Gamma, neutron, and heavy charged ion shielding properties of Er 3 + - doped and Sm 3 + doped zinc borate glasses

: This study aimed to investigate the nuclear radiation shielding properties of erbium ( Er )- reinforced and samarium ( Sm )- reinforced borate glasses. In the 0.015 – 15MeV photon energy range, attenuation coe ﬃ cients, as well as half - value layer tenth - value layers, and the mean - free path have been calculated. Additionally, e ﬀ ective, and equivalent atomic num -bers, e ﬀ ective atomic weight, electron density, and exposure and energy absorption build - up factors were also calcu lated. To evaluate the overall nuclear radiation attenuation competencies of Er - rich and Sm - rich glasses, e ﬀ ective removal cross - section values for fast neutrons and pro jected range/mass stopping power values for alpha and proton particles were also determined. The glass sample BZBEr2.0 had the highest linear and mass attenuation coe ﬃ cients ( µ and µ m ) , e ﬀ ective conductivity ( C e ﬀ ) , the e ﬀ ective number of electrons ( N e ﬀ ) , and e ﬀ ective atomic number ( Z e ﬀ ) values as well as the lowest half - value layer ( T 1/2 ) , tenth value layers ( T 1/10 ) , mean free path ( λ ) , expo sure build - up factor, and energy absorption build - up factor values. µ m values were reported as 2.337, 2.556, 2.770, 2.976, 2.108, 2.266, 2.421, 2.569, and 2.714 for BZBEr0.5, BZBEr1.0, BZBEr1.5, BZBEr2.0, BZBSm0.0, BZBSm0.5, BZBSm1.0, BZBSm1.5, and BZBSm2.0 glass samples at 0.06 MeV, respectively. The results showed that Er has a greater e ﬀ ect than Sm regarding the gamma - ray shielding prop erties of borate glasses. The results of this investigation could be used in further investigations and added to older investigations with the same aim, to aid the scien ti ﬁ c community in determining the most appropriate rare - earth additive, to provide adequate shielding prop erties based on the requirement.


Introduction
Gamma and X-ray are the most common types of ionizing radiation emitted and used in nuclear medicine, radiation therapy, and nuclear reactors. As these rays have no mass, they can easily travel long distances through the air [1]. As a result, gamma and X-ray are thought to be the most penetrating and difficult to shield. When a high radiation dosage is absorbed, it may result in radiation sickness, organ failure, skin rashes, carcinogenesis, genetic damage, bone-marrow loss, and death. Consequently, radiation shielding, and safety is becoming a more widespread research subject. The radiation must be reduced to safe levels by the shielding materials to protect medical professionals, patients, and the public against the harmful impacts of ionizing radiation. Due to its cheap cost, simplicity of availability, and flexibility to be molded into any form or size, concrete is the most often used shielding material in nuclear reactors and cyclotrons. However, the use of concrete has several limitations. These include cracks in concrete that occur after extended use, the presence of water in concrete decreases the density and structural strength of the material. As concrete absorbs nuclear radiation, it heats up, causing water to evaporate, causing instability in shielding parameters calculations and inhomogeneity in the material's composition. Concrete is nonportable, making transporting it from one location to another impossible. Moreover, concrete is opaque by nature, which makes it difficult to see through [2]. Lead and lead-based compounds are also extensively used as shielding materials in hot labs and transport of radioactive materials; however, the toxic effects of lead and lead-based compounds on human health and the environment are numerous. Lead toxicity necessitates the resolution of several hygiene challenges, including dosage monitoring, supplementary protective equipment, worker training, and correct waste disposal [3]. Thus, it becomes essential to look for better shielding materials than concrete and lead. A material that incorporates transparency, nontoxicity, and radiation shielding potential is currently of great interest in the medical field. Steel, alloys, polymers, gemstones, and glasses have all been tested for their shielding properties. Glass, which has the virtue of being transparent in the visible spectrum, maybe the best possible substitute for concrete-based shielding [4][5][6].
Glasses are unique in their ability to accommodate a wide range of elements. As a result of this property, they can serve as a shield against harmful ionizing radiation. Zinc borate glasses and lead-free compounds with high chemical resistance, transparency, and radiation protection are being explored as possible replacements. Borate (B 2 O 3 ) is a compound with the highest glass formation tendency because molten B 2 O 3 does not crystallize by itself even when cooled at the slowest rate. Recent publications have discussed the X-ray and gamma-ray shielding capabilities of several glasses containing barium oxide (BaO), including BaO:B 2 O 3 :fly ash glass [7]. PbO, Bi 2 O 3 [8][9][10][11], and BaO in borate glass [7,12], and silicate glasses [13][14][15][16], and PbO:BaO:P 2 O 5 glass [17]. These investigations demonstrate that BaO may be used effectively in various glass matrices as a radiation shielding material. This is owing to BaO's high effective atomic number and its great X-ray and gamma-ray absorption. In a study done in 2017, ZnO was added to the glass to improve its transparency [7]. When B 2 O 3 is added to glass material, it confers to the glass many valuable properties such as improving the fusibility, increasing the mechanical resistance, and high thermal resistance [18]. Osman et al. conducted research to examine the shielding parameters of glass systems from lead against neutrons and gamma rays. Attenuation parameters were evaluated and theoretically calculated using cylindrical soda-lime-silica glass samples, and lead oxide was added in various percentages to make the mixtures by weight as simple as possible. Their results indicated that the displayed spectra exhibit a similar shape and photon attenuation behavior across the investigated composites [19]. Tekin et al. conducted another significant investigation on phosphate glass materials due to their ethereality in a large spectrum range between infrared and ultraviolet, making them suitable for producing optical fibers, shielding material for radiation detection, and sensing applications. Numerous features of phosphate glass materials were discovered when the lead oxide was added to phosphate-glass samples. Lead oxide is an effective shielding material for high-energy nuclear radiations [20]. The literature review showed that different types of additives could be used for the improvement of nuclear radiation shielding properties of different glass structures. This has encouraged us to perform a comprehensive investigation on numerous glass samples in terms of their attenuation competencies against different types of radiations such as gamma, fast neutrons, and charges particles (alpha and proton). Accordingly, BZBEr [21] and BZBSm [22] glass systems were selected to study the gamma shielding properties using Phy-X/PSD [23] and Py-MLBUF [24] online platforms for energy levels between 0.015 and 15 MeV. Besides, rare earth-doped phosphate glass gives such excellent improvement in the development of many optical devices [25]. It gives higher emission efficiency with the enhancement in emission line from visible to the infrared spectral region under suitable excitation conditions as reported elsewhere [26]. Among the rare-earth ions, Er 3+ ion has higher potential application in developing the optical and laser device. The presence of Er 3+ ion in phosphate glass can generate 1.54 μm wavelengths, which can be utilized for optical amplification, and its visible up conversion emission can be used as a solid-state laser [27]. In this study, it was hypothesized that various types of reinforcements (e.g., Er and Sm) used to optimize the characteristics of glass will also change the basic properties of glass that protect against nuclear radiation. Therefore, it was sought to identify the potential effect of erbium (Er) and samarium (Sm) additives on the protective properties of these glasses against nuclear radiation. This study aims to search for a new, highly efficient, and environmentally friendly protective material that can replace lead or lead-based shielding materials in different types of radiation facilities. The effectiveness and quality of each sample as the additive increases will be checked and discussed. The results of this investigation can be used in further investigations and added to previous investigations for the same purpose. Table 1 contains the sample codes along with the elemental compositions, densities, and weight fractions of the glass samples. The linear attenuation coefficient expresses the percent of photons that are attenuated when they travel through a certain thickness of a material. To get the linear attenuation linear attenuation coefficients value, one must examine the reactions of the material with ionizing radiation photoelectric effect, Compton scattering, and pair production (PE, CS, and PP). As shown in the following equation (1), the Beer-Lambert law is used to compute the μ value:

Materials and methods
where (I) is the intensity of gamma-ray after it has been transmitted through an absorber, and (I 0 ) is the initial intensity of the gamma-ray [28]. The μ represents the linear attenuation coefficient value, which is given by cm −1 . The mass attenuation coefficient (µ m ) is an important quality, which provides critical and basic information regarding the glass sample's ability to attenuate the intensity of the gamma radiation. Next, µ m were calculated using equation (2).
where w i is the weight fraction of the ith constituent element, μ is the linear attenuation coefficient, and ρ is the density [28,29]. The half-value layer T 1/2 is basically the required thickness of the glass sample that can make the radiation intensity get reduced to one-half of its initial value. The T 1/2 is an important quality that determines whether the glass sample works sufficiently as a shielding material [30]. Similarly, to the T 1/2 , we have the tenth-value layer T 1/10 ; which is the required thickness of the glass sample to reduce the radiation intensity to onetenth of its initial value [31]. The way we calculate the half value layer (HVL) and the T 1/10 is by using the following equations: equations (3) and (4).

(4)
A mean free path λ is the mean range traveled by a photon before it interacts with the shielding material for photons traversing a substance, as stated by the American Nuclear Society-standard and shown in equation (5).

Results and discussion
Apart from the basic material features of produced glass materials, researchers continue to be intrigued by their radiation properties factors to gain a better understanding of their multifunctional behaviors [52][53][54][55][56][57][58][59][60][61][62]. Figure 1 demonstrates the changes of µ with energy. It is evident from the graph that there is a sharp decrement from 0.015 to 0.030 MeV, which demonstrates the dominance of photoelectric absorption. Then, a sudden change occurred in the energy range from 0.03 to 0.04 MeV, which is a result of the K-absorption edge of the two elements (Er = 0.0574 MeV and Sm = 0.0468 MeV) [44]. Following that, a sudden decrement in the µ values was seen again in the energy range of (0.05 MeV to around 1 MeV). After 1.02 MeV, a smooth decrement is a result of PP, which usually happens in the high-energy range. The increment of Er and Sm in the glasses increases the values of the µ. For example, µ values for BZBEr1.0, BZBEr1.5, and BZBEr2.0 at 0.015 MeV was reported as 136.860, 142.930, and 148.030, respectively. In addition, as the energy increases, the µ values decrease. According to this study, it is observed that BZBEr2.0 has the highest µ value. The mass attenuation coefficient expresses the chance of incoming photons interacting with unit mass/unit area stuff. As observed in the graph in Figure 2, when the energy increases, the total µ m decreases. The tendency of µ m is like µ; therefore, similar behaviors were obtained for both parameters. Figure 2 shows variation of mass attenuation coefficient (µ m ) against photon energy for (a) BZBEr and (b) BZBSm glasses. The maximum value of µ m is reported at 0.015 MeV. As the energy increased, a sharp decrement was reported in the energy range from 0.015 MeV to around 0.03 MeV. This is due to the PE predominance at low energies. Furthermore, a sudden change occurred in the energy range (0.030-0.0.040 MeV) because of the K-absorption edge effect. Moreover, it has been reported that as the percentage of the additives (Er and Sm) increases in the glass sample, the mass attenuation coefficient increases as well. According to this study, it has been reported that BZBEr2.0 has the greatest µ m value and BZBSm0.0 has the lowest µ m value.  MeV, the sample BZBEr2.0 had the lowest T 1/2, equal 6.8164 cm. However, this value is not that big of a difference compared to the other samples, such as BZBEr1.5 and BZBSm2.0, which both had T 1/2 approximately equal to 6.9 cm. As shown Figure 4, the half value layer T 1/2 values of the investigated BZBEr2.0 and BZBSm2.0 samples dependent on photon energy at specific energies and compared with Glass1 [45], Glass2 [46], Glass3 [47], Glass4 [48], Glass5 [49], Glass6 [8], Glass7 [50], Glass8 [51], and standard shielding materials (ordinary concrete: OC [52], and hematite-serpentine concrete: HSC [28]), where BZBEr2.0 and BZBSm2.0 samples are lower than the T 1/2 values of all samples even OC and HSC. The tenth-value layer T 1/10 is quite close to the HVL definition in terms of significance as it is the thickness of the shielding glass material necessary to lower the initial intensity to a tenth (10%) of its value. A single T 1/2 is equal to 0.3 T 1/10 . In Figure 5, sample with the highest T 1/10 25.170 cm was BZBSm0.0. However, the term of a mean free path (mfp − λ) is an essential parameter that demonstrates the average distance traveled by a photon within the glass sample before any interaction between the photon and the glass shielding material occurs. As the mfp equals 1/µ, it will have an inverse relation to µ, and accordingly, the mfp and µ will have opposite relations with incident photon energy. Noting that the lowest the mfp value, the better the shielding material is. The effective conductivity is a parameter that is affected by the changes in photon energies. In other words, the C eff values change when the energy is changed. The maximum value of C eff in Figure 7 has been reported at 0.06 MeV, which is 26.108 S/m for BZBEr2.0. Starting from 0.015 MeV, a slight decrement in the C eff values for all the studied elements was reported. After that, a sudden  BZBsm1.5, and BZBsm2.0 samples at 0.3 MeV. Figure 9 shows the variation in effective atomic weight absorption A eff for all glasses as a function of the photon energy. The additive properties have a clear relationship with the variations in the total atomic weight of the mixture, resulting in densities ranging from 3.42 to 3.493 g/cm 3 . As a result, BZBEr2.0 was found to have the highest A eff value of all the glasses examined, with a value of 25.123, and BZBSm0.0 had the lowest value, 23.630. Figure 10 presents values of Z eff as a function of photon energy. The term Z eff is used to describe how various elemental structures react to ionizing radiation. When it comes to gamma-ray attenuation, elements with higher atomic numbers are generally thought to be superior. However, in this study, both the additives have very similar atomic numbers (Er-68 and Sm-62). Additionally, Z eff is proportional to photon energy, and the discrepancy between Z eff and energy may be accounted for by the photoelectric absorption, CS, and PP processes. An obvious pattern can be seen from the graph that as energy increases, Z eff values decrease. The mechanisms by which photons interact with matter can provide an explanation for this fluctuation. Radiation physics notions imply that the PE dominates at low energies. As the energy level rises, the likelihood of this mechanism occurring decreases, and CS takes over as the dominant process. As   absorption build-up factor (EABF) and the exposure buildup factor (EBF) are critical photon shielding characteristics that have been used to characterize scattering in irradiated materials. Figures 11 and 12 illustrate the variance in EBF and EABF values for all glass samples calculated using the geometric progression fitting approach for the energy range of 0.015-15 MeV and penetration-depths ranging from 0.5 to 40 mfp. As the precision of the shielding parameters increases, the accuracy of the radiation measurements increases as well, resulting in a reduction in the findings' abnormalities. As per the graphs in Figure 11, the EBF of the glass samples is low at low energies, increases to a maximum at medium energies, and then lowers again at high energies, where pair formation interactions occur. CS occurs when entering photons scatter with varying energies despite the photons being totally absorbed by pair formation and photoelectric absorption processes. Because this scattering facilitates the accumulation of low-energy photons in the generated glasses, the EBF values of the glasses are highest at medium energies.
The sharp peaks observed in the figures are due to the Kabsorption edges of the elements present in the glass samples. Additionally, the EBF curves for BZBEr and BZBSm glasses are almost identical. Almost all glass samples had  has the lowest value. This is an excellent demonstration of how effectively materials can guard against gamma radiation. As a result, BZBEr2.0 with the lowest EBF values may be considered the appropriate sample among the glass samples studied. As for EABF, it is a quantity influenced by the amount of energy in the substance as well as the detector function in the interacting material. A trend like that seen in EBF graphs is observed. Hence, it can be noted from Figure 12 that BZBSm0.0 has the highest EABF value, and BZBEr2.0 has the lowest value. The current investigation additionally examined the produced glass specimens' fast neutron shielding capability. When a fast neutron engages with an absorbing medium,   it can take one of three distinct pathways, depending on the attenuator's composition and energy of the incident neutrons. This probability may be quantified or subjectively represented in terms of the macroscopic (or effective) cross section, or alternatively as the effective removal cross sections for fast neutrons Σ R . The Σ R values for the studied glass specimens are shown in Figure 13. The Σ R values were reported as 0.1051, 0.1049, 0.1049, 0.1044, 0.1045, 0.1051, 0.1049, 0.1049, and 0.1045 cm −1 for BZBEr0.5, BZBEr1.0, BZBEr1.5, BZBEr2.0, BZBSm0.0, BZBSm0.5, BZBSm1.0, BZBSm1.5, and BZBSm2.0, respectively. As it can be observed from the reported numerical values, there are differences between the Σ R values of the studied glass samples. However, among the investigated glass specimens, the BZBSm0.5 glass exhibits the highest fast neutron shielding capability. Finally, we will briefly address the ability of the investigated glass specimens to protect against charged particles (e.g., proton and alpha particles). According to Coulomb's law, a charged particle interacts with a substance. As a result, these particles may collide several times before losing all their kinetic energy. Stopping power (SP) and particle ranges may be used to quantify the charged particle's gradual loss of energy through matter (PR). Figures 14-17 display the effect of increasing kinetic energy on the proton mass stopping power (PMSP), alpha mass stopping power (AMSP), proton projected range (PPR), and alpha projected range (APR) values of the examined glasses obtained from SRIM code [63]. The given comprehensive graphs depict that the attenuation properties of the studied glasses against charged alpha and proton particles are similar. Similar elemental compositions or slight increments can explain this in Er and Sm reinforcements through glass structures. Our findings, however, indicate that the BZBEr2.0 sample with the highest Er additive has higher attenuation characteristics against alpha and proton particles. These findings may help explain the attenuation capabilities of examined glasses against charged alpha and proton particles, which are more likely to be seen than other analyzed radiation types such as gamma and fast neutrons.

Conclusion
Recent investigations have illustrated that lead and leadbased materials have a number of important drawbacks, including short life span, toxicity, high cost, and lack of transparency. Considering these properties, several studies have been done to examine the gamma shielding properties of rare-earth-doped glass materials because of their numerous advantages. In this study, nine different zinc borate glasses doped with Er and Sm were examined for several different nuclear shielding properties, including linear and mass attenuation coefficients, half and tenth value layers, mean free path, build up factors, and so forth. ii) The findings indicated that BZBEr2.0 had the lowest T 1/2 , T 1/10, and λ values at the photon energies investigated. iii) BZBEr2.0 glass sample reported the highest Z eff value. iv) BZBEr2.0 glass sample had the highest N eff and A eff values v) EBF and EABF values were the lowest for the BZBEr2.0 glass sample.
As the BZBEr2.0 with the greatest Er additive demonstrated better nuclear radiation attenuation capabilities, it was obvious that Er reinforcement had a significant favorable effect on nuclear radiation attenuation qualities. Our results indicate that Er reinforced glasses zinc glasses may be an appropriate candidate material for nuclear shielding applications. Furthermore, the findings indicate that Er is more effective at shielding nuclear radiation than Sm. According to the literature study, researchers are exploring a variety of different types of studies into additives for nuclear radiation shielding improvements. Consequently, our results may contribute to the existing body of knowledge and will aid in identifying special additives and associated glass compositions that offer the most appropriate shielding characteristics for the needs and applications.