shielding material. Fig. 5(b) shows the γ-ray shielding ratios with energies. With increasing the gamma ray energy from 100 to 1000 keV, the gamma ray shielding ratio decreases from 99.99% to 18.76%. This can be explained as, at low γ-ray energy the composite material mainly reduces the γ-ray intensity through the photoelectric effect, and the occurrence probability of photoelectric effect is inversely proportional to the third power of the γ-ray energy. With the rise of γ-ray energy, Compton scattering will happen between some of the γ-ray and composite material, where Compton scattering probability is inversely proportional to the γ-ray energy. Therefore, γ-ray shielding ratio decreases with the increase of γ-ray energy in this medium energy region. 2.2.3 High energy gamma shielding The high energy of the γ ray is set to 1~10 MeV, and the attenuation of γ-ray intensity is shown in Fig. 6 . The γ-ray intensity of different energies incident on the composite material presents a similar trend as the intermediate energy. The attenuation amplitude and rate of γ-ray intensity both decreases with the increase of γ-ray energy. When the γ-ray energy is 1 MeV, the γ-ray intensity decreases to about 80% after passing through 1 cm composite material, while when the γ-ray energy is 10 MeV, the γ-ray intensity decreases only to about 93% after passing through 1 cm composite material. Fig. 6(b) shows the change of gamma shielding ratio with different energy values in the high energy region. As can be seen from the figure, as the gamma ray energy increases from 1 to 10 MeV, the gamma ray shielding ratio decreases from 18.76% to 7.02%. This is mainly due to the fact that the composite material mainly reduces the gamma-ray intensity through photoelectric effect and Compton scattering for relatively low energy; with the further increase of γ-ray energy, γ-ray is absorbed mainly from Compton scattering. We note that the electron pair effect can be ignored since the probability is extremely low for the electrons in heavy element. The probability of Compton scattering is inversely proportional to the incident gamma ray energy and proportional to the atomic number of the composite material, so the gamma ray shielding ratio decreases with the increase of gamma ray energy. Therefore, we conclude that for the gamma ray with energies from 10 to 100 keV, the γ-ray shielding ratio of the composite decreases with the increase of γ-ray energy except for the energies at the absorption edge of Gd and Bi elements. The gamma-rays are almost completely absorbed at the depth of 1 cm, and the rapid reduction in gamma-rays density occurs at the depths less than 0.1 cm. From 100~1000 keV, with the increase of γ-ray energy, γ-ray shielding ratio decreased from 99.99% to 18.76%. From 1~10 MeV, the gamma ray shielding ratio decreases from 18.76% to 7.02% with the increase of gamma ray energy, where Compton scattering is dominant. 2.3 Gamma shielding with different sizes and arrangement of the fillers Now we will discuss the gamma shielding effects of epoxy resin materials added with spherical fillers of Bi 2 O 3 and Gd 2 O 3 with the mass ratio of 1:1. The energies of incident gamma rays were selected as 50, 100, 500 and 1000 keV, respectively. The particle radius of the functional filler was selected as 0.5, 0.25, 0.1 and 0.05 mm, respectively, and the mass fraction of the functional filler was set to 15.43%. Tab. 1 The relationship between the particle size and the number of functional packing particles Functional packing particle radius (mm) Number of functional filler particles 0.5 50 0.25 400 0.1 6250 0.05 50000 According to the filling content and the radius of the functional fillers set above, the number of functional fillers corresponding to the radius of different functional fillers is calculated, as shown in Tab. 1. The composite X-Y and Y-Z cross sections of particle’s distributions is shown in Fig. 7 . X-Y cross sections and Y-Z cross sections are selected respectively to indicate the distribution of functional fillers in composite materials. Gamma-ray shielding ratios after γ-rays with different energies incident on composites with different packing sizes are shown in Fig. 8 . One can find that at lower gamma ray energy, the shielding ratio is opposite to the filler’s size, but with increasing the γ-ray energy up to 500 keV, the influence of the filler’s size on the γ-ray shielding ratio can be ignored. The γ-ray shielding ratio with different filler sizes for γ-ray energies of 50, 100, 500 and 1000 keV are shown in Fig. 9 . It can be found that when the incident γ-ray energy is 50 and 100 keV, the γ-ray shielding ratio increases from 23.3% and 20.2% to 63.9% and 55.5% with the decrease of the fillers’ size, respectively. The γ-ray shielding ratio of the composite material increases by about 175%. It can also be clearly found from Fig. 8(a)-(b) that, the decline rate and amplitude of gamma ray intensity of the composite material with 0.05 mm filler particle size are both significantly higher than that of other filler particle size. It can be seen from Fig. 9 that the smaller the particle size of the filler, the greater the attenuation amplitude of the γ-ray intensity, and when the γ-ray energy increases, the influence of the particle size of the filler on the shielding performance of the composite is weakened. Table 2 presented the projected areas of different particle sizes of fillers in the gamma ray incident direction. As can be seen from the table, when the packing radius decreases from 0.5 to 0.05 mm, the projected area increases from 7.85 to 78.54 mm 2 . It can be inferred that the projected area of the fillers in the gamma incident direction increases when the particle size of the functional fillers decreases. Then, the collision cross section between the gamma rays and the functional fillers increases, resulting in the significant increase in the shielding ratio. Table 2 Projective area of different packing particle size in gamma ray incident direction Packing radius /mm Fill number Projected area /mm 2 0.5 50 7.85 0.25 400 15.70 0.1 6250 39.26 0.05 50000 78.54 In order to prove the above inference, we studied the shielding under different packing arrangement while the shape of the composite material, the gamma ray source, the shape and content of the functional fillers were kept unchanged. The radius of the functional fillers was fixed at 0.05 mm and the filling number of the functional fillers was set to 5E4. Fig. 10 shows the cross sections of different functional fillers arranged in composite materials, named as T1, T2, T3 and T4. X-Y cross sections and Y-Z cross sections are selected respectively to indicate the arrangement of functional fillers in composite materials. The distribution of packing particles in XY section of T1-T4 material are 100×100, 50×100, 50×50 and 10×50, respectively. The distribution of packing particles in YZ section are 1×5, 1×10, 1×20 and 1×100, respectively. The arrangement of the four materials and the projected area data of the filler in the gamma ray incident direction are shown in Table 3 . Tab. 3 Projected area of different packing arrangement in gamma ray incidence direction Material number Fill number Arrangement mode Projected area /mm 2 T1 50000 100×100×5 78.54 T2 50×100×10 39.26 T3 50×50×20 19.63 T4 10×50×100 3.93 Gamma rays with 50 keV and 1 MeV are selected to study the γ-ray shielding under different particle packing arrangement. Figs. 11(a)-(b) shows the attenuation of gamma rays intensity after four composite materials irradiated with gamma rays of 50 keV and 1 MeV, respectively. The four materials had the same packing radius, the same filling number, and different packing arrangement. Among them, the projected area in the incident direction of γ-rays was the highest in T1, and that in T4 was the smallest. As can be seen from Fig. 11(a) , the gamma ray intensity of the material T1 attenuates to the smallest after passing through the 1 cm composite material, indicating that the shielding material T1 has the best shielding of 50 keV gamma ray. This shielding effect gets worse for packing arrangement from T2 to T4. The situation is similar for 1 MeV gamma ray, shown in Fig. 11(b) . The shielding effect of materials T1, T2 and T3 is close to each other, and obviously better than that of shielding material T4. Therefore, we conclude that the functional filler with the same size and same filling number, but with a different arrangement of the filler will result in different gamma-ray shielding effects. This is mainly because, different arrangements of the fillers leads to different projected areas of the fillers in the direction of gamma ray incidence. The larger the projected area, the larger the collision cross section between gamma rays and filler particles will be, then the corresponding γ-ray shielding effect of the material will be improved. III. Conclusion To investigate the shielding effect of the γ-ray, epoxy resins composites added with Gd 2 O 3 and Bi 2 O 3 particles with different size and arrangement were simulated with Monte Carlo simulation platform Geant4. It is found that the γ-ray shielding ratio of the material decreases with the increase of γ-ray energy while there are abrupt increase at 50.5 and 91 keV due to the K absorption edge of Gd and Bi elements. For the same gamma-ray energy, the gamma-ray shielding effects can be improved via optimizing particle size and arrangement of the packing fillers, which can be attributed to the increased collision induced by higher projected area. These studies will be helpful for the design of the lightweight shielding materials for space nuclear power. Declarations Acknowledgments This work was supported by the National Natural Science Foundation of China (61474096, 12004329), the Yangzhou Science and Technology Bureau (YZ2020263), Open Project of State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (SKLIPR2115) and Foundation of National Key Laboratory of Materials Behavior and Evaluation Technology in Space Environment (WDZC-HGD-2022-11). Availability of Data and Materials The datasets used and analyzed during the current study are available from the corresponding author on reasonable request. ■ AUTHOR INFORMATION † R. Cao and G. Li contributed equally to this work. Corresponding Authors * E-mail: X. Zeng: [email protected] ; Y. Xue: [email protected] Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References Limarun P, Markpin T, Sombatsompop N, et al. 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Cite Share Download PDF Status: Published Journal Publication published 15 Jun, 2024 Read the published version in Journal of Inorganic and Organometallic Polymers and Materials → Version 1 posted Editorial decision: Revision requested 21 Apr, 2024 Reviews received at journal 20 Apr, 2024 Reviewers agreed at journal 19 Apr, 2024 Reviewers agreed at journal 19 Apr, 2024 Reviewers agreed at journal 18 Apr, 2024 Reviewers agreed at journal 18 Apr, 2024 Reviewers agreed at journal 17 Apr, 2024 Reviews received at journal 17 Apr, 2024 Reviewers agreed at journal 16 Apr, 2024 Reviewers agreed at journal 16 Apr, 2024 Reviewers agreed at journal 16 Apr, 2024 Reviewers agreed at journal 16 Apr, 2024 Reviewers agreed at journal 16 Apr, 2024 Reviewers invited by journal 16 Apr, 2024 Editor assigned by journal 16 Apr, 2024 Submission checks completed at journal 15 Apr, 2024 First submitted to journal 07 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4233481","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":292905036,"identity":"db872f48-a43e-48a1-80f5-b5663d321825","order_by":0,"name":"Rongxing Cao","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"prefix":"","firstName":"Rongxing","middleName":"","lastName":"Cao","suffix":""},{"id":292905037,"identity":"cc4b646f-0463-4c9a-9ade-07b6b0e2b100","order_by":1,"name":"Guangyao Li","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"prefix":"","firstName":"Guangyao","middleName":"","lastName":"Li","suffix":""},{"id":292905041,"identity":"15bc27b4-fffc-4df6-b59b-12bc601d94f2","order_by":2,"name":"Hongxia Li","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"prefix":"","firstName":"Hongxia","middleName":"","lastName":"Li","suffix":""},{"id":292905044,"identity":"c05951b4-2c7d-417f-9ece-ae0af17b8456","order_by":3,"name":"Yuxiong Xue","email":"","orcid":"","institution":"Yangzhou University","correspondingAuthor":false,"prefix":"","firstName":"Yuxiong","middleName":"","lastName":"Xue","suffix":""},{"id":292905046,"identity":"b7f9df13-999f-4cd3-ab09-4ed5da4b1b1b","order_by":4,"name":"Xianghua Zeng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYDACCTBpA+HwkKAljXQth0nQYnC7/eHjgl/nE+fPSGB88LaNQd6ckBbJOQeSjWf23U5snJHAbDi3jcFwZwMBLfwSCcekeXtuJzZLJLBJ87YxJBgcIKCFTSKx/Tdvz7nENokE9t9EaeGXSGZj5vlxILEHaAszUVokZ6QxS/M2JBvP4HnYLDnnnIThBkJaDG6kP/zM88dOdn578sEPb8ps5AnaAgaMbQyODQyMDQywaCIC/GGwJ1bpKBgFo2AUjEAAAINAPYAa+smyAAAAAElFTkSuQmCC","orcid":"","institution":"Yangzhou University","correspondingAuthor":true,"prefix":"","firstName":"Xianghua","middleName":"","lastName":"Zeng","suffix":""}],"badges":[],"createdAt":"2024-04-08 02:59:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4233481/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4233481/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10904-024-03161-w","type":"published","date":"2024-06-15T15:12:29+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":54990889,"identity":"cb4486e0-a2dd-455e-9cba-58f4b13f27c5","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":92258,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Simulation diagram. (b) Effect of different functional filler ratio on γ-ray shielding.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/86aac0fd3cd1422cbe9bbc45.png"},{"id":54990887,"identity":"1b50cdec-c9c6-4586-ad24-289a1cfbcfba","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":455915,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of different functional filler content on γ-ray shielding effect.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/ed67e13c553884780041b8b9.png"},{"id":54991204,"identity":"9be8a79e-aa6f-4ac1-97bd-12e1a748caba","added_by":"auto","created_at":"2024-04-19 17:17:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":534209,"visible":true,"origin":"","legend":"\u003cp\u003eLow energy gamma intensity attenuation diagram.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/10befab237e3305b583f92cf.png"},{"id":54991203,"identity":"11d8a0e3-6c35-4d05-bcb2-c251a05646eb","added_by":"auto","created_at":"2024-04-19 17:17:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":290498,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Low energy gamma-ray shielding ratio at the depth of 0.1 cm; (b) Mass attenuation coefficient with energy for Ga and Bi elements.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/c2a4b8be96cc6eab52aec054.png"},{"id":54990891,"identity":"2b6f608e-612a-4ff4-bd60-8da72b1f491f","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":357942,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Medium energy gamma intensity attenuation diagram; (b) shielding ratio with gamma-ray energy at the depth of 1 cm.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/15965dc1d8524b3c468ddaba.png"},{"id":54990894,"identity":"ec81449b-a8a1-4481-8e4b-e0ba084b1d6b","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":390967,"visible":true,"origin":"","legend":"\u003cp\u003e(a) High energy gamma intensity attenuation diagram, (b) shielding ratio with gamma-ray energy at the depth of 1 cm.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/044a7a41a941be910a9866aa.png"},{"id":54990892,"identity":"904660c3-5e11-41c2-b08c-c8a5e2a72b0c","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":137009,"visible":true,"origin":"","legend":"\u003cp\u003eComposite X-Y and Y-Z cross sections, (a) 0.5, (b) 0.25, (c) 0.1, (d) 0.05mm.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/acfe5fa7789b90450595fe66.png"},{"id":54990896,"identity":"b9b40b91-c0bc-4024-a317-5ad71f787676","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":423894,"visible":true,"origin":"","legend":"\u003cp\u003eGamma-ray intensity attenuation diagram. (a)50 keV, (b)100 keV, (c)500 keV and (d)1 MeV.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/4232e94bddac5e2d2712b1db.png"},{"id":54990893,"identity":"5fad9988-459a-4f2f-8741-c6760b35f2ba","added_by":"auto","created_at":"2024-04-19 17:09:35","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":13088,"visible":true,"origin":"","legend":"\u003cp\u003eThe γ-ray shielding ratio with filler size for γ-ray energies of 50, 100, 500 and 1000 keV.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/3c474f998c41ac6906da400f.png"},{"id":54991205,"identity":"8988ccf8-dbd7-4a0c-a0a9-ba410dd52cf3","added_by":"auto","created_at":"2024-04-19 17:17:36","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":231408,"visible":true,"origin":"","legend":"\u003cp\u003eX-Y and Y-Z cross sections of different functional fillers arrangement. (a) T1; (b) T2; (c) T3; (d) T4.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/f4a5c383208f6c9b8ffb1121.png"},{"id":54990897,"identity":"a5e8a92c-0a51-4e94-8863-597699aa414a","added_by":"auto","created_at":"2024-04-19 17:09:36","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":208682,"visible":true,"origin":"","legend":"\u003cp\u003eγ-ray attenuation diagram for different particle packing arrangement, (a) 50 keV, (b) 1 MeV.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/23c66f37debfe80972cb45ed.png"},{"id":58822911,"identity":"7c41e44b-5539-454a-a120-9d79edbdb419","added_by":"auto","created_at":"2024-06-21 16:49:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3184153,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4233481/v1/5801575c-fb8e-4773-9966-aefcd45ca586.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eSimulation of γ-Ray Radiation Shielding Utilizing Gd\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/Bi\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eO\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e/Epoxy Resin\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"I. Introduction","content":"\u003cp\u003eFor \u0026gamma;-ray protection materials, bismuth oxide (Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e), gadolinium oxide (Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e) or other heavy metals and rare earth element oxides can effectively improve the \u0026gamma;-ray shielding ability.\u003csup\u003e[1],[2],[3],[4]\u003c/sup\u003e Different \u0026gamma;-ray irradiation sources were used to measure the \u0026gamma;-ray mass attenuation coefficient of the composites, and the results showed that the mass attenuation coefficient significantly increased with the increase of Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e filler content in the composites.[\u003csup\u003e5]\u003c/sup\u003e Several different composites by adding Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u0026nbsp;\u003c/sub\u003econtent have be studied previously, including WO\u003csub\u003e3\u003c/sub\u003e/Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/ waterborne polyurethane composites[\u003csup\u003e6]\u003c/sup\u003e, NaO/CdO/Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e glass material[\u003csup\u003e7]\u003c/sup\u003e, silicone rubber as matrix material with Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and hexagonal BN[\u003csup\u003e8]\u003c/sup\u003e, Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/polyvinyl alcohol composite[\u003csup\u003e9]\u003c/sup\u003e, Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/hydroxy-nitrile butadiene rubber[\u003csup\u003e10]\u003c/sup\u003e, and polyvinyl alcohol /polypyrrole /Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e nanocomposites\u0026nbsp;[\u003csup\u003e11]\u003c/sup\u003e, etc.\u003c/p\u003e\n\u003cp\u003eOn the other hand, Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e was regarded as a good filler for \u0026gamma;-ray shielding. For example, Saenboonruang et al. [\u003csup\u003e12]\u003c/sup\u003e studied the \u0026gamma;-ray shielding effect of high density polyethylene (HDPE) composites containing rare earth oxides (Sm\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, Eu\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e) and found that the \u0026gamma;-ray shielding performance is obviously improved with the increase of rare earth oxide content. Yu et al. [\u003csup\u003e13]\u003c/sup\u003e studied the \u0026gamma;-ray shielding effects with Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e-BaO-P\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e glass samples and found that the addition of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e enhanced the material\u0026apos;s tolerance to \u0026gamma;-rays. Ge et al.\u0026nbsp;[\u003csup\u003e14]\u003c/sup\u003e studied the \u0026gamma;-ray shielding effects of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e ceramic composites and found that the shielding ratio of the composite against \u0026gamma;-rays increased with the increase of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e content and the composite still showed good mechanical stability when exposed to continuous \u0026gamma;-rays.\u003c/p\u003e\n\u003cp\u003eMoreover, the epoxy-based shielding samples have significant capacities in the \u0026gamma;-ray and neutron radiation shielding, which has been proved experimentally and theoretically previously. And polymers used for radiation shielding will be reinforced by doping certain metals, metal oxides, or chemical compounds. For example, WO\u003csub\u003e3\u003c/sub\u003e/epoxy resin samples were prepared with nano and micro particles and found that nanoscale WO\u003csub\u003e3\u003c/sub\u003e/epoxy sample has the best \u0026gamma;-ray absorbing ability.[\u003csup\u003e15]\u003c/sup\u003e The studies of the epoxy resin matrix composites filled with dispersed Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e particles revealed that nano-Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e composites have better ability to shield \u003cem\u003eX-\u003c/em\u003e and \u003cem\u003e\u0026gamma;-\u003c/em\u003eray than micro-Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e composites.[\u003csup\u003e16]\u003c/sup\u003e The composites consisted with epoxy resin 60% and NiO 40% exhibited excellent shielding properties.[\u003csup\u003e17]\u003c/sup\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eActually, polymer-based samples will be good gamma-ray shielding materials used in\u0026nbsp;space nuclear reactors\u0026nbsp;due to lightweight and excellent properties in corrosion-resistance and mechanical strength, etc. In this paper, the shielding effects of the epoxy resin composites filled with dispersed Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e particles have been studied with Geant4 simulation and the optimum mixing ratios were determined. The results showed\u0026nbsp;that Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e have the same shielding effect on\u0026nbsp;\u003cem\u003e\u0026gamma;-\u003c/em\u003erays.\u0026nbsp;With the increase of \u003cem\u003e\u0026gamma;-\u003c/em\u003eray energy, the shielding ratio of \u003cem\u003e\u0026gamma;-\u003c/em\u003eray of the composite materials showed a downward trend except for the energies at the absorption edge of Gd and Bi elements (50.5 and 91.0 keV). The effect of the particle size and arrangement of the filler on the shielding properties was studied, demonstrating that smaller particle size and larger projection area will bring better shielding performance. Those studies will be helpful for designing shielding materials for space nuclear reactors.\u003c/p\u003e"},{"header":"II. Analog simulation","content":"\u003cp\u003e2.1 Simulation of gamma-ray shielding of functional fillers\u003c/p\u003e\n\u003cp\u003eThe gamma rays in space nuclear reactor are mainly produced by two parts, one is in the active region, which is mainly produced by fission reaction and neutron inelastic scattering. The other part is mainly the secondary gamma rays released after neutron absorption in the structural material, which is not considered in this paper. Herein, the gamma rays generated by fission reaction in the active region are mainly targeted. The gamma rays produced by the fission reaction have an energy of about 1~3 MeV and are mainly concentrated near 1 MeV. Therefore, the energy of gamma ray source was set to be 1 MeV. The simulated structure diagram is shown in \u003cstrong\u003eFig. 1(a)\u003c/strong\u003e. Both the \u0026gamma;-ray source and the shielding material are placed in vacuum. The \u0026gamma;-ray is vertically incident on the shielding material along the positive direction of the Z axis. The radiation area of the ray surface source is\u0026nbsp;consistent\u0026nbsp;with the cross-section area of the shielding material which is 10\u0026times;10 mm\u003csup\u003e2\u003c/sup\u003e, and the thickness of the shielding material is set to 1 cm.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn order to study the shielding\u0026nbsp;performance\u0026nbsp;of different ratios of functional fillers, the content range of functional fillers Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e is set to 0%~50% respectively. The content range of functional fillers is set to 0%~60% in the research of different content of functional fillers.\u003c/p\u003e\n\u003cp\u003eGeant4 program was used to simulate the shielding effect of composite materials with different functional filling ratios for 1 MeV gamma rays, and the simulation results were shown in \u003cstrong\u003eFig. 1(b)\u003c/strong\u003e. In the figure, the X and Y axes represent the content of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e respectively, and the Z axis represents the transmittance of gamma rays. It can be seen from \u003cstrong\u003eFig. 1(b)\u003c/strong\u003e that the shielding effect of the composite materials with different Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e filler ratios on gamma rays is obvious, i.e., with the same content of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, the transmission of gamma rays\u0026nbsp;decreases\u0026nbsp;with the increase of Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e content, and vice versa. These results indicate that the functional fillers Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e have good shielding properties for 1 MeV \u0026gamma;-rays with almost the same improvement amplitude. Therefore, Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e are mixed in equal proportions.\u003c/p\u003e\n\u003cp\u003eThe shielding effects of the depth dependent \u0026gamma;-ray intensity are studied after adding equal Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e in epoxy resin, as shown in \u003cstrong\u003eFig. 2.\u0026nbsp;\u003c/strong\u003eIt shows the \u0026gamma;-ray shielding performance of different functional fillers contents. \u003cstrong\u003eFig. 2(a)\u0026nbsp;\u003c/strong\u003eshows the attenuation of gamma rays entering epoxy resin composites with different functional fillers content. The horizontal and vertical coordinates are the depth and intensity of gamma rays entering the shielding material respectively. One can find that, after \u0026gamma;-rays enter the composite materials with different functional filler content, the \u0026gamma;-ray intensity declines with increasing incident depth. Without the filler in epoxy resin material, the attenuation amplitude of \u0026gamma;-ray intensity is the smallest, and when the filler content is 60%, the attenuation amplitude of \u0026gamma;-ray intensity is the largest. At the same incident depth, with the increasing of functional particle content, the intensity of gamma rays decreases significantly.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFig. 2(b)\u0026nbsp;\u003c/strong\u003eshows the effect of functional particle filling content on the \u0026gamma;-ray shielding ratio of the composite material. As can be seen from the figure, the gamma ray shielding ratio rises when the content increases from 0% to 60%. This is mainly because when the content of functional fillers is low, the collision probability of gamma rays entering the shielding material with Gd and Bi elements is small, so the shielding effect of the material for gamma rays is relatively weak. With the increase of the total content of functional fillers, Gd and Bi elements can form a network structure in the epoxy resin material. Therefore, the probability of collision of gamma ray with the effective element is greatly increased, so that the shielding performance of the composite material is significantly improved.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eGamma shielding in different energy regions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eGamma rays produced by space nuclear reactors are concerned with energies ranging from a few keV to about 10 MeV. The \u0026gamma;-ray with low energies can be easily absorbed by the shielding material, so it does not need to be considered. The energies of gamma rays are divided into three regions, i.e., low-energy (10~100 keV), medium-energy (100 ~1000 keV), and high-energy (1~10 MeV). The simulated structure in this section is the same as that in \u003cstrong\u003eFig. 1(a)\u003c/strong\u003e. According to the above calculation results, the mass ratio of Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u0026nbsp;\u003c/sub\u003eis set at 1:1, and the mass ratio of the functional filler and the base material is also set at 1:1.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2.1 Low energy gamma shielding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFirstly, we considered the gamma rays with energies from 10 to ~100 keV, the attenuation of \u0026gamma;-ray intensity entering epoxy resin composites with different energy values is shown in \u003cstrong\u003eFig. 3\u003c/strong\u003e. In \u003cstrong\u003eFig. 3(a)\u003c/strong\u003e where the \u0026gamma;-ray energy ranges from 10 to 51 keV, the \u0026gamma;-ray intensity presents a different decreasing trend with the increase of incident depth under different \u0026gamma;-ray energies. The gamma ray intensities with the energy of 10-50 keV have slower attenuation with the depth when the energy increasing, however, the attenuation suddenly gets faster when the energy increases to 50.5-51 keV. Similarly, in the range of 60-100 keV, the depth dependent attenuation of gamma ray intensities shows a sudden increment when the energy increases to 91 keV as shown in \u003cstrong\u003eFig. 3(b)\u003c/strong\u003e.\u003c/p\u003e\n\u003cp\u003eFrom the calculations, we found that the gamma-rays are almost completely absorbed after the 1cm shielding material, and the rapid reduction in gamma-rays density happens at the depths less than 0.1 cm for energies from 10 to 100 keV. Here, we present the gamma-ray shielding ratio at the depth of 0.1cm shielding material under different energies, as shown in\u003cstrong\u003e\u0026nbsp;Fig. 4(a)\u003c/strong\u003e. It shows that, with the gamma ray energy less than 20 keV, the gamma ray is completely absorbed by the composite material. This is mainly because when the gamma ray energy is low, the composite material mainly reduces the gamma ray intensity through the photoelectric effect, and the probability of photoelectric effect is inversely proportional to the third power of the gamma ray energy. When the \u0026gamma;-ray energy is higher than 20 keV, the \u0026gamma;-ray shielding ratio of the composite decreases with the increase of \u0026gamma;-ray energy. At 50.5 and 91keV, the \u0026gamma;-ray shielding ratio increases abruptly, and then continues to decline with the increase of \u0026gamma;-ray energy. The sudden increase in the shielding ratio of gamma rays is due to the Gd element and Bi element contained in the composite material, and the K absorption edge of Gd element and Bi element is 50.2 and 90.7 keV respectively, as shown in \u003cstrong\u003eFig. 4(b)\u003c/strong\u003e. When the energy of gamma rays is exactly equal to the K absorption edge of Gd element or Bi element, the gamma ray energy will be completely absorbed by electrons. Moreover, \u0026gamma;-rays are also prone to photoelectric effects, so the shielding ratio of \u0026gamma;-rays of composite materials is significantly increased. Subsequently, with the increase of \u0026gamma;-ray energy, the \u0026gamma;-ray shielding ratio of the material decreases significantly with the increase of \u0026gamma;-ray energy, which is because the probability of photoelectric effect is inversely proportional to the third power of the \u0026gamma;-ray energy.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2.2 Medium energy gamma shielding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe medium energy of the gamma-ray is selected from 100 to 1000 keV, and the attenuation of \u0026gamma; ray intensity entering epoxy resin composite materials is shown in\u003cstrong\u003e\u0026nbsp;Fig. 5.\u0026nbsp;\u003c/strong\u003eIt shows that the \u0026gamma;-ray intensity with different energies incident on the composite material presents a different decreasing trend with the increase of incident depth. The attenuation amplitude and rate of \u0026gamma;-ray intensity both decreases with the increase of \u0026gamma;-ray energy. When the \u0026gamma;-ray energy is 100 keV, the \u0026gamma;-ray intensity decreases quickly and almost all the gamma rays are absorbed by the composite at 0.5 cm. When the gamma ray energy is 1 MeV, the gamma ray intensity only attenuates to 80% after passing through the 1cm shielding material. \u003cstrong\u003eFig. 5(b)\u003c/strong\u003e shows the \u0026gamma;-ray shielding ratios with energies. With increasing the gamma ray energy from 100 to 1000 keV, the gamma ray shielding ratio decreases from 99.99% to 18.76%. This can be explained as, at low \u0026gamma;-ray energy the composite material mainly reduces the \u0026gamma;-ray intensity through the photoelectric effect, and the occurrence probability of photoelectric effect is inversely proportional to the third power of the \u0026gamma;-ray energy. With the rise of \u0026gamma;-ray energy, Compton scattering will happen between some of the \u0026gamma;-ray and composite material, where Compton scattering probability is inversely proportional to the \u0026gamma;-ray energy. Therefore, \u0026gamma;-ray shielding ratio decreases with the increase of \u0026gamma;-ray energy in this medium energy region.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2.3 High energy gamma shielding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe high energy of the \u0026gamma; ray is set to 1~10 MeV, and the attenuation of \u0026gamma;-ray intensity is shown in \u003cstrong\u003eFig. 6\u003c/strong\u003e. The \u0026gamma;-ray intensity of different energies incident on the composite material presents a similar trend as the intermediate energy.\u0026nbsp;The\u0026nbsp;attenuation\u0026nbsp;amplitude and rate of \u0026gamma;-ray intensity both decreases with the increase of \u0026gamma;-ray energy.\u0026nbsp;When the \u0026gamma;-ray energy is 1 MeV, the \u0026gamma;-ray intensity decreases to about 80% after passing through 1 cm composite material, while when the \u0026gamma;-ray energy is 10 MeV, the \u0026gamma;-ray intensity decreases only to about 93% after passing through 1 cm composite material.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFig. 6(b)\u003c/strong\u003e shows the change of gamma shielding ratio with different energy values in the high energy region. As can be seen from the figure, as the gamma ray energy increases from 1 to 10 MeV, the gamma ray shielding ratio decreases from 18.76% to 7.02%. This is mainly due to the fact that the composite material mainly reduces the gamma-ray intensity through photoelectric effect and Compton scattering for relatively low energy; with the further increase of \u0026gamma;-ray energy, \u0026gamma;-ray is absorbed mainly from Compton scattering. We note that the electron pair effect can be ignored since the probability is extremely low for the electrons in heavy element. The probability of Compton scattering is inversely proportional to the incident gamma ray energy and proportional to the atomic number of the composite material, so the gamma ray shielding ratio decreases with the increase of gamma ray energy.\u003c/p\u003e\n\u003cp\u003eTherefore, we conclude that for the gamma ray with energies from 10 to 100 keV, the \u0026gamma;-ray shielding ratio of the composite decreases with the increase of \u0026gamma;-ray energy except for the energies at the absorption edge of Gd and Bi elements. The gamma-rays are almost completely absorbed at the depth of 1 cm, and the rapid reduction in gamma-rays density occurs at the depths less than 0.1 cm. From 100~1000 keV, with the increase of \u0026gamma;-ray energy, \u0026gamma;-ray shielding ratio decreased from 99.99% to 18.76%. From 1~10 MeV, the gamma ray shielding ratio decreases from 18.76% to 7.02% with the increase of gamma ray energy, where Compton scattering is dominant.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.3\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eGamma shielding with different\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003esizes and arrangement of the fillers\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNow we will\u0026nbsp;discuss\u0026nbsp;the gamma shielding effects of epoxy resin materials added with spherical fillers of Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with the mass ratio of 1:1. The energies of incident gamma rays were selected as 50, 100, 500 and 1000 keV, respectively. The particle radius of the functional filler was selected as 0.5, 0.25, 0.1 and 0.05 mm, respectively, and the mass fraction of the functional filler was set to 15.43%.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTab. 1\u0026nbsp;\u003c/strong\u003eThe relationship between the particle size and the number of functional packing particles\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"48.50574712643678%\"\u003e\n \u003cp\u003e\u003cstrong\u003eFunctional packing particle radius (mm)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.49425287356322%\"\u003e\n \u003cp\u003e\u003cstrong\u003eNumber of functional filler particles\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"48.50574712643678%\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.49425287356322%\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"48.50574712643678%\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.25\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.49425287356322%\"\u003e\n \u003cp\u003e400\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"48.50574712643678%\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.49425287356322%\"\u003e\n \u003cp\u003e6250\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"48.50574712643678%\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.05\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"51.49425287356322%\"\u003e\n \u003cp\u003e50000\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eAccording to the filling content and the radius of the functional fillers set above, the number of functional fillers corresponding to the radius of different functional fillers is calculated, as shown in\u003cstrong\u003e\u0026nbsp;Tab. 1.\u0026nbsp;\u003c/strong\u003eThe composite X-Y and Y-Z cross sections of particle\u0026rsquo;s distributions is shown in \u003cstrong\u003eFig. 7\u003c/strong\u003e.\u0026nbsp;X-Y cross sections and Y-Z cross sections are selected respectively to indicate the distribution of functional fillers in composite materials.\u003c/p\u003e\n\u003cp\u003eGamma-ray shielding ratios after \u0026gamma;-rays with different energies incident on composites with different packing sizes are shown in \u003cstrong\u003eFig. 8\u003c/strong\u003e. One can find that at lower gamma ray energy, the shielding ratio is opposite to the filler\u0026rsquo;s size, but with increasing the \u0026gamma;-ray energy up to 500 keV, the influence of the filler\u0026rsquo;s size on the \u0026gamma;-ray shielding ratio can be ignored.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe \u0026gamma;-ray shielding ratio with different filler sizes for \u0026gamma;-ray energies of 50, 100, 500 and 1000 keV are shown in \u003cstrong\u003eFig. 9\u003c/strong\u003e. It can be found that when the incident \u0026gamma;-ray energy is 50 and 100 keV, the \u0026gamma;-ray shielding ratio increases from 23.3% and 20.2% to 63.9% and 55.5% with the decrease of the fillers\u0026rsquo; size, respectively. The \u0026gamma;-ray shielding ratio of the composite material increases by about 175%. It can also be clearly found from \u003cstrong\u003eFig. 8(a)-(b)\u003c/strong\u003e that, the decline rate and amplitude of gamma ray intensity of the composite material with 0.05 mm filler particle size are both significantly higher than that of other filler particle size. It can be seen from \u003cstrong\u003eFig. 9\u003c/strong\u003e that the smaller the particle size of the filler, the greater the attenuation amplitude of the \u0026gamma;-ray intensity, and when the \u0026gamma;-ray energy increases, the influence of the particle size of the filler on the shielding performance of the composite is weakened.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e presented the projected areas of different particle sizes of fillers in the gamma ray incident direction. As can be seen from the table, when the packing radius decreases from 0.5 to 0.05 mm, the projected area increases from 7.85 to 78.54 mm\u003csup\u003e2\u003c/sup\u003e. It can be inferred that the projected area of the fillers in the gamma incident direction increases when the particle size of the functional fillers decreases. Then, the collision cross section between the gamma rays and the functional fillers increases, resulting in the significant increase in the shielding ratio.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e2\u003c/strong\u003e Projective area of different packing particle size in gamma ray incident direction\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003ePacking radius /mm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eFill number\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eProjected area /mm\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.5\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e7.85\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.25\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e400\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e15.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e6250\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e39.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.05\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e50000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e78.54\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eIn order to prove the above inference, we studied the shielding under different packing arrangement while the shape of the composite material, the gamma ray source, the shape and content of the functional fillers were kept unchanged. The radius of the functional fillers was fixed at 0.05 mm and the filling number of the functional fillers was set to 5E4.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFig. 10\u003c/strong\u003e shows the cross sections of different functional fillers arranged in composite materials, named as T1, T2, T3 and T4. X-Y cross sections and Y-Z cross sections are selected respectively to indicate the arrangement of functional fillers in composite materials. The distribution of packing particles in XY section of T1-T4 material are 100\u0026times;100, 50\u0026times;100, 50\u0026times;50 and 10\u0026times;50, respectively. The distribution of packing particles in YZ section are 1\u0026times;5, 1\u0026times;10, 1\u0026times;20 and 1\u0026times;100, respectively. The arrangement of the four materials and the projected area data of the filler in the gamma ray incident direction are shown in\u003cstrong\u003e\u0026nbsp;Table 3\u003c/strong\u003e.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTab. 3\u003c/strong\u003e Projected area of different packing arrangement in gamma ray incidence direction\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.36823104693141%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eMaterial number\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.895306859205775%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eFill number\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.465703971119133%\" valign=\"top\" style=\"width: 23.6074%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eArrangement mode\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25.270758122743683%\" valign=\"top\" style=\"width: 16.5176%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eProjected area /mm\u003csup\u003e2\u003c/sup\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.36823104693141%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eT1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"26.895306859205775%\" rowspan=\"4\"\u003e\n \u003cp\u003e50000\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.465703971119133%\" valign=\"top\" style=\"width: 23.6074%;\"\u003e\n \u003cp\u003e100\u0026times;100\u0026times;5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"25.270758122743683%\" valign=\"top\" style=\"width: 16.5176%;\"\u003e\n \u003cp\u003e78.54\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eT2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"32.098765432098766%\" valign=\"top\" style=\"width: 23.6074%;\"\u003e\n \u003cp\u003e50\u0026times;100\u0026times;10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"34.5679012345679%\" valign=\"top\" style=\"width: 16.5176%;\"\u003e\n \u003cp\u003e39.26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eT3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"32.098765432098766%\" valign=\"top\" style=\"width: 23.6074%;\"\u003e\n \u003cp\u003e50\u0026times;50\u0026times;20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"34.5679012345679%\" valign=\"top\" style=\"width: 16.5176%;\"\u003e\n \u003cp\u003e19.63\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"33.333333333333336%\" valign=\"top\"\u003e\n \u003cp\u003e\u003cstrong\u003eT4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"32.098765432098766%\" valign=\"top\" style=\"width: 23.6074%;\"\u003e\n \u003cp\u003e10\u0026times;50\u0026times;100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"34.5679012345679%\" valign=\"top\" style=\"width: 16.5176%;\"\u003e\n \u003cp\u003e3.93\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eGamma rays with 50 keV and 1 MeV are selected to study the \u0026gamma;-ray shielding under different particle packing arrangement. \u003cstrong\u003eFigs. 11(a)-(b)\u003c/strong\u003e shows the attenuation of gamma rays intensity after four composite materials irradiated with gamma rays of 50 keV and 1 MeV, respectively. The four materials had the same packing radius, the same filling number, and different packing arrangement. Among them, the projected area in the incident direction of \u0026gamma;-rays was the highest in T1, and that in T4 was the smallest.\u003c/p\u003e\n\u003cp\u003eAs can be seen from \u003cstrong\u003eFig. 11(a)\u003c/strong\u003e, the gamma ray intensity of the material T1 attenuates to the smallest after passing through the 1 cm composite material, indicating that the shielding material T1 has the best shielding of 50 keV gamma ray. This shielding effect gets worse for packing arrangement from T2 to T4. The situation is similar for 1 MeV gamma ray, shown in \u003cstrong\u003eFig. 11(b)\u003c/strong\u003e. The shielding effect of materials T1, T2 and T3 is close to each other, and obviously better than that of shielding material T4.\u003c/p\u003e\n\u003cp\u003eTherefore, we conclude that the functional filler with the same size and same filling number, but with a different arrangement of the filler will result in different gamma-ray shielding effects. This is mainly because, different arrangements of the fillers leads to different projected areas of the fillers in the direction of gamma ray incidence. The larger the projected area, the larger the collision cross section between gamma rays and filler particles will be, then the corresponding \u0026gamma;-ray shielding effect of the material will be improved.\u003c/p\u003e"},{"header":"III. Conclusion","content":"\u003cp\u003eTo investigate the shielding effect of the γ-ray, epoxy resins composites added with Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e particles with different size and arrangement were simulated with Monte Carlo simulation platform Geant4. It is found that the γ-ray shielding ratio of the material decreases with the increase of γ-ray energy while there are abrupt increase at 50.5 and 91 keV due to the K absorption edge of Gd and Bi elements. For the same gamma-ray energy, the gamma-ray shielding effects can be improved via optimizing particle size and arrangement of the packing fillers, which can be attributed to the increased collision induced by higher projected area. These studies will be helpful for the design of the lightweight shielding materials for space nuclear power.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eThis work was supported by the National Natural Science Foundation of China (61474096, 12004329), the Yangzhou Science and Technology Bureau (YZ2020263), Open Project of State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (SKLIPR2115) and Foundation of National Key Laboratory of Materials Behavior and Evaluation Technology in Space Environment (WDZC-HGD-2022-11).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of Data and Materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets used and analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e■\u0026nbsp;AUTHOR INFORMATION\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026dagger; R. Cao and G. Li contributed equally to this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorresponding Authors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003csup\u003e*\u003c/sup\u003eE-mail: X. Zeng: [email protected]; Y. Xue: [email protected]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of competing interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. \u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLimarun P, Markpin T, Sombatsompop N, et al. Cellular Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/natural rubber composites for light-weight and lead-free gamma-shielding materials and their properties under gamma irradiation. 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Radiation Shielding Properties for NaO-CdO-Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e-Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e Glasses Using XCOM, Phy-X/PSD and Srim Programs. Glass Physics and Chemistry, 2021, 47(SUPPL 1): S10-S20.\u003c/li\u003e\n\u003cli\u003eYilmaz S N, Akbay I K, Ozdemir T. A metal-ceramic-rubber composite for hybrid gamma and neutron radiation shielding. Radiation Physics and Chemistry, 2021, 180: 109316.\u003c/li\u003e\n\u003cli\u003eMuthamma M V, Bubbly S G, Gudennavar S B, et al. Poly(vinyl alcohol)-bismuth oxide composites for X-ray and gamma-ray shielding applications, J. Applied Polymer Science, 2019, 136(37): 47949.\u003c/li\u003e\n\u003cli\u003eLiao Y C, Xu D G, Zhang P C. 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Effect of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3 \u003c/sub\u003eaddition on mechanical, thermal and shielding properties of Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e ceramics, J. Materials Science-Materials in Electronics, 2017, 28(8): 5898-5905.\u003c/li\u003e\n\u003cli\u003eAli, K.M., Mohammad, K.K., Atallah, F.S., Calculation of radiation doses using shields for nanoparticles tungsten oxide WO\u003csub\u003e3\u003c/sub\u003e mixed with epoxy, J. Radiation and Nuclear Applications, 2018, 3, 191-197.\u003c/li\u003e\n\u003cli\u003eLi, R., Gu, Y., Wang, Y., Yang, Z., Li, M., Zhang, Z., Effect of particle size on gamma radiation shielding property of gadolinium oxide dispersed epoxy resin matrix composite, Mater. Res. Express, 2017, 4: 035035.\u003c/li\u003e\n\u003cli\u003eB\u0026uuml;nyamin Ayg\u0026uuml;na, Erdem S\u0026cedil;akarb, V.P. Singhc, M.I. Sayyedd, Turgay Korkutf, Abdulhalik Karabulut, Experimental and Monte Carlo simulation study on potential new composite materials to moderate neutron-gamma radiation, Progress in Nuclear Energy, 2020, 130: 103538.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-inorganic-and-organometallic-polymers-and-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"joip","sideBox":"Learn more about [Journal of Inorganic and Organometallic Polymers and Materials](https://www.springer.com/journal/10904)","snPcode":"10904","submissionUrl":"https://submission.nature.com/new-submission/10904/3","title":"Journal of Inorganic and Organometallic Polymers and Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Gamma ray shielding, Gd2O3/Bi2O3, epoxy resin, Geant4 simulation","lastPublishedDoi":"10.21203/rs.3.rs-4233481/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4233481/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn order to meet the requirement of radiation shielding materials for space nuclear reactors, gamma shielding effect of epoxy resin base added with Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e particles was studied by Monte Carlo simulation platform Geant4 in this paper. Firstly, the gamma ray shielding effects of functional filler with different ratios and content were simulated. Then, based on the gamma-ray energy range generated by space nuclear reactors, the γ-ray protection performance of epoxy resin composites under different energy ranges was studied. Finally, the effects of the particle size and arrangement of the fillers on the γ-ray shielding properties of the composites were presented, and the results showed that the smaller of the particle size, the better the shielding effect will be; for the same size of the filler, the arrangement of the filler with a larger projection area has a better γ-ray shielding performance. The effect of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e added to epoxy resin base on low-energy gamma rays is obvious, but the effect on high-energy rays is less.\u003c/p\u003e","manuscriptTitle":"Simulation of γ-Ray Radiation Shielding Utilizing Gd2O3/Bi2O3/Epoxy Resin","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-19 17:09:30","doi":"10.21203/rs.3.rs-4233481/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-04-21T09:11:06+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-20T19:49:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"f850e909-0751-4e41-945e-3689d664b5bf","date":"2024-04-19T10:00:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"8baeb348-282a-4263-8a7f-9330abff9a26","date":"2024-04-19T06:11:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"f47288bc-1306-4988-baf8-f5cdeea8ac4d","date":"2024-04-18T07:58:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"b4a543eb-81ad-421e-8e81-d5226c1744c0","date":"2024-04-18T07:41:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"16723721-fe55-42bf-9656-ae9912d084f1","date":"2024-04-17T11:18:37+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-04-17T07:00:14+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"3b5ea0ad-bb0d-4dd2-9fa3-4af79a6b20b9","date":"2024-04-16T21:24:38+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"5829b70c-aeb2-4f1d-9d2e-1a7ca8082ab6","date":"2024-04-16T21:16:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"442cf293-370a-484b-b299-9fc56cf14f63","date":"2024-04-16T18:52:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"046244b1-8cba-47bc-b930-b9ff22217b83","date":"2024-04-16T18:28:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"6c915b26-ba4f-42d6-8ad1-aca63f44ed03_SNPRID","date":"2024-04-16T18:23:24+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-04-16T18:20:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-04-16T17:00:39+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-04-15T04:16:48+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Inorganic and Organometallic Polymers and Materials","date":"2024-04-08T02:55:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-inorganic-and-organometallic-polymers-and-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"joip","sideBox":"Learn more about [Journal of Inorganic and Organometallic Polymers and Materials](https://www.springer.com/journal/10904)","snPcode":"10904","submissionUrl":"https://submission.nature.com/new-submission/10904/3","title":"Journal of Inorganic and Organometallic Polymers and Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"3aa51699-623b-4de6-9f8f-5605cba2d800","owner":[],"postedDate":"April 19th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-06-21T15:12:29+00:00","versionOfRecord":{"articleIdentity":"rs-4233481","link":"https://doi.org/10.1007/s10904-024-03161-w","journal":{"identity":"journal-of-inorganic-and-organometallic-polymers-and-materials","isVorOnly":false,"title":"Journal of Inorganic and Organometallic Polymers and Materials"},"publishedOn":"2024-06-15 15:12:29","publishedOnDateReadable":"June 15th, 2024"},"versionCreatedAt":"2024-04-19 17:09:30","video":"","vorDoi":"10.1007/s10904-024-03161-w","vorDoiUrl":"https://doi.org/10.1007/s10904-024-03161-w","workflowStages":[]},"version":"v1","identity":"rs-4233481","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4233481","identity":"rs-4233481","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}