Theoretical investigation of X-ray shielding properties of bismuth-titanium-phosphate glass materials

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The results revealed that sample S1 (with no Nb₂O₅) exhibited the lowest LAC (ranging from 95,129.721 cm⁻¹ at 15 keV to 2.956 cm⁻¹ at 80 keV), whereas sample S4 (with 5 mol% Nb₂O₅) had the highest LAC, confirming that increasing Nb₂O₅ enhances X-ray shielding. The sample S4 with 5 mol% of Nb 2 O 5 has the highest linear attenuation coefficient (6.861–0.703 cm − 1 ) at photon energies between 80 to 300 keV. These calculations indicated that adding more Nb 2 O 5 content makes the glass more effective for shielding X-rays in this low energy range. bismuth-titanium-phosphate glass x-ray shielding LAC MAC radiation shielding Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction X-rays are ionizing electromagnetic waves with the typical energy range of a few eV to hundreds of keV and can be produced in the form of bremsstrahlung radiation or characteristic X-rays. They have a wide range of industrial applications. In particular, they are used for applications such as computed tomography scans, dental x-rays, screening freight trains, screening luggage, maintenance of fluid supply pipes in power plants, and detection of unwanted objects in food. X-rays are hazardous and pose health risks to people who work in the aforementioned industries if they are not properly shielded. There are numerous materials that can be used for x-ray shielding. The usage of lead-based materials is one of the most traditional methods. However, lead is not user-friendly due to its toxicity, even though it is very effective because of its high electron density and linear attenuation coefficient for photons [ 1 ]. Thus, there is currently a lot of research interest, globally, in searching for the best possible nontoxic lead-free glass materials for shielding x-rays and γ-rays [ 2 – 11 ]. For example, Ref. [ 12 ] recently conducted a comprehensive study on the x-ray shielding properties of bismuth-borate glass samples, doped with rare-earth ions, and found that the Sm 3+ -doped bismuth-borate glass is more effective in shielding x-rays than those that are doped with Nd 3+ and Ce 3+ . Similarly, Ref. [ 13 ] also did a computational study to investigate the x-ray shielding characteristics of Bi 2 O 3 – B 2 O 3 – TeO 2 – TiO 2 glass, in the 30 to 80 keV energy region which is the dental diagnostic energy range. The results showed that this glass type can be used to fabricate protection masks worn during diagnostic irradiation of the oral cavity. Furthermore, Ref. [ 14 ] studied the photon shielding properties of Li 2 O – B 2 O 3 – MgO – Er 2 O 3 glass samples, doped with Sm 2 O 3 , and showed that they improve with the increase in the content of Sm 2 O 3 . In the same vein, the x-ray shielding capacity of La 2 O 3 – CaO – B 2 O 3 – SiO 3 glass material has been studied [ 15 ], and the results revealed that this material becomes more effective as the content of La 2 O 3 increases. In a similar manner, Refs. [ 16 – 22 ] recently examined the radiation shielding properties of different borate glass compositions. Their research uncovered that the inclusion of Cr 2 O 3 , TeO 2 , Gd 2 O 3 , WO 3 , TeO 2 /MoO 3 , and CeO 2 enhanced the ability of Cr 2 O 3 –doped borosilicate, TeO 2 -doped borosilicate, Gd 2 O 3 –doped alumina borate, B 2 O 3 – PbO – TeO 2 – CeO 2 – WO 3 , TeO 2 – B 2 O 3 – Li 2 O – MoO 3 – CuO, and CeO 2 /sand reinforced borate glasses, respectively, to shield against x-rays and γ-rays. Furthermore, among the investigated TeO 2 – BaO – B 2 O 3 – PbO – V 2 O 5 samples, the 34TeO 2 – 35B 2 O 3 – 30PbO – V 2 O 5 glass demonstrated the most effective photon shielding characteristics. Very recently, a novel bismuth-titanium-phosphate glass samples were synthesized by Ref. [ 23 ]. However, the radiation shielding properties of these glass materials have only been investigated in the energy region above 284 keV. They have not been investigated for their x-ray shielding properties in the photon energy region below 284 keV, and this is the main objective of this study. This energy region is of interest, particularly, because applications such as computed tomography scans, airport security scans and dental diagnosis use x-ray beams of energies below 284 keV. Hence, it is vital to study x-ray shielding properties in this region and find the best possible shielding material to prevent possible radiation hazards, in these industries. Thus, in this work, we investigated the X-ray shielding properties of 45Na₂O + 10 Bi₂O₃ + (5 - x)TiO₂ + (x) Nb₂O₅ + 40 P₂O₅ glass samples, with x = 0, 1, 3, and 5 mol% in the 15 keV to 300 keV energy range, and discussed in details. In particular, we studied the mass attenuation coefficient (MAC) and linear attenuation coefficient (LAC) using the Phy-X/PSD software and compared the result to geant4. 2. Methods The x-ray shielding properties of 45Na 2 O + 10 Bi 2 O 3 + 5 TiO 2 + 40 P 2 O 5 , 45Na 2 O + 10 Bi 2 O 3 + 4 TiO 2 + 1 Nb 2 O 5 + 40 P 2 O 5 , 45Na 2 O + 10 Bi 2 O 3 + 2 TiO 2 + 3 Nb 2 O 5 + 40 P 2 O 5 , and 45Na 2 O + 10 Bi 2 O 3 + 5 Nb 2 O 5 + 40 P 2 O 5 glass materials were computed using Phy-X/PSD software and validated using the geant4. Phy-X/PSD is a user-friendly simulation package which runs remotely on the Ubuntu operating system [ 24 , 25 ]. It is for calculating radiation shielding properties such as MAC and LAC in the 1 keV to 100 GeV photon energy range. GEANT4 is a software toolkit developed and maintained at CERN that simulates particle passage through matter. It is used in a wide range of experiments and projects, including high-energy physics, astrophysics and space science, medical physics, and radiation protection [ 28 ]. As a result, geant4 results were compared to validate the MAC and LAC values obtained through the PHY-X/PSD method. This approach has been recently used in the literature [ 12 ]. Table 1 and Table 2 show the summary of the properties of the glass samples used in this study. They are critical input data for the PHY-X/PSD and geant4, in which the calculations are based on the principles discussed below. The mass attenuation coefficient, MAC, and liner attenuation coefficient, µ, describe the likelihood of interaction between x-rays and a radiation shielding material. The linear attenuation coefficient is related to the photon intensity and the thickness of an absorber, x, according to [ 25 ]. Table 1 Chemical content (mol%) of glass samples used in Phy-X/PSD [ 23 ]. Code Na 2 O Bi 2 O 3 TiO 2 Nb 2 O 5 P 2 O 5 S1 45 10 5 - 40 S2 45 10 4 1 40 S3 45 10 2 3 40 S4 45 10 - 5 40 Table 2 Table 2 : Chemical content (wt%) of glass samples used in GEANT4 calculations. Code Na 2 O Bi 2 O 3 TiO 2 Nb 2 O 5 P 2 O 5 S1 0.21 0.34 0.03 - 0.42 S2 0.2 0.34 0.02 0.02 0.41 S3 0.2 0.33 0.01 0.06 0.4 S4 0.19 0.32 - 0.09 0.39 I f = I i exp(-µx), (1) where I i and I f are initial and attenuated photon intensities, respectively. High values of µ imply better radiation shielding capacity. The rest of the radiation shielding properties are derived from the µ. In particular, the MAC is computed from µ and the density, ρ, of the absorber using [ 25 ] MAC = \(\:\frac{\mu\:}{\rho\:}\) . (2) Similarly, the half-value thickness (HVT) and tenth-value thickness (TVT), which respectively represent the thicknesses of materials required to attenuate photons by 50% and 90%, are given by [ 25 ] HVT = \(\:\frac{ln2}{\mu\:}\) (3) and TVT = \(\:\frac{ln10}{\mu\:}\) . (4) The smaller the values of HVT and TVT, the better the radiation shielding material is in shielding X-rays. Furthermore, the mean-free path MFP, is the average distance between two consecutive interactions between a photon of a given energy and the absorber material. It is related to the linear attenuation coefficient, µ, through the following expression [ 25 ] MFP = \(\:\frac{1}{\mu\:}\) . (5) These parameters will be analysed for each glass sample to quantify their shielding effectiveness. The lower the MFP, the more effective a material is in shielding electromagnetic radiation. The effective atomic number is determined by analysing the linear attenuation coefficient in conjunction with the absorber’s density, as detailed in the following formula: $$\:{Z}_{\text{eff}}=\frac{{\sum\:}_{j}{f}_{j}{A}_{j}{\left(\frac{\mu\:}{\rho\:}\right)}_{j}}{{\sum\:}_{j}\frac{{f}_{j}{A}_{j}}{{Z}_{j}}{\left(\frac{\mu\:}{\rho\:}\right)}_{j}}$$ 6 where f j , A j , and Z j denote the mole fraction, atomic weight, and atomic number of each constituent element within the sample, respectively. Higher values of Z eff correspond to heightened radiation shielding efficacy exhibited by the material. The effective electron density for each glass sample is calculated from its mass attenuation coefficient using the formula below: $$\:{N}_{eff}=\frac{MAC}{{\sigma\:}_{e}}$$ 7 where \(\:{\sigma\:}_{e}\) represents the total electronic cross-section, which is determined using the following equation: $$\:{\sigma\:}_{e}=\frac{\frac{1}{{N}_{A}}\frac{MAC}{\sum\:_{i}\left({w}_{i}/{A}_{i}\right)}}{{Z}_{eff}}$$ 8 In this context, \(\:{A}_{i}\) denotes the atomic weight of the ith element in the sample, and \(\:{w}_{i}\) represents its weight fraction. Additionally, \(\:{N}_{A}\) refers to Avogadro’s number. 3. Results and discussions The linear attenuation coefficients were obtained to investigate the radiation shielding properties of glass materials using the PHY-X/PSD simulation code, and the results were compared with the calculations performed by geant4. This section contains the discussion of our results on the linear attenuation coefficient (LAC) of the glass samples S1, S2, S3, and S4 shown in Table 1 and Table 2 . Table 3 shows the comparison of the MAC values which were computed using Phy-X/PSD software and geant4. The two-simulation software’s are in excellent agreement. This provides confidence in the calculated MAC values for all four glass samples. Table 3: Comparison of the mass attenuation coefficient obtained by using PHY-X/PSD and GEANT4 MAC (cm 2 /g) from PHY-X/PSD MAC (cm 2 /g) from GEANT4 Energy (MeV) S1 S2 S3 S4 S1 S2 S3 S4 1.50E-02 40.07 39.77 39.20 38.65 38.13 35.93 37.61 37.81 2.00E-02 29.53 30.12 31.26 32.34 28.05 26.22 30.25 30.58 3.00E-02 10.38 10.58 10.97 11.35 9.73 9.04 10.48 10.58 4.00E-02 4.96 5.05 5.22 5.39 4.52 4.19 4.86 4.91 5.00E-02 2.82 2.86 2.96 3.04 2.52 2.33 2.70 2.72 6.00E-02 1.79 1.82 1.88 1.93 1.58 1.46 1.69 1.71 8.00E-02 0.91 0.92 0.95 0.97 0.78 0.73 0.83 0.84 1.00E-01 1.89 1.88 1.85 1.83 1.78 1.56 1.77 1.78 1.50E-01 0.74 0.73 0.73 0.72 0.70 0.62 0.69 0.70 2.00E-01 0.40 0.40 0.40 0.39 0.38 0.34 0.38 0.38 3.00E-01 0.15 0.2 0.2 0.17 0.15 0.2 0.2 0.17 These MAC values were used to compute LAC values for all glass samples. Figure 1 shows the Linear Attenuation Coefficient (LAC) for all glass samples as a function of photon energy in the 15 keV to 300 keV energy range. It demonstrates the strong correlation between the mass attenuation coefficients obtained from PHY-X/PSD and Geant4 simulations for all glass materials. The results indicate that LAC has a sharp decrease with an increase in photon energy. This trend is consistent with the literature [ 26 ]. Sample S1, which has the lowest Nb 2 O 5 content has the lowest LAC while S4 has the highest LAC in the energy range. This indicated that adding more content of Nb 2 O 5 makes the glass material more effective at shielding X-ray energies. The linear attenuation coefficients for S1, S2, S3 and S4, range from 129.72 to 0.65 cm − 1 , 129.03 to 0.65 cm − 1 , 135.58 to 0.69 cm − 1 and 137.56 to 0.70 cm − 1 respectively. It is also observed that there is an enhancement in the LAC at the photon energy of 0.1 MeV. This is because of the K-absorption edge electrons which start contributing to the photoelectric effect at the energy of 0.1 MeV. To see the effect of the Nb 2 0 5 rate in glasses regarding radiation shielding properties, the linear attenuation coefficients have been plotted as a function of the Nb 2 0 5 rate and are displayed in Fig. 2 for 0.015, 0.08 and 0.3 MeV photon energies. The figure shows that the linear attenuation coefficients increased with the increasing Nb 2 0 5 rate in glasses. Figure 2 shows that there is good agreement between the two calculations and that the LAC increased as the Nb 2 0 5 rate in glasses increased. This is due to the increment in glass density as Nb 2 0 5 substances increase in glasses compared to the original S1 glass sample, and this is because the higher the glass density the higher the LAC values. Figure 3 illustrates the result obtained for both PHY-X/PSD and geant4 as a function of glass density. It is evident from this figure that the LAC increases as the density of the glass increases for 0.015, 0.08 and 0.3 MeV photon energies. The LAC obtained by PHY-X/PSD and geant4 has been calculated as a function of full energy between the following region 0.015–0.3 MeV. Figure 4 shows the results for S1–S4, demonstrating good agreement between both simulation methods. Furthermore, this figure depicts that LAC is energy-dependent and as a result, it behaves differently in different energy regions. At low energy between 0 and 0.08 MeV there is a sharp decrease then a slight increase due to K-electron absorption and then a further decrease between 0.01 and 0.3 MeV. The effective atomic number shown in Fig. 5 (a) is calculated as a function of full energy between the following region 0.015–0.3 MeV. The samples S1, S2, S3 and S4 demonstrate good agreement indicating that the attenuation properties are similar. At low energies between 0 and 0.08 MeV the effective atomic number stays relatively stable with a slight drop and there is a slight increase due to K-electron absorption then a further decrease between 0.01 and 0.3 MeV. The response of Zeff to increasing energy is influenced by atomic number and the density of the material indicating that heavier material exhibits greater changes in Zeff with energy variations. The effective neutron density shown in Fig. 5 (b) exhibits notable variations across all four samples as photon energy increases. At lower energies, the N eff of all samples appears relatively stable, suggesting similar attenuation characteristics for neutron interactions. However, as photon energy increases, distinct trends emerge among all four samples. However, sample S4 demonstrates significant fluctuations, particularly at higher energies, indicating a unique response to neutron radiation. This behaviour may be attributed to the specific atomic composition and structural characteristics of the material, which could lead to differential scattering and absorption mechanisms The half-value thickness is shown in Fig. 7 as a function of photon energy. All four samples S1, S2, S3, and S4, show a very close correlation, indicating minimal variations among the samples. The graph shows a sharp increase in HVT at low photon energies (0–0.1 MeV), followed by a noticeable dip around 0.1 MeV. This behavior has been reported in other studies [ 27 ]. This drop corresponds to K-edge absorption, where photons have enough energy to eject K-shell electrons, leading to a sudden increase in photon interaction probability. Beyond this region, HVT rises again as Compton scattering becomes the dominant interaction mechanism, reducing the attenuation efficiency of the material. The tenth-value thickness is shown in Fig. 6 as a function of photon energy. The TVT show a similar trend as HVT, the TVT increasing at lower energies, exhibiting a sharp decrease around 0.1 MeV due to K-edge absorption, and rising again at higher energies. The K-edge absorption occurs when photon energy surpasses the binding energy of K-shell electrons, leading to an abrupt enhancement in attenuation efficiency. The mean-free path is illustrated in Fig. 8 . Figure 8 illustrates the variation of Mean Free Path (MFP) with photon energy for four different samples, namely: S1, S2, S3, and S4. At lower photon energies - below 0.1 MeV, MFP increases gradually, indicating that photons interact more frequently with the material, leading to effective attenuation. However, a noticeable dip occurs around 0.1 MeV due to the K-edge absorption effect, where photons attain enough energy to eject K-shell electrons, significantly increasing interaction probability and consequently reducing MFP. After 0.1 MeV, the MFP rises again as Compton scattering becomes the dominant interaction mechanism. In this range, photons travel longer distances before undergoing interactions, leading to a higher mean free path. 4. Summary and Conclusions In this study, the X-ray shielding properties of bismuth-titanium-phosphate glass samples with varying Nb₂O₅ content were investigated using Phy-X/PSD simulations and validated with Geant4 calculations. The results showed that increasing the Nb₂O₅ content in the glass composition significantly enhances the shielding effectiveness. Specifically, sample S4, which contains the highest Nb₂O₅ concentration (5 mol%), exhibited the highest linear attenuation coefficient (LAC) values across the studied energy range (15 keV to 300 keV). This indicates that Nb₂O₅ contributes to improved radiation attenuation due to its higher density and atomic number. The LAC values obtained from both simulation methods were in strong agreement, confirming the reliability of the computational approach. The study also demonstrated that the mass attenuation coefficient (MAC), half-value thickness (HVT), tenth-value thickness (TVT), and mean free path (MFP) followed expected trends, further validating the effectiveness of Nb₂O₅ in enhancing X-ray shielding performance. The effective atomic number (Zeff) and effective electron density (Neff) analyses reinforced these findings, showing a clear correlation between higher Nb₂O₅ content and improved shielding characteristics. Overall, this work highlights the potential of Nb₂O₅-doped bismuth-titanium-phosphate glasses as promising candidates for X-ray shielding applications, particularly in medical imaging, security screening, and radiation protection industries. Future work could explore further optimization of these materials to balance shielding performance with mechanical and optical properties. Declarations Conflict of interest: The authors declare no conflict of interest in this work. Funding declaration No Funding. Author Contribution Lucky Makhathini - Produced the manuscript and performed the simulations.Vincent Bonginkosi Kheswa - Reading of the manuscript and calculations. Siyabonga Ntokozo Thandoluhle Majola - Reading and editing of the manuscript Data availability statement: All data presented in this article are available on request. Ethical approval : This research work does not involve humans or animals. References Klein RC, Weilandics C. Potential health hazards from lead shielding. Am. Ind. Hyg. Assoc J. 1996; 57(12):1124-6. doi: 10.1080/15428119691014215. Tekin HO, ALMisned G, Zakaly HMH, Zamil A, Khoucheich D, Bilal G, et al. Gamma, neutron, and heavy charged ion shielding properties of Er 3+ -doped and Sm 3+ -doped zinc borate glasses. Open Chem. 2022; 20: 130-45. doi: 10.1515/chem-2022-0128. Waly ESA, Fusco MA, Bourham MA. 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Enhancement of the shielding capability of soda–lime glasses with Sb 2 O 3 dopant: A potential material for radiation safety in nuclear installations. Appl Sci. 2021;11:326. doi: 10.3390/app11010326. https://geant4.web.cern.ch/ Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6287971","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":457256914,"identity":"e6f9eab3-7c08-4edb-940e-74a3d4334a7f","order_by":0,"name":"Lucky Makhathini","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYBACPgYGZmYgncDGwNj4gCgtbBAtBiAtzQakaQGxJYjTInb4sXFBzZ88PunmtmreNjsG/vYDzB9+4NMinWacPOOYQTGbzMG227xtyQwSZxIYDHvwakkwPszDZpDYJpEI1LLtAAPDDWBg8ODVkv75MM8/iJZikBZ5oJaDf/BqyTFO5m2DaGEGaTG4AQw7/LbkFBvz9hmDtDRLzv2XzGN4JrGZWQaPFn7p9M3SPN/kEufPSH/44c0ZOzm544cPf3yDRwsGADqJsYEUDaNgFIyCUTAKsAAAHNNDwj9vNfQAAAAASUVORK5CYII=","orcid":"","institution":"University of the Western Cape","correspondingAuthor":true,"prefix":"","firstName":"Lucky","middleName":"","lastName":"Makhathini","suffix":""},{"id":457256915,"identity":"d8d81bb1-c8eb-4a1f-8cb8-c21a2ac1acf8","order_by":1,"name":"Vincent Bongikosi Kheswa","email":"","orcid":"","institution":"University of Johannesburg","correspondingAuthor":false,"prefix":"","firstName":"Vincent","middleName":"Bongikosi","lastName":"Kheswa","suffix":""},{"id":457256916,"identity":"fc7f93ba-ad30-4396-8afd-860b22a0b781","order_by":2,"name":"Siyabonga Ntokozo Thandoluhle Majola","email":"","orcid":"","institution":"University of Johannesburg","correspondingAuthor":false,"prefix":"","firstName":"Siyabonga","middleName":"Ntokozo Thandoluhle","lastName":"Majola","suffix":""}],"badges":[],"createdAt":"2025-03-23 11:38:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6287971/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6287971/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82881575,"identity":"0f269003-abdf-4f47-8b5d-b01bc4cf3b7d","added_by":"auto","created_at":"2025-05-16 10:58:04","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":32811,"visible":true,"origin":"","legend":"\u003cp\u003ePHY-X/PSD calculations for all types of glass, S1, S2, S3 and S4.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/3275d7dd4eb14e6e731dd7e9.jpg"},{"id":82880873,"identity":"cd7899db-1ea6-4817-a5f3-7a4f251477db","added_by":"auto","created_at":"2025-05-16 10:50:04","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":56581,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of LAC for PHY-X/PSD and GEANT4 as a function of Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e in glass at 0.15 MeV, 0.08 MeV and 0.3 MeV.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/161244c2d4e5d15b91276b67.jpg"},{"id":82881576,"identity":"0ee602c1-1105-4358-a0fd-aaf00cd2a626","added_by":"auto","created_at":"2025-05-16 10:58:05","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":51411,"visible":true,"origin":"","legend":"\u003cp\u003eThe LAC as function of glass density at 0.015 MeV, 0.08 MeV and 0.3 MeV\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/4054cf40da85e3bb9077ae1a.jpg"},{"id":82880874,"identity":"98e0aa5f-d0b8-4ac3-9f95-3f21dc1f307c","added_by":"auto","created_at":"2025-05-16 10:50:05","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":58507,"visible":true,"origin":"","legend":"\u003cp\u003eLinear Attenuation Coefficient for S1, S2, S3 and S4 obtained using the PHY-X/PSD and Geant4.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/ef98597f6d1a6b14a0d4205c.jpg"},{"id":82880876,"identity":"3fd977ed-a1f5-4b51-acf5-11454baf4fca","added_by":"auto","created_at":"2025-05-16 10:50:05","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":52427,"visible":true,"origin":"","legend":"\u003cp\u003eEffective atomic (a) number and effective electron density (b) for S1, S2, S3 and S4 obtained using the PHY-X/PSD\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/98ff997a40d1b6f6b045ac53.jpg"},{"id":82880879,"identity":"8fcb3548-eefe-4bb0-a782-0a2c8b98e15c","added_by":"auto","created_at":"2025-05-16 10:50:05","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":24336,"visible":true,"origin":"","legend":"\u003cp\u003eTenth-Value Thickness of all four glass samples.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/98135b74def24f812d15aac8.jpg"},{"id":82880877,"identity":"5a3c3b53-064d-4bc8-89f2-8d926453d4c4","added_by":"auto","created_at":"2025-05-16 10:50:05","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":26069,"visible":true,"origin":"","legend":"\u003cp\u003eHalf-Value Thickness for all four glass samples.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/bb5404dbeb91c08393bc3e39.jpg"},{"id":82881577,"identity":"bfd3e9ed-f86c-4256-ac9b-80d9b3426bd4","added_by":"auto","created_at":"2025-05-16 10:58:05","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":27653,"visible":true,"origin":"","legend":"\u003cp\u003eThe Mean-Free Path of All four glass samples.\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/7bb4d33a428a2abfbab16cf5.jpg"},{"id":107200509,"identity":"6fe37c1f-aeee-4e56-a56c-7fece89661f1","added_by":"auto","created_at":"2026-04-18 03:39:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":743463,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6287971/v1/63d52e83-00f5-48ac-9e4c-837cc6f84276.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Theoretical investigation of X-ray shielding properties of bismuth-titanium-phosphate glass materials","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eX-rays are ionizing electromagnetic waves with the typical energy range of a few eV to hundreds of keV and can be produced in the form of bremsstrahlung radiation or characteristic X-rays. They have a wide range of industrial applications. In particular, they are used for applications such as computed tomography scans, dental x-rays, screening freight trains, screening luggage, maintenance of fluid supply pipes in power plants, and detection of unwanted objects in food. X-rays are hazardous and pose health risks to people who work in the aforementioned industries if they are not properly shielded.\u003c/p\u003e \u003cp\u003eThere are numerous materials that can be used for x-ray shielding. The usage of lead-based materials is one of the most traditional methods. However, lead is not user-friendly due to its toxicity, even though it is very effective because of its high electron density and linear attenuation coefficient for photons [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Thus, there is currently a lot of research interest, globally, in searching for the best possible nontoxic lead-free glass materials for shielding x-rays and γ-rays [\u003cspan additionalcitationids=\"CR3 CR4 CR5 CR6 CR7 CR8 CR9 CR10\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. For example, Ref. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] recently conducted a comprehensive study on the x-ray shielding properties of bismuth-borate glass samples, doped with rare-earth ions, and found that the Sm\u003csup\u003e3+\u003c/sup\u003e-doped bismuth-borate glass is more effective in shielding x-rays than those that are doped with Nd\u003csup\u003e3+\u003c/sup\u003e and Ce\u003csup\u003e3+\u003c/sup\u003e. Similarly, Ref. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] also did a computational study to investigate the x-ray shielding characteristics of Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; TeO\u003csub\u003e2\u003c/sub\u003e \u0026ndash; TiO\u003csub\u003e2\u003c/sub\u003e glass, in the 30 to 80 keV energy region which is the dental diagnostic energy range. The results showed that this glass type can be used to fabricate protection masks worn during diagnostic irradiation of the oral cavity. Furthermore, Ref. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] studied the photon shielding properties of Li\u003csub\u003e2\u003c/sub\u003eO \u0026ndash; B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; MgO \u0026ndash; Er\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e glass samples, doped with Sm\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, and showed that they improve with the increase in the content of Sm\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e. In the same vein, the x-ray shielding capacity of La\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; CaO \u0026ndash; B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; SiO\u003csub\u003e3\u003c/sub\u003e glass material has been studied [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], and the results revealed that this material becomes more effective as the content of La\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e increases. In a similar manner, Refs. [\u003cspan additionalcitationids=\"CR17 CR18 CR19 CR20 CR21\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] recently examined the radiation shielding properties of different borate glass compositions. Their research uncovered that the inclusion of Cr\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, TeO\u003csub\u003e2\u003c/sub\u003e, Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, WO\u003csub\u003e3\u003c/sub\u003e, TeO\u003csub\u003e2\u003c/sub\u003e/MoO\u003csub\u003e3\u003c/sub\u003e, and CeO\u003csub\u003e2\u003c/sub\u003e enhanced the ability of Cr\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026ndash;doped borosilicate, TeO\u003csub\u003e2\u003c/sub\u003e-doped borosilicate, Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026ndash;doped alumina borate, B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; PbO \u0026ndash; TeO\u003csub\u003e2\u003c/sub\u003e \u0026ndash; CeO\u003csub\u003e2\u003c/sub\u003e \u0026ndash; WO\u003csub\u003e3\u003c/sub\u003e, TeO\u003csub\u003e2\u003c/sub\u003e \u0026ndash; B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; Li\u003csub\u003e2\u003c/sub\u003eO \u0026ndash; MoO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; CuO, and CeO\u003csub\u003e2\u003c/sub\u003e/sand reinforced borate glasses, respectively, to shield against x-rays and γ-rays. Furthermore, among the investigated TeO\u003csub\u003e2\u003c/sub\u003e \u0026ndash; BaO \u0026ndash; B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; PbO \u0026ndash; V\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e samples, the 34TeO\u003csub\u003e2\u003c/sub\u003e \u0026ndash; 35B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e \u0026ndash; 30PbO \u0026ndash; V\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e glass demonstrated the most effective photon shielding characteristics.\u003c/p\u003e \u003cp\u003eVery recently, a novel bismuth-titanium-phosphate glass samples were synthesized by Ref. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. However, the radiation shielding properties of these glass materials have only been investigated in the energy region above 284 keV. They have not been investigated for their x-ray shielding properties in the photon energy region below 284 keV, and this is the main objective of this study. This energy region is of interest, particularly, because applications such as computed tomography scans, airport security scans and dental diagnosis use x-ray beams of energies below 284 keV. Hence, it is vital to study x-ray shielding properties in this region and find the best possible shielding material to prevent possible radiation hazards, in these industries. Thus, in this work, we investigated the X-ray shielding properties of 45Na₂O\u0026thinsp;+\u0026thinsp;10 Bi₂O₃ + (5 - x)TiO₂ + (x) Nb₂O₅ + 40 P₂O₅ glass samples, with x\u0026thinsp;=\u0026thinsp;0, 1, 3, and 5 mol% in the 15 keV to 300 keV energy range, and discussed in details. In particular, we studied the mass attenuation coefficient (MAC) and linear attenuation coefficient (LAC) using the Phy-X/PSD software and compared the result to geant4.\u003c/p\u003e"},{"header":"2. Methods","content":"\u003cp\u003eThe x-ray shielding properties of 45Na\u003csub\u003e2\u003c/sub\u003eO\u0026thinsp;+\u0026thinsp;10 Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;5 TiO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;40 P\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e, 45Na\u003csub\u003e2\u003c/sub\u003eO\u0026thinsp;+\u0026thinsp;10 Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;4 TiO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1 Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;40 P\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e, 45Na\u003csub\u003e2\u003c/sub\u003eO\u0026thinsp;+\u0026thinsp;10 Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;2 TiO\u003csub\u003e2\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;3 Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;40 P\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e, and 45Na\u003csub\u003e2\u003c/sub\u003eO\u0026thinsp;+\u0026thinsp;10 Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;5 Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;40 P\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e glass materials were computed using Phy-X/PSD software and validated using the geant4. Phy-X/PSD is a user-friendly simulation package which runs remotely on the Ubuntu operating system [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. It is for calculating radiation shielding properties such as MAC and LAC in the 1 keV to 100 GeV photon energy range. GEANT4 is a software toolkit developed and maintained at CERN that simulates particle passage through matter. It is used in a wide range of experiments and projects, including high-energy physics, astrophysics and space science, medical physics, and radiation protection [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. As a result, geant4 results were compared to validate the MAC and LAC values obtained through the PHY-X/PSD method. This approach has been recently used in the literature [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e show the summary of the properties of the glass samples used in this study. They are critical input data for the PHY-X/PSD and geant4, in which the calculations are based on the principles discussed below.\u003c/p\u003e \u003cp\u003eThe mass attenuation coefficient, MAC, and liner attenuation coefficient, \u0026micro;, describe the likelihood of interaction between x-rays and a radiation shielding material. The linear attenuation coefficient is related to the photon intensity and the thickness of an absorber, x, according to [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eChemical content (mol%) of glass samples used in Phy-X/PSD [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCode\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNa\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eP\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e: Chemical content (wt%) of glass samples used in GEANT4 calculations.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCode\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNa\u003csub\u003e2\u003c/sub\u003eO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTiO\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eNb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eP\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eS4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.39\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eI\u003csub\u003ef\u003c/sub\u003e = I\u003csub\u003ei\u003c/sub\u003e exp(-\u0026micro;x), (1)\u003c/p\u003e \u003cp\u003ewhere I\u003csub\u003ei\u003c/sub\u003e and I\u003csub\u003ef\u003c/sub\u003e are initial and attenuated photon intensities, respectively. High values of \u0026micro; imply better radiation shielding capacity. The rest of the radiation shielding properties are derived from the \u0026micro;. In particular, the MAC is computed from \u0026micro; and the density, ρ, of the absorber using [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eMAC = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\mu\\:}{\\rho\\:}\\)\u003c/span\u003e\u003c/span\u003e. (2)\u003c/p\u003e \u003cp\u003eSimilarly, the half-value thickness (HVT) and tenth-value thickness (TVT), which respectively represent the thicknesses of materials required to attenuate photons by 50% and 90%, are given by [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eHVT = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{ln2}{\\mu\\:}\\)\u003c/span\u003e\u003c/span\u003e (3)\u003c/p\u003e \u003cp\u003eand\u003c/p\u003e \u003cp\u003eTVT = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{ln10}{\\mu\\:}\\)\u003c/span\u003e\u003c/span\u003e. (4)\u003c/p\u003e \u003cp\u003eThe smaller the values of HVT and TVT, the better the radiation shielding material is in shielding X-rays. Furthermore, the mean-free path MFP, is the average distance between two consecutive interactions between a photon of a given energy and the absorber material. It is related to the linear attenuation coefficient, \u0026micro;, through the following expression [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eMFP = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{\\mu\\:}\\)\u003c/span\u003e\u003c/span\u003e. (5)\u003c/p\u003e \u003cp\u003eThese parameters will be analysed for each glass sample to quantify their shielding effectiveness. The lower the MFP, the more effective a material is in shielding electromagnetic radiation. The effective atomic number is determined by analysing the linear attenuation coefficient in conjunction with the absorber\u0026rsquo;s density, as detailed in the following formula:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{Z}_{\\text{eff}}=\\frac{{\\sum\\:}_{j}{f}_{j}{A}_{j}{\\left(\\frac{\\mu\\:}{\\rho\\:}\\right)}_{j}}{{\\sum\\:}_{j}\\frac{{f}_{j}{A}_{j}}{{Z}_{j}}{\\left(\\frac{\\mu\\:}{\\rho\\:}\\right)}_{j}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere f\u003csub\u003ej\u003c/sub\u003e, A\u003csub\u003ej\u003c/sub\u003e, and Z\u003csub\u003ej\u003c/sub\u003e denote the mole fraction, atomic weight, and atomic number of each constituent element within the sample, respectively. Higher values of Z\u003csub\u003eeff\u003c/sub\u003e correspond to heightened radiation shielding efficacy exhibited by the material.\u003c/p\u003e \u003cp\u003eThe effective electron density for each glass sample is calculated from its mass attenuation coefficient using the formula below:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{N}_{eff}=\\frac{MAC}{{\\sigma\\:}_{e}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{e}\\)\u003c/span\u003e\u003c/span\u003e represents the total electronic cross-section, which is determined using the following equation:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\sigma\\:}_{e}=\\frac{\\frac{1}{{N}_{A}}\\frac{MAC}{\\sum\\:_{i}\\left({w}_{i}/{A}_{i}\\right)}}{{Z}_{eff}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this context, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{A}_{i}\\)\u003c/span\u003e\u003c/span\u003e denotes the atomic weight of the ith element in the sample, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{i}\\)\u003c/span\u003e\u003c/span\u003e represents its weight fraction. Additionally, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{A}\\)\u003c/span\u003e\u003c/span\u003e refers to Avogadro\u0026rsquo;s number.\u003c/p\u003e"},{"header":"3. Results and discussions","content":"\u003cp\u003eThe linear attenuation coefficients were obtained to investigate the radiation shielding properties of glass materials using the PHY-X/PSD simulation code, and the results were compared with the calculations performed by geant4. This section contains the discussion of our results on the linear attenuation coefficient (LAC) of the glass samples S1, S2, S3, and S4 shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Table\u0026nbsp;3 shows the comparison of the MAC values which were computed using Phy-X/PSD software and geant4. The two-simulation software\u0026rsquo;s are in excellent agreement. This provides confidence in the calculated MAC values for all four glass samples.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;3: Comparison of the mass attenuation coefficient obtained by using PHY-X/PSD and GEANT4\u003c/p\u003e\n\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"579\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"\" valign=\"bottom\" style=\"width: 35.7303%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\u003ctd colspan=\"4\" valign=\"bottom\" style=\"width: 35.7303%;\"\u003e\n \u003cp\u003eMAC (cm\u003csup\u003e2\u003c/sup\u003e/g) from PHY-X/PSD \u003c/p\u003e\n \u003c/td\u003e\u003ctd colspan=\"4\" valign=\"bottom\" style=\"width: 35.7303%;\"\u003e\n \u003cp\u003eMAC (cm\u003csup\u003e2\u003c/sup\u003e/g) from GEANT4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003eEnergy (MeV)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003eS1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003eS2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003eS3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003eS4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003eS1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003eS2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003eS3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003eS4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e1.50E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e40.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e39.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e39.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e38.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e38.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e35.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e37.61\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e37.81\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e2.00E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e29.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e30.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e31.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e32.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e28.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e26.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e30.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e30.58\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e3.00E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e10.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e10.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e10.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e11.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e9.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e9.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e10.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e10.58\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e4.00E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e4.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e5.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e5.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e5.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e4.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e4.19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e4.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e4.91\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e5.00E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e2.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e2.86\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e2.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e3.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e2.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e2.33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e2.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e2.72\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e6.00E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.79\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e1.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e1.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e1.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e1.71\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e8.00E-02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e0.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.84\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e1.00E-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e1.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e1.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e1.56\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e1.77\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e1.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e1.50E-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e2.00E-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e0.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"bottom\" style=\"width: 8.7792%;\"\u003e\n \u003cp\u003e3.00E-01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.1905%;\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.8658%;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.5281%;\"\u003e\n \u003cp\u003e0.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"bottom\" style=\"width: 6.303%;\"\u003e\n \u003cp\u003e0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e \u003cp\u003eThese MAC values were used to compute LAC values for all glass samples. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the Linear Attenuation Coefficient (LAC) for all glass samples as a function of photon energy in the 15 keV to 300 keV energy range. It demonstrates the strong correlation between the mass attenuation coefficients obtained from PHY-X/PSD and Geant4 simulations for all glass materials. The results indicate that LAC has a sharp decrease with an increase in photon energy. This trend is consistent with the literature [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. Sample S1, which has the lowest Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e content has the lowest LAC while S4 has the highest LAC in the energy range. This indicated that adding more content of Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e makes the glass material more effective at shielding X-ray energies. The linear attenuation coefficients for S1, S2, S3 and S4, range from 129.72 to 0.65 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 129.03 to 0.65 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, 135.58 to 0.69 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 137.56 to 0.70 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e respectively. It is also observed that there is an enhancement in the LAC at the photon energy of 0.1 MeV. This is because of the K-absorption edge electrons which start contributing to the photoelectric effect at the energy of 0.1 MeV.\u003c/p\u003e \u003cp\u003eTo see the effect of the Nb\u003csub\u003e2\u003c/sub\u003e0\u003csub\u003e5\u003c/sub\u003e rate in glasses regarding radiation shielding properties, the linear attenuation coefficients have been plotted as a function of the Nb\u003csub\u003e2\u003c/sub\u003e0\u003csub\u003e5\u003c/sub\u003e rate and are displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e for 0.015, 0.08 and 0.3 MeV photon energies. The figure shows that the linear attenuation coefficients increased with the increasing Nb\u003csub\u003e2\u003c/sub\u003e0\u003csub\u003e5\u003c/sub\u003e rate in glasses. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows that there is good agreement between the two calculations and that the LAC increased as the Nb\u003csub\u003e2\u003c/sub\u003e0\u003csub\u003e5\u003c/sub\u003e rate in glasses increased. This is due to the increment in glass density as Nb\u003csub\u003e2\u003c/sub\u003e0\u003csub\u003e5\u003c/sub\u003e substances increase in glasses compared to the original S1 glass sample, and this is because the higher the glass density the higher the LAC values. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the result obtained for both PHY-X/PSD and geant4 as a function of glass density. It is evident from this figure that the LAC increases as the density of the glass increases for 0.015, 0.08 and 0.3 MeV photon energies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe LAC obtained by PHY-X/PSD and geant4 has been calculated as a function of full energy between the following region 0.015\u0026ndash;0.3 MeV. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the results for S1\u0026ndash;S4, demonstrating good agreement between both simulation methods. Furthermore, this figure depicts that LAC is energy-dependent and as a result, it behaves differently in different energy regions. At low energy between 0 and 0.08 MeV there is a sharp decrease then a slight increase due to K-electron absorption and then a further decrease between 0.01 and 0.3 MeV.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe effective atomic number shown in \u003cem\u003eFig.\u0026nbsp;5\u003c/em\u003e(a) is calculated as a function of full energy between the following region 0.015\u0026ndash;0.3 MeV. The samples S1, S2, S3 and S4 demonstrate good agreement indicating that the attenuation properties are similar. At low energies between 0 and 0.08 MeV the effective atomic number stays relatively stable with a slight drop and there is a slight increase due to K-electron absorption then a further decrease between 0.01 and 0.3 MeV. The response of Zeff to increasing energy is influenced by atomic number and the density of the material indicating that heavier material exhibits greater changes in Zeff with energy variations.\u003c/p\u003e \u003cp\u003eThe effective neutron density shown in \u003cem\u003eFig.\u0026nbsp;5\u003c/em\u003e(b) exhibits notable variations across all four samples as photon energy increases. At lower energies, the N\u003csub\u003eeff\u003c/sub\u003e of all samples appears relatively stable, suggesting similar attenuation characteristics for neutron interactions. However, as photon energy increases, distinct trends emerge among all four samples. However, sample S4 demonstrates significant fluctuations, particularly at higher energies, indicating a unique response to neutron radiation. This behaviour may be attributed to the specific atomic composition and structural characteristics of the material, which could lead to differential scattering and absorption mechanisms\u003c/p\u003e\u003cp\u003eThe half-value thickness is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e as a function of photon energy. All four samples S1, S2, S3, and S4, show a very close correlation, indicating minimal variations among the samples. The graph shows a sharp increase in HVT at low photon energies (0\u0026ndash;0.1 MeV), followed by a noticeable dip around 0.1 MeV. This behavior has been reported in other studies [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. This drop corresponds to K-edge absorption, where photons have enough energy to eject K-shell electrons, leading to a sudden increase in photon interaction probability. Beyond this region, HVT rises again as Compton scattering becomes the dominant interaction mechanism, reducing the attenuation efficiency of the material.\u003c/p\u003e \u003cp\u003eThe tenth-value thickness is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e as a function of photon energy. The TVT show a similar trend as HVT, the TVT increasing at lower energies, exhibiting a sharp decrease around 0.1 MeV due to K-edge absorption, and rising again at higher energies. The K-edge absorption occurs when photon energy surpasses the binding energy of K-shell electrons, leading to an abrupt enhancement in attenuation efficiency.\u003c/p\u003e \u003cp\u003eThe mean-free path is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates the variation of Mean Free Path (MFP) with photon energy for four different samples, namely: S1, S2, S3, and S4. At lower photon energies - below 0.1 MeV, MFP increases gradually, indicating that photons interact more frequently with the material, leading to effective attenuation. However, a noticeable dip occurs around 0.1 MeV due to the K-edge absorption effect, where photons attain enough energy to eject K-shell electrons, significantly increasing interaction probability and consequently reducing MFP. After 0.1 MeV, the MFP rises again as Compton scattering becomes the dominant interaction mechanism. In this range, photons travel longer distances before undergoing interactions, leading to a higher mean free path.\u003c/p\u003e"},{"header":"4. Summary and Conclusions","content":"\u003cp\u003eIn this study, the X-ray shielding properties of bismuth-titanium-phosphate glass samples with varying Nb₂O₅ content were investigated using Phy-X/PSD simulations and validated with Geant4 calculations. The results showed that increasing the Nb₂O₅ content in the glass composition significantly enhances the shielding effectiveness. Specifically, sample S4, which contains the highest Nb₂O₅ concentration (5 mol%), exhibited the highest linear attenuation coefficient (LAC) values across the studied energy range (15 keV to 300 keV). This indicates that Nb₂O₅ contributes to improved radiation attenuation due to its higher density and atomic number.\u003c/p\u003e \u003cp\u003eThe LAC values obtained from both simulation methods were in strong agreement, confirming the reliability of the computational approach. The study also demonstrated that the mass attenuation coefficient (MAC), half-value thickness (HVT), tenth-value thickness (TVT), and mean free path (MFP) followed expected trends, further validating the effectiveness of Nb₂O₅ in enhancing X-ray shielding performance. The effective atomic number (Zeff) and effective electron density (Neff) analyses reinforced these findings, showing a clear correlation between higher Nb₂O₅ content and improved shielding characteristics.\u003c/p\u003e \u003cp\u003eOverall, this work highlights the potential of Nb₂O₅-doped bismuth-titanium-phosphate glasses as promising candidates for X-ray shielding applications, particularly in medical imaging, security screening, and radiation protection industries. Future work could explore further optimization of these materials to balance shielding performance with mechanical and optical properties.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflict of interest:\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest in this work.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding declaration\u003c/h2\u003e \u003cp\u003eNo Funding.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eLucky Makhathini - Produced the manuscript and performed the simulations.Vincent Bonginkosi Kheswa - Reading of the manuscript and calculations. Siyabonga Ntokozo Thandoluhle Majola - Reading and editing of the manuscript\u003c/p\u003e\u003ch2\u003eData availability statement:\u003c/h2\u003e \u003cp\u003eAll data presented in this article are available on request.\u003c/p\u003e \u003cp\u003e \u003cb\u003eEthical approval\u003c/b\u003e: This research work does not involve humans or animals.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eKlein RC, Weilandics C. Potential health hazards from lead shielding. Am. Ind. Hyg. Assoc J. 1996; 57(12):1124-6. doi: 10.1080/15428119691014215.\u003c/li\u003e\n\u003cli\u003eTekin HO, ALMisned G, Zakaly HMH, Zamil A, Khoucheich D, Bilal G, et al. Gamma, neutron, and heavy charged ion shielding properties of Er\u003csup\u003e3+\u003c/sup\u003e-doped and Sm\u003csup\u003e3+\u003c/sup\u003e-doped zinc borate glasses. Open Chem. 2022; 20: 130-45. doi: 10.1515/chem-2022-0128.\u003c/li\u003e\n\u003cli\u003eWaly ESA, Fusco MA, Bourham MA. 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Solids 2022;163:110543. https://doi.org/10.1016/j.jpcs.2021.110543 \u003c/li\u003e\n\u003cli\u003eSolak BB, Aktas B, Yilmaz D, Kalecik S, Yalcin S, Acikgoz A, Demircan G. Exploring the radiation shielding properties of B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e-PbO-TeO\u003csub\u003e2\u003c/sub\u003e-CeO\u003csub\u003e2\u003c/sub\u003e-WO\u003csub\u003e3\u003c/sub\u003e glasses: A comprehensive study on structural, mechanical, gamma, and neutron attenuation characteristics. Mater. Chem. Phys. 2024;312:128672. https://doi.org/10.1016/j.matchemphys.2023.128672 \u003c/li\u003e\n\u003cli\u003eYorulmaz N, Yasar MM, Acikgoz A, Kavun Y, Demircan G, Kamislioglu M, Aktas B, Ulas EO. Influence of Gd\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e on structural, optical, radiation shielding, and mechanical properties of borate glasses. Opt. 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Impact of Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e on radiation shielding properties of the bismuth-titanium-phosphate glasses. Optik 2023;274:170511. https://doi.org/10.1016/j.ijleo.2023.170511 \u003c/li\u003e\n\u003cli\u003ehttps://phy-x.net/PSD.\u003c/li\u003e\n\u003cli\u003eSakar E, Ozpolat O, Alım B, Sayyed M, Kurudirek M. Phy-X/PSD: Development of a user friendly online software for calculation of parameters relevant to radiation shielding and dosimetry. Radiat Phys Chem. 2020;166:108496. doi: 10.1016/j.radphyschem.2019.108496.\u003c/li\u003e\n\u003cli\u003eAkyildirim H, Kavazb E, El-Agawany F, Yousef E, Rammah Y. Radiation shielding features of zirconolite silicate glasses using XCOM and FLUKA simulation code. J Non Cryst Solids. 2020;545:120245. doi: 10.1016/j.jnoncrysol.2020.120245.\u003c/li\u003e\n\u003cli\u003eSayyed MI, Mahmoud KA, Tashlykov OL, Khandaker MU, Faruque MRI. Enhancement of the shielding capability of soda\u0026ndash;lime glasses with Sb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e dopant: A potential material for radiation safety in nuclear installations. Appl Sci. 2021;11:326. doi: 10.3390/app11010326. \u003c/li\u003e\n\u003cli\u003ehttps://geant4.web.cern.ch/\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"bismuth-titanium-phosphate glass, x-ray shielding, LAC, MAC, radiation shielding","lastPublishedDoi":"10.21203/rs.3.rs-6287971/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6287971/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this work, the x-ray shielding properties of novel 45Na\u003csub\u003e2\u003c/sub\u003eO\u0026thinsp;+\u0026thinsp;10 Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e + (5 - x)TiO\u003csub\u003e2\u003c/sub\u003e + (x) Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;40 P\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e, were x\u0026thinsp;=\u0026thinsp;0, 1, 3, 5 mol%, glass materials were studied using the Phy-X/PSD software and geant4 was used to validate the funding\u0026rsquo;s. The results revealed that sample S1 (with no Nb₂O₅) exhibited the lowest LAC (ranging from 95,129.721 cm⁻\u0026sup1; at 15 keV to 2.956 cm⁻\u0026sup1; at 80 keV), whereas sample S4 (with 5 mol% Nb₂O₅) had the highest LAC, confirming that increasing Nb₂O₅ enhances X-ray shielding. The sample S4 with 5 mol% of Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e has the highest linear attenuation coefficient (6.861\u0026ndash;0.703 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e) at photon energies between 80 to 300 keV. These calculations indicated that adding more Nb\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e5\u003c/sub\u003e content makes the glass more effective for shielding X-rays in this low energy range.\u003c/p\u003e","manuscriptTitle":"Theoretical investigation of X-ray shielding properties of bismuth-titanium-phosphate glass materials","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-16 10:50:00","doi":"10.21203/rs.3.rs-6287971/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0b79f8ae-6ee7-40e5-9282-ae12a5d875d4","owner":[],"postedDate":"May 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-18T03:39:02+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-16 10:50:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6287971","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6287971","identity":"rs-6287971","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}