Comparative Study of Gamma Radiation Shielding Parameters of BaO, Dy2O3 and Co-doped Bismuth Borate Glasses

Comparative Study of Gamma Radiation Shielding Parameters of BaO, Dy2O3 and Co-doped Bismuth Borate Glasses | 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 Comparative Study of Gamma Radiation Shielding Parameters of BaO, Dy 2 O 3 and Co-doped Bismuth Borate Glasses Shah Zeb Ullah, Mubashir Ahmad This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7034073/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this work, we investigated the effectiveness of bismuth borate glass doped with Dy 2 O 3 , BaO, and co-doped systems for a variety of radiation shielding uses. Within the various energy ranges (MeV), the linear attenuation coefficients (LAC) and mass attenuation coefficients (MAC) for glasses with the compositions 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O 3 , 20BaO + 60B 2 O 3 + 20Bi 2 O 3 , and 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 were computed via the Phy-X/PSD simulation code. The acquired mass attenuation coefficients are further utilized to determine the effective atomic number (Zeff), half value layer (HVL), and mean free path (MFP) of the glasses. The co-doped glass containing BaO and Dy 2 O 3 was shown to have greater gamma-ray shielding efficacy due to higher LAC, MAC, and effective atomic number values significantly reduced HVL and MFP values. By changing the photon energy, densities, or chemical composition of the glass samples, the substantial variations in all interaction parameters were observed. A co-doped bismuth borate glass sample comprising BaO and Dy 2 O 3 exhibited superior shielding capabilities. These findings suggested that a glass sample with 20BaO + 60 B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 is an effective radiation shielding material. High Energy and Particle Physics Computational Physics Phy-X/PSD Bismuth Borate glass Gamma rays Dysprosium Shielding Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction Diverse glass systems doped with rare-earth ions have lately gained extensive scientific interest due to their distinct properties, especially in the field of high-energy physics for the assessment of particle energy [ 1 – 3 ]. Heavy metal oxide glasses are becoming more prevalent in this field. The most important interaction parameters are the mass attenuation coefficient, mean free path, exposure buildup factors, effective atomic number, and electron density [ 4 , 5 ]. Typical lead-based radiation Shields are frequently employed for ionizing radiation shielding due to their superior physical properties. The biggest danger caused by lead is a hazardous chemical that accumulates and lingers in the environment, creating a serious health concern [ 6 , 7 ]. Radioactive isotopes have been employed in many livelihoods, including nuclear research, medicine, industry, and agriculture [ 8 – 10 ]. The usage of these radioactive isotopes can endanger employees and expose tissues [ 11 ]. Transparent radiation shielding materials have been a curious field in nuclear engineering because they provide effective radiation protection while retaining the ability to see through them. [ 12 ]. Glasses have been discovered to accomplish the dual functions of being transparent to visible light and absorbing radiation, therefore protecting the viewer from radiation [ 13 ]. Thus, due to their distinctive features, such as high density, non-toxicity, high refractive index, extraordinary third-order nonlinear optical susceptibility, enhanced radioactive resistance, resistance to moistness and long infrared cut-off wavelengths, there has recently been a revival in interest in the preparation of HMO glasses like bismuth oxide (Bi 2 O 3 ) containing glasses as a replacement for PbO, For radiation shielding purposes [ 14 – 16 ]. Borate is a well-known glass forming that has received extensive research due to its several appealing properties such as excellent transparency, exceptional chemical resistance, robust thermal stability, and superior solubility for rare earth ions [ 17 ]. When barium oxide (BaO) is combined with borate oxide (B 2 O 3 ), barium borate (BaO-B 2 O 3 ) glass is formed, which traverses all radiation shielding criteria. A variety of theoretical, experimental and Monte Carlo simulation investigations have been conducted to explore the radiation shielding capabilities of various BaO-B 2 O 3 glass mixtures [ 18 – 20 ]. To examine the relationship between shielding materials and γ-rays, the Linear Attenuation Coefficient (LAC), Mass Attenuation Coefficient (MAC), Half Value Layer (HVL), Mean Free Path (MFP), and Effective Atomic Number (Zeff) are often used parameters. In this work, 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O 3 [ 21 ], 20BaO + 60B 2 O 3 + 20Bi 2 O 3 [ 22 ] and 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 [ 22 ] glasses have been selected. An analysis has been conducted on the potential of utilizing these systems for gamma radiation shielding, employing the PhyX/PSD platform to compute the MAC, MFP, HVL, and Z eff . 2. Materials and Method 2.1 Materials The glass samples investigated in this work were chosen from previous research results as 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O, 20BaO + 60B 2 O 3 + 20Bi 2 O 3 and 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 . The chemical composition and density of the selected glass samples are presented in Table 01 . 2.2 Method The radiation shielding features of bismuth borate glasses, the chemical compositions of which are shown in Table 01 , have been investigated using Phy-X/PSD computations; The web application Phy-X/PSD was created by Şakar et al. [ 23 ] and is capable of calculating a multitude of shielding parameters at varying energies. It is written using Nginx 1.15.8 and NodeJS v8.4.0. 256-bit PositiveSSL is used to create security between the client browser and the server. The Phy-X/PSD program is available online at https://phy-x.net/ and is open source. Table 01 The density and chemical composition of chosen rare earth and barium-doped glasses. Sample code Chemical composition Density (gcm − 3 ) Ref. BBiDy 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O 3 4.964 [ 21 ] BaBBi 20 BaO + 60B 2 O 3 + 20Bi 2 O 3 6.375 [ 22 ] BaBBiDy 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 6.876 [ 22 ] 2.2.1. Theoretical background Beer Lambert's law has described the gamma photon attenuation process as [ 16 ]: $$\:I={I}_{o}\:{e}^{-\mu\:t}$$ 1 I o and I indicate the incoming and transmitted photon beam intensities, t is the thickness of the absorber and µ represents linear attenuation coefficient (LAC). The LAC uses cm − 1 to express the likelihood of photon interactions per unit length. The absorber's Mass Attenuation Coefficient (MAC) is derived by dividing LAC values by absorber density and represented as cm 2 /g. The MAC describes γ-ray penetration and interaction with absorbing materials and may potentially be determined via mixing rule [ 24 ]. MAC = µ m = \(\:\frac{\:\mu\:}{\rho\:}\) = \(\:{\sum\:}_{i}^{\:}Wi\left(\left(\frac{\mu\:}{\rho\:}\right)\right)\) (2) In the above formula, Wi represents the weight fraction of the ith constituent element, and (µ/ρ)i represents the mass attenuation coefficient of the ith constituent element of glass samples. Half Value Layer (HVL) is a crucial metric for assessing the shielding properties of gamma rays and calculating the amount of gamma radiation that penetrates the sample. It represents the thickness of medium that diminishes incident photon intensity by 50% and illustrates photon penetrating capacity as energy increases. HVL = \(\:\frac{ln\:2\:}{\mu\:}\) (3) The Mean Free Path (MFP) is the mean length between the two subsequent photon collisions for the shielding material is given by Ref. [ 25 ]. MFP = \(\:\frac{1}{\mu\:}\) (4) Another important parameter, effective atomic number (Zeff) relate to the gamma-ray attenuation caused by partial photon interactions with matter. Z eff may be computed using the following relationships. Z eff = \(\:\frac{{\sum\:}_{i}^{\:}fiAi\left(\:\frac{\:\mu\:}{\rho\:}\right)i}{{\sum\:}_{j}^{\:}\frac{Aj}{Zj}\left(\frac{\mu\:}{\rho\:}\right)j}\) (5) In the above relation, f i , A i and Z j represent to the fractional abundance, atomic weight and atomic number respectively of the i th constituent element. 3. Results and Discussion Table 01 displays the density and chemical composition of the glass samples utilized in this investigation. LAC, MAC, HVL, MFP, and Zeff changes with incoming photon energy are illustrated in Figures form 1–5. Figures 1 and 2 provide a comparison of the LAC and MAC of selected glasses. Figure 3 depicts the estimated half-value layer thickness of the glasses. Figure 4 depicts the computed mean free path. Effective atomic numbers were calculated using MAC values as shown in Fig. 5 . 3.1 Linear attenuation coefficient The linear attenuation coefficient (LAC) of glass samples distinctively doped with Dy 3+ and Ba are close to each other in Fig. 1 , but Co-doped glass samples have a substantially broader value at a given energy range. For photons energy range of 0.2 to 0.35 MeV, BBiDy and BaBBi glasses exhibit very steep declines in LAC, but BaBBiDy glass has a gentler drop. After 0.75 MeV, distinctly doped samples become parallel to the energy axis, but co-doped samples exhibit a little increase in LAC at higher energies. At energy 0.3 M eV, Ba-doped glass has a slightly higher LAC than Dy-doped glass, which is 1.75 cm − 1 and 1.48 cm − 1 , respectively, whereas Ba and Dy 3+ co-doped glass has 35 cm − 1 . 3.2 Mass attenuation Coefficient Figure 2 depicts the fluctuation of mass attenuation coefficients with incoming photon energy ranging from 0.1 MeV to 1.5 MeV for the chosen glasses. The MAC of chosen samples demonstrates that co-doped samples have a greater MAC than distinct doped glasses with Ba and Dy 3+ . Clearly, as shown in Fig. 2, the values of MAC for all glass samples decline exponentially as photon energy increases. It is also noted that the MAC values of the chosen glass systems are quite large in the lower energy region (i.e E < 0.15 MeV) and for Co-doped glass (E < 0.3 MeV) and diminish slickly as the energy increases. . Figure 2 Mass attenuation coefficient of investigated glass samples The rapid decline in LAC and MAC readings in the region of low energy is caused by photoelectric effect, which dominates in the low energy range. There is a modest drop in the intermediate energy zone, which may be attributed to the dominance of Compton scattering process. Following that, the values gradually grow in the high energy area in Fig. 1 because of the pair production process [ 4 , 26 , 27 ]. 3.3 Half Value Layer (HVL) HVL is a useful parameter for determining a material's Ⓒ-ray shielding potential. HVL is the material’s thickness that reduces the intensity of impacting beam by half. The relationship between HVL values and photon energy for investigated glasses is shown in Fig. 3 . The density and composition of the glasses, as shown in Fig. 3 , have an effect on HVL values. Figure 3 depicts the HVL values of the existing glass systems and their fluctuations across Ⓒ-ray energy, in the range (0–4 MeV). It is discovered that the HVL values stay roughly constant for photon energies greater than 4 MeV, then quickly rise to their maximum value at 4 MeV. At photon energies about 200 keV (i.e in low energy region), the HVLs are relatively small and fall between 0.01 and 0.2 cm.. As mentioned in the mass attenuation coefficients above, the dominance of distinct photon interaction mechanisms in various energy regions may account for the variation in HVL with photon energy for the present glasses [ 28 , 29 ]. The bismuth borate glasses' HVL values drop with the incorporation of Ba and Dy 3+ content, as seen in Fig. 3 . Remarkably, lower HVL levels are essential for an efficient gamma ray shielding material since they increase the potential for interactions between the substance and photons. As a result, We may conclude that the glass with the highest density, MAC value, and lowest HVL has superior shielding capabilities compared to the other samples. 3.4 Mean Free Path (MFP) This parameter indicates the average distance traveled between two consecutive photon encounters. A shorter MFP indicates that a material has more gamma-ray interactions, which has higher shielding qualities. It is essential to match the MFP values of investigated glass systems in order to analyze them for the real-world applications. For this, Fig. 2 displays the MFP variation of all selected glass samples with incoming gamma-ray energies ranging from 0 to 50 MeV after the MFP values for the current glasses were compared. The MFP varied between 0 and 0.003 cm for Dy3 + and Ba glass samples and nearly zero for co-doped bismuth borate glasses, clearly tending to its lowest values at low energy (for 20 keV). The MFP then grows fast as the incident energy increases for (Dy 3+ and Ba) bismuth borate glasses due to the photoelectric cross-section. The MFP steadily decreases as input energy rises in the middle energy range because of the Compton scattering cross-section [ 30 ], which only depends on the atomic number of the attenuator, while there is a low variation in the MFP of co-doped glass sample at high energy (50 MeV) due to the pair production cross section [ 31 ]. The MFP reaches its maximum at high energies (for 5 MeV), and it varies between 5.35, 4.28 cm, and 0.028 cm for Dy 3+ , Ba, and co-doped bismuth borate glasses, respectively. The sample with the lowest MFP is BaBBiDy, whereas the sample with the greatest MFP is BBiDy. Based on these findings, we may conclude that co-doped bismuth borate glasses could be created as radiation shielding materials. 3.5 Effective Atomic Number (Z eff ) It is a crucial variable computed in nuclear research and materials science. Z eff represents a compound's or mixture's average atomic number. Our investigations into the glass samples' gamma radiation shielding characteristics are crucial for determining the Zeff value. According to Fig. 5 , the Z eff value has reached its maximum range E < 0.1 MeV. The Z eff value drops dramatically from 0.12 MeV to 0.68 MeV as seen in Fig. 5 , after which the rate of dropout slows. The changes in the Zeff function reveal that the energy-dependent nature of the photons' interactions with the absorbing material [ 32 – 34 ]. For this interaction, the consequences of the photoelectric effects are significant. Additionally, it can be shown in Fig. 5 that the Z eff function for co-doped glass is roughly constant at an energy value of 0.68 MeV despite an increase in energy, but for other samples, it is constant up to 1.9 MeV before beginning to surge with an increase in photon energy. The Z eff of the Co-doped glass was discovered to be the largest of the chosen glasses. As a result, the BaBBiDy glass has demonstrated the highest level of γ–ray shielding proficiency. 4. Conclusion This study looked at the effectiveness of three doped bismuth borate glasses for shielding against gamma radiation (Dy 2 O 3 , BaO, and Dy 2 O 3 + BaO). The program Phy-X/PSD has been utilized to simulate the linear attenuation coefficient (LAC) and mass attenuation coefficient (MAC) for photon energies between 0–20 MeV and 0.1–1.5 MeV, respectively. Numerous Ⓒ-ray shielding parameters of the glasses have been evaluated and compared using the LAC and MAC values. These parameters include the mean free path (MFP), half value layer (HVL), and effective atomic number (Zeff). Findings indicate that: The glass sample 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 with density (6.375 g/cm − 3 ) had the greatest LAC and MAC, whereas the glass sample 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O 3 with density (4.964 g/cm − 3 ) had the lowest LAC and MAC. The sample 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 has a lowest HVL that ranged from 0 to 0.01 cm for gamma ray energies between 0 MeV and 4 MeV. The samples 20BaO + 60B 2 O 3 + 20Bi 2 O 3 and 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O 3 had the greatest HVL, measuring 3.57 cm and 2.81 cm, respectively. Co-doped glass samples has lowest mean free path equate to the other sample that evidence that attenuation will be greater and varied between 0 and 0.003 cm for (Dy 3+ and Ba) and for co-doped bismuth borate glasses nearly zero in for same energy range. The glass samples with the greatest and lowest Zeff values were 20BaO + 60B 2 O 3 + 20Bi 2 O 3 and 70B 2 O 3 + 29Bi 2 O 3 + 1Dy 2 O 3 , respectively, varying between 72.51–29.64 and 68.37–28.39 accordingly. The glass sample with the lowest Zeff value was 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 , varying between 44.97 and 13. The glass sample 20BaO + 60B 2 O 3 + 19Bi 2 O 3 + 1Dy 2 O 3 has strong shielding qualities comparable to other competent glass samples, one may believe. 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RB (2021) MUTLU, An investigation on radiation shielding properties of borosilicate glass systems, International Journal of Computational and Experimental Science and Engineering , vol. 7, pp. 99–108 Sayyed M, Lakshminarayana G, Moghaddasi M, Kityk I, Mahdi M (2018) Physical properties, optical band gaps and radiation shielding parameters exploration for Dy 3+-doped alkali/mixed alkali multicomponent borate glasses. Glass Phys Chem 44:279–291 Additional Declarations The authors declare no competing interests. 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. 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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-7034073","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":479945903,"identity":"1b50d26c-3bd7-4a3a-a9f3-053b881eb2fa","order_by":0,"name":"Shah Zeb 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glass\u003c/p\u003e","description":"","filename":"image.png","url":"https://assets-eu.researchsquare.com/files/rs-7034073/v1/6ea0e9de7bb25e1aa5bfa88e.png"},{"id":86463780,"identity":"29aa6fb1-3ed2-44e1-afef-ec3c8917ad96","added_by":"auto","created_at":"2025-07-11 02:49:16","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":107919,"visible":true,"origin":"","legend":"\u003cp\u003eMass attenuation coefficient of investigated glass samples\u003c/p\u003e","description":"","filename":"image.png","url":"https://assets-eu.researchsquare.com/files/rs-7034073/v1/ff6ef53b6dd1686871086042.png"},{"id":86463778,"identity":"28816c7d-de03-42bb-9053-39bdff1d7a35","added_by":"auto","created_at":"2025-07-11 02:49:16","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":68060,"visible":true,"origin":"","legend":"\u003cp\u003eEffective atomic Number (HVL) of selected glass compared\u003c/p\u003e","description":"","filename":"image.png","url":"https://assets-eu.researchsquare.com/files/rs-7034073/v1/0ae7e4ece7a9de014443c324.png"},{"id":86464756,"identity":"bee10358-5dbb-4577-b4af-f3fc12fd23c4","added_by":"auto","created_at":"2025-07-11 03:05:17","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":111007,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of\u003cstrong\u003e \u003c/strong\u003eMean Free Path (MFP) values of the investigated glass samples\u003c/p\u003e","description":"","filename":"image.png","url":"https://assets-eu.researchsquare.com/files/rs-7034073/v1/230a6b144137da327c64fc48.png"},{"id":86464757,"identity":"34912452-1cd6-48e2-8e78-2c23518f921a","added_by":"auto","created_at":"2025-07-11 03:05:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":72682,"visible":true,"origin":"","legend":"\u003cp\u003eEffective atomic Number of selected glass compared\u003c/p\u003e","description":"","filename":"image.png","url":"https://assets-eu.researchsquare.com/files/rs-7034073/v1/87f131f1c02c0ea0ca29bcd2.png"},{"id":86465213,"identity":"63cba2f1-dcfd-42fa-a575-204fef3bde89","added_by":"auto","created_at":"2025-07-11 03:13:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":951215,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7034073/v1/f59c28ae-817d-42e2-bbb6-d177e2c3a065.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eComparative Study of Gamma Radiation Shielding Parameters of BaO, Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and Co-doped Bismuth Borate Glasses\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eDiverse glass systems doped with rare-earth ions have lately gained extensive scientific interest due to their distinct properties, especially in the field of high-energy physics for the assessment of particle energy [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Heavy metal oxide glasses are becoming more prevalent in this field. The most important interaction parameters are the mass attenuation coefficient, mean free path, exposure buildup factors, effective atomic number, and electron density [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Typical lead-based radiation Shields are frequently employed for ionizing radiation shielding due to their superior physical properties. The biggest danger caused by lead is a hazardous chemical that accumulates and lingers in the environment, creating a serious health concern [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Radioactive isotopes have been employed in many livelihoods, including nuclear research, medicine, industry, and agriculture [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. The usage of these radioactive isotopes can endanger employees and expose tissues [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Transparent radiation shielding materials have been a curious field in nuclear engineering because they provide effective radiation protection while retaining the ability to see through them. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Glasses have been discovered to accomplish the dual functions of being transparent to visible light and absorbing radiation, therefore protecting the viewer from radiation [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. Thus, due to their distinctive features, such as high density, non-toxicity, high refractive index, extraordinary third-order nonlinear optical susceptibility, enhanced radioactive resistance, resistance to moistness and long infrared cut-off wavelengths, there has recently been a revival in interest in the preparation of HMO glasses like bismuth oxide (Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e) containing glasses as a replacement for PbO, For radiation shielding purposes [\u003cspan additionalcitationids=\"CR15\" citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Borate is a well-known glass forming that has received extensive research due to its several appealing properties such as excellent transparency, exceptional chemical resistance, robust thermal stability, and superior solubility for rare earth ions [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. When barium oxide (BaO) is combined with borate oxide (B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e), barium borate (BaO-B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e) glass is formed, which traverses all radiation shielding criteria. A variety of theoretical, experimental and Monte Carlo simulation investigations have been conducted to explore the radiation shielding capabilities of various BaO-B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e glass mixtures [\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eTo examine the relationship between shielding materials and γ-rays, the Linear Attenuation Coefficient (LAC), Mass Attenuation Coefficient (MAC), Half Value Layer (HVL), Mean Free Path (MFP), and Effective Atomic Number (Zeff) are often used parameters. In this work, 70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;20Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] and 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] glasses have been selected. An analysis has been conducted on the potential of utilizing these systems for gamma radiation shielding, employing the PhyX/PSD platform to compute the MAC, MFP, HVL, and Z\u003csub\u003eeff\u003c/sub\u003e.\u003c/p\u003e"},{"header":"2. Materials and Method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Materials\u003c/h2\u003e\u003cp\u003eThe glass samples investigated in this work were chosen from previous research results as 70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO, 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;20Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e. The chemical composition and density of the selected glass samples are presented in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e01\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2 Method\u003c/h2\u003e\u003cp\u003eThe radiation shielding features of bismuth borate glasses, the chemical compositions of which are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e01\u003c/span\u003e, have been investigated using Phy-X/PSD computations; The web application Phy-X/PSD was created by Şakar et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] and is capable of calculating a multitude of shielding parameters at varying energies. It is written using Nginx 1.15.8 and NodeJS v8.4.0. 256-bit PositiveSSL is used to create security between the client browser and the server. The Phy-X/PSD program is available online at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://phy-x.net/\u003c/span\u003e\u003cspan address=\"https://phy-x.net/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e and is open source.\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 01\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eThe density and chemical composition of chosen rare earth and barium-doped glasses.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" 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\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSample code\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eChemical composition\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDensity (gcm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eRef.\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBBiDy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.964\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBaBBi\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e20 BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;20Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6.375\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBaBBiDy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6.876\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\u003ch2\u003e2.2.1. Theoretical background\u003c/h2\u003e\u003cp\u003eBeer Lambert's law has described the gamma photon attenuation process as [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:I={I}_{o}\\:{e}^{-\\mu\\:t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003eo\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eI\u003c/em\u003e indicate the incoming and transmitted photon beam intensities, \u003cem\u003et\u003c/em\u003e is the thickness of the absorber and \u003cem\u003e\u0026micro;\u003c/em\u003e represents linear attenuation coefficient (LAC). The LAC uses cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e to express the likelihood of photon interactions per unit length. The absorber's Mass Attenuation Coefficient (MAC) is derived by dividing LAC values by absorber density and represented as cm\u003csup\u003e2\u003c/sup\u003e/g. The MAC describes γ-ray penetration and interaction with absorbing materials and may potentially be determined via mixing rule [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eMAC\u0026thinsp;=\u0026thinsp;\u0026micro;\u003csub\u003em\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{\\:\\mu\\:}{\\rho\\:}\\)\u003c/span\u003e\u003c/span\u003e= \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sum\\:}_{i}^{\\:}Wi\\left(\\left(\\frac{\\mu\\:}{\\rho\\:}\\right)\\right)\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn the above formula, \u003cem\u003eWi\u003c/em\u003e represents the weight fraction of the \u003cem\u003eith\u003c/em\u003e constituent element, and \u003cem\u003e(\u0026micro;/ρ)i\u003c/em\u003e represents the mass attenuation coefficient of the \u003cem\u003eith\u003c/em\u003e constituent element of glass samples.\u003c/p\u003e\u003cp\u003eHalf Value Layer (HVL) is a crucial metric for assessing the shielding properties of gamma rays and calculating the amount of gamma radiation that penetrates the sample. It represents the thickness of medium that diminishes incident photon intensity by 50% and illustrates photon penetrating capacity as energy increases.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eHVL = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{ln\\:2\\:}{\\mu\\:}\\)\u003c/span\u003e\u003c/span\u003e (3)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe Mean Free Path (MFP) is the mean length between the two subsequent photon collisions for the shielding material is given by Ref. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eMFP = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{\\mu\\:}\\)\u003c/span\u003e\u003c/span\u003e (4)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAnother important parameter, effective atomic number (Zeff) relate to the gamma-ray attenuation caused by partial photon interactions with matter. Z\u003csub\u003eeff\u003c/sub\u003e may be computed using the following relationships.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eZ\u003csub\u003eeff\u003c/sub\u003e = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{{\\sum\\:}_{i}^{\\:}fiAi\\left(\\:\\frac{\\:\\mu\\:}{\\rho\\:}\\right)i}{{\\sum\\:}_{j}^{\\:}\\frac{Aj}{Zj}\\left(\\frac{\\mu\\:}{\\rho\\:}\\right)j}\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn the above relation, \u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eA\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e represent to the fractional abundance, atomic weight and atomic number respectively of the \u003cem\u003ei\u003c/em\u003eth constituent element.\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e01\u003c/span\u003e displays the density and chemical composition of the glass samples utilized in this investigation. LAC, MAC, HVL, MFP, and Zeff changes with incoming photon energy are illustrated in Figures form 1\u0026ndash;5. Figures\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and 2 provide a comparison of the LAC and MAC of selected glasses. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e depicts the estimated half-value layer thickness of the glasses. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e depicts the computed mean free path. Effective atomic numbers were calculated using MAC values as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e3.1 Linear attenuation coefficient\u003c/h2\u003e\u003cp\u003eThe linear attenuation coefficient (LAC) of glass samples distinctively doped with Dy\u003csup\u003e3+\u003c/sup\u003e and Ba are close to each other in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, but Co-doped glass samples have a substantially broader value at a given energy range. For photons energy range of 0.2 to 0.35 MeV, BBiDy and BaBBi glasses exhibit very steep declines in LAC, but BaBBiDy glass has a gentler drop. After 0.75 MeV, distinctly doped samples become parallel to the energy axis, but co-doped samples exhibit a little increase in LAC at higher energies. At energy 0.3 M eV, Ba-doped glass has a slightly higher LAC than Dy-doped glass, which is 1.75 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 1.48 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, respectively, whereas Ba and Dy\u003csup\u003e3+\u003c/sup\u003e co-doped glass has 35 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Mass attenuation Coefficient\u003c/h2\u003e\u003cp\u003eFigure 2 depicts the fluctuation of mass attenuation coefficients with incoming photon energy ranging from 0.1 MeV to 1.5 MeV for the chosen glasses. The MAC of chosen samples demonstrates that co-doped samples have a greater MAC than distinct doped glasses with Ba and Dy\u003csup\u003e3+\u003c/sup\u003e. Clearly, as shown in Fig.\u0026nbsp;2, the values of MAC for all glass samples decline exponentially as photon energy increases. It is also noted that the MAC values of the chosen glass systems are quite large in the lower energy region (i.e E\u0026thinsp;\u0026lt;\u0026thinsp;0.15 MeV) and for Co-doped glass (E\u0026thinsp;\u0026lt;\u0026thinsp;0.3 MeV) and diminish slickly as the energy increases.\u003c/p\u003e\u003cp\u003e.\u003c/p\u003e\u003cp\u003e\u003cb\u003eFigure\u0026nbsp;2\u003c/b\u003e Mass attenuation coefficient of investigated glass samples\u003c/p\u003e\u003cp\u003eThe rapid decline in LAC and MAC readings in the region of low energy is caused by photoelectric effect, which dominates in the low energy range. There is a modest drop in the intermediate energy zone, which may be attributed to the dominance of Compton scattering process. Following that, the values gradually grow in the high energy area in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e because of the pair production process [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Half Value Layer (HVL)\u003c/h2\u003e\u003cp\u003eHVL is a useful parameter for determining a material's Ⓒ-ray shielding potential. HVL is the material\u0026rsquo;s thickness that reduces the intensity of impacting beam by half. The relationship between HVL values and photon energy for investigated glasses is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The density and composition of the glasses, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e, have an effect on HVL values. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e depicts the HVL values of the existing glass systems and their fluctuations across Ⓒ-ray energy, in the range (0\u0026ndash;4 MeV). It is discovered that the HVL values stay roughly constant for photon energies greater than 4 MeV, then quickly rise to their maximum value at 4 MeV. At photon energies about 200 keV (i.e in low energy region), the HVLs are relatively small and fall between 0.01 and 0.2 cm.. As mentioned in the mass attenuation coefficients above, the dominance of distinct photon interaction mechanisms in various energy regions may account for the variation in HVL with photon energy for the present glasses [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. The bismuth borate glasses' HVL values drop with the incorporation of Ba and Dy\u003csup\u003e3+\u003c/sup\u003e content, as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Remarkably, lower HVL levels are essential for an efficient gamma ray shielding material since they increase the potential for interactions between the substance and photons. As a result, We may conclude that the glass with the highest density, MAC value, and lowest HVL has superior shielding capabilities compared to the other samples.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.4 Mean Free Path (MFP)\u003c/h2\u003e\u003cp\u003eThis parameter indicates the average distance traveled between two consecutive photon encounters. A shorter MFP indicates that a material has more gamma-ray interactions, which has higher shielding qualities. It is essential to match the MFP values of investigated glass systems in order to analyze them for the real-world applications. For this, Fig.\u0026nbsp;2 displays the MFP variation of all selected glass samples with incoming gamma-ray energies ranging from 0 to 50 MeV after the MFP values for the current glasses were compared. The MFP varied between 0 and 0.003 cm for Dy3\u0026thinsp;+\u0026thinsp;and Ba glass samples and nearly zero for co-doped bismuth borate glasses, clearly tending to its lowest values at low energy (for 20 keV). The MFP then grows fast as the incident energy increases for (Dy\u003csup\u003e3+\u003c/sup\u003e and Ba) bismuth borate glasses due to the photoelectric cross-section. The MFP steadily decreases as input energy rises in the middle energy range because of the Compton scattering cross-section [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], which only depends on the atomic number of the attenuator, while there is a low variation in the MFP of co-doped glass sample at high energy (50 MeV) due to the pair production cross section [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. The MFP reaches its maximum at high energies (for 5 MeV), and it varies between 5.35, 4.28 cm, and 0.028 cm for Dy\u003csup\u003e3+\u003c/sup\u003e, Ba, and co-doped bismuth borate glasses, respectively. The sample with the lowest MFP is BaBBiDy, whereas the sample with the greatest MFP is BBiDy. Based on these findings, we may conclude that co-doped bismuth borate glasses could be created as radiation shielding materials.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.5 Effective Atomic Number (Z\u003csub\u003eeff\u003c/sub\u003e)\u003c/h2\u003e\u003cp\u003eIt is a crucial variable computed in nuclear research and materials science. Z\u003csub\u003eeff\u003c/sub\u003e represents a compound's or mixture's average atomic number. Our investigations into the glass samples' gamma radiation shielding characteristics are crucial for determining the Zeff value. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the Z\u003csub\u003eeff\u003c/sub\u003e value has reached its maximum range E\u0026thinsp;\u0026lt;\u0026thinsp;0.1 MeV. The Z\u003csub\u003eeff\u003c/sub\u003e value drops dramatically from 0.12 MeV to 0.68 MeV as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e, after which the rate of dropout slows. The changes in the Zeff function reveal that the energy-dependent nature of the photons' interactions with the absorbing material [\u003cspan additionalcitationids=\"CR33\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. For this interaction, the consequences of the photoelectric effects are significant. Additionally, it can be shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e that the Z\u003csub\u003eeff\u003c/sub\u003e function for co-doped glass is roughly constant at an energy value of 0.68 MeV despite an increase in energy, but for other samples, it is constant up to 1.9 MeV before beginning to surge with an increase in photon energy. The Z\u003csub\u003eeff\u003c/sub\u003e of the Co-doped glass was discovered to be the largest of the chosen glasses. As a result, the BaBBiDy glass has demonstrated the highest level of γ\u0026ndash;ray shielding proficiency.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis study looked at the effectiveness of three doped bismuth borate glasses for shielding against gamma radiation (Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, BaO, and Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;BaO). The program Phy-X/PSD has been utilized to simulate the linear attenuation coefficient (LAC) and mass attenuation coefficient (MAC) for photon energies between 0\u0026ndash;20 MeV and 0.1\u0026ndash;1.5 MeV, respectively. Numerous Ⓒ-ray shielding parameters of the glasses have been evaluated and compared using the LAC and MAC values. These parameters include the mean free path (MFP), half value layer (HVL), and effective atomic number (Zeff). Findings indicate that:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe glass sample 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with density (6.375 g/cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e) had the greatest LAC and MAC, whereas the glass sample 70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e with density (4.964 g/cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e) had the lowest LAC and MAC.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe sample 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e has a lowest HVL that ranged from 0 to 0.01 cm for gamma ray energies between 0 MeV and 4 MeV. The samples 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;20Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and 70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e had the greatest HVL, measuring 3.57 cm and 2.81 cm, respectively.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eCo-doped glass samples has lowest mean free path equate to the other sample that evidence that attenuation will be greater and varied between 0 and 0.003 cm for (Dy\u003csup\u003e3+\u003c/sup\u003e and Ba) and for co-doped bismuth borate glasses nearly zero in for same energy range.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe glass samples with the greatest and lowest Zeff values were 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;20Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e and 70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, respectively, varying between 72.51\u0026ndash;29.64 and 68.37\u0026ndash;28.39 accordingly. The glass sample with the lowest Zeff value was 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, varying between 44.97 and 13.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eThe glass sample 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e has strong shielding qualities comparable to other competent glass samples, one may believe.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eChiodini N, Vedda A, Veronese I (2014) Rare earth doped silica optical fibre sensors for dosimetry in medical and technical applications, \u003cem\u003eAdvances in Optics\u003c/em\u003e, vol. 2014\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKaur P, Singh D, Singh T (2018) Gamma rays shielding and sensing application of some rare earth doped lead-alumino-phosphate glasses. 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J Non-cryst Solids 512:33\u0026ndash;40\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSayyed M (2017) Half value layer, mean free path and exposure buildup factor for tellurite glasses with different oxide compositions. J Alloys Compd 695:3191\u0026ndash;3197\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSingh VP, Badiger N (2012) Comprehensive study of energy absorption and exposure build-up factors for concrete shielding in photon energy range 0.015\u0026ndash;15 MeV up to 40 mfp penetration depth: dependency of density, chemical elements, photon energy. Int J Nucl Energy Sci Technol 7:75\u0026ndash;99\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAlgarni SA, El-Maaref A, Alotaibi B, Alharbiy N, El-Rehim AA, Wahab EA, Shaaban KS (2022) Physical, optical, and radiation shielding features of yttrium lithium borate glasses. J Inorg Organomet Polym Mater 32:2873\u0026ndash;2881\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKaewkhao J, Limsuwan P (2010) Mass attenuation coefficients and effective atomic numbers in phosphate glass containing Bi2O3, PbO and BaO at 662 keV, \u003cem\u003eNuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment\u003c/em\u003e, vol. 619, pp. 295\u0026ndash;297\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBAYKAL DŞ, TEKİN HO, \u0026Ccedil;. RB (2021) MUTLU, An investigation on radiation shielding properties of borosilicate glass systems, \u003cem\u003eInternational Journal of Computational and Experimental Science and Engineering\u003c/em\u003e, vol. 7, pp. 99\u0026ndash;108\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSayyed M, Lakshminarayana G, Moghaddasi M, Kityk I, Mahdi M (2018) Physical properties, optical band gaps and radiation shielding parameters exploration for Dy 3+-doped alkali/mixed alkali multicomponent borate glasses. Glass Phys Chem 44:279\u0026ndash;291\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Kohat University of Science and Technology","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":"Phy-X/PSD, Bismuth Borate glass, Gamma rays, Dysprosium, Shielding","lastPublishedDoi":"10.21203/rs.3.rs-7034073/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7034073/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this work, we investigated the effectiveness of bismuth borate glass doped with Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, BaO, and co-doped systems for a variety of radiation shielding uses. Within the various energy ranges (MeV), the linear attenuation coefficients (LAC) and mass attenuation coefficients (MAC) for glasses with the compositions 70B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;29Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;20Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, and 20BaO\u0026thinsp;+\u0026thinsp;60B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e were computed via the Phy-X/PSD simulation code. The acquired mass attenuation coefficients are further utilized to determine the effective atomic number (Zeff), half value layer (HVL), and mean free path (MFP) of the glasses. The co-doped glass containing BaO and Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e was shown to have greater gamma-ray shielding efficacy due to higher LAC, MAC, and effective atomic number values significantly reduced HVL and MFP values. By changing the photon energy, densities, or chemical composition of the glass samples, the substantial variations in all interaction parameters were observed. A co-doped bismuth borate glass sample comprising BaO and Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e exhibited superior shielding capabilities. These findings suggested that a glass sample with 20BaO\u0026thinsp;+\u0026thinsp;60 B\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;19Bi\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e\u0026thinsp;+\u0026thinsp;1Dy\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e is an effective radiation shielding material.\u003c/p\u003e","manuscriptTitle":"Comparative Study of Gamma Radiation Shielding Parameters of BaO, Dy2O3 and Co-doped Bismuth Borate Glasses","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-11 02:49:12","doi":"10.21203/rs.3.rs-7034073/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":"2db42b52-fdce-4a6e-980c-23e30497662b","owner":[],"postedDate":"July 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":51312006,"name":"High Energy and Particle Physics"},{"id":51312007,"name":"Computational Physics"}],"tags":[],"updatedAt":"2025-07-11T02:49:12+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-11 02:49:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7034073","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7034073","identity":"rs-7034073","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}