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The radiation shielding characteristics of the polyester resin composites reinforced with cerium(iv) oxide (CeO2) have been studied. The prepared composites were pure polyester–resin (Poly/CeO2-0), 90% per weight polyester resin and 10% CeO2 (Poly/CeO2-10), (Poly/CeO2-30), (Poly/CeO2-50), and (Poly/CeO2-60). The linear attenuation coefficient (LAC) values for the free polyester and polyester samples with CeO2 were experimentally measured compared with the XCOM data. The experimental LAC value was found to be 0.2377 cm−1 at 0.0595 MeV, which is in good agreement with the calculated value of 0.2454 cm−1. Also, for the same sample, the experimental LAC was found to be 0.1034 cm−1 at 0.662 MeV, showing a good agreement with the calculated value of 0.1057 cm−1. The LAC values for the free polyester, Pol/CeO2-30, and Pol/CeO2-60 are 1.43, 31.82, and 107.77 cm−1 at 0.015 MeV, respectively. The big difference in the LAC values between the composite with 0 and 60% CeO2 is evident. The radiation shielding efficiency (RSE) of the polyester with different amounts of CeO2 was experimentally measured at four energy values. Also, we extended the calculation of RSE at other energy values in the range of 0.015–15 MeV). The exposure buildup factor (EBF) values for the free CeO2 sample and the samples with CeO2 are calculated. The EBF is small at low energies, then increases, and attains a maximum value at moderate energy; the EBF shows a decreasing trend with an increase in the energy.

In this work, the attenuation properties of silicon rubber (SR) composites reinforced by both micro- and nano-sized Tungsten trioxide (WO3) particles are studied. Different SR composites with different combinations of micro-WO3 and nano-WO3 have been prepared. The main composite, SR-(WO3)60m (40% SR containing 60% micro-WO3), and other compositions were prepared by replacing percentages of microparticles with nanoparticles of WO3. The linear attenuation coefficient for these composites was measured in the range of 0.06–1.333 MeV. The existence of micro and nanoparticles together may result in enhanced interactions with incoming photons, leading to greater shielding. In other words, micro-WO3 and nano-WO3 have various sizes and surface areas. At 0.06 MeV, we notice a distinguished decrease in the half value layer (HVL) from SR-W60m to SR-W60n. The sequence of reducing HVL values (SR-(WO3)60m > SR-(WO3)60n > SR-(WO3)40m20n > SR-(WO3)20m40n > SR-(WO3)30m30n) suggest that the inclusion of both micro- and nano-WO3 contributes to more efficient radiation shielding compared to the reference material. The radiation shielding efficiency (RSE) for SR-(WO3)30m30n at 0.662 MeV is 38.40%. This means that if a beam of photons with energy of 0.662 MeV interacts with SR-W40m20n sample, only 38.12% of the photons are successfully absorbed or stopped, whereas the remaining 61.88% can pass through this sample. At 1.333 MeV, the lowest RSE is observed, which means that the prepared composites have weak attenuation ability at higher energy levels.

We fabricated porcelain ceramics embedded with WO3 nanoparticles (NPs) for radiation shielding applications. The linear attenuation coefficients were experimentally determined to study the efficiency of the manufactured samples against gamma rays. When the thickness increases from 0.5 to 2 cm, there is a reduction in the photon transmission through the ceramics. At 0.662 MeV, the transmission factor for Porc-1 changes from 0.91 (thickness: 0.5 cm) to 0.83 (thickness: 1 cm), and to 0.69 (thickness: 2 cm). From I/I 0 results, we found that attenuation performance is improved as the sample thickness increases. We evaluated the mass attenuation coefficient (MAC) and examined the influence of the concentration of WO3 NPs on the MAC. We found that Porc-5 which contains a greater quantity of WO3 NPs compared to the other samples has the highest MAC. At 0.06 MeV, the HVL (half value layer) for Porc-1 is 1.063 cm, while at 1.333 MeV this increases to 5.247 cm. Meanwhile, for Porc-2, at 0.06 MeV, a thin layer of thickness 0.806 cm is required to shield 50% of the photons, and at 1.333 MeV, the thickness of the layer must increase to 5.058 cm to shield the photons.

A study was conducted to investigate how the addition of WO3 affects the mechanical, optical, and photon attenuation properties of TeO2–Na2O glass systems. In this study, four glass systems categorized as W5, W10, W15, and W20 were studied to evaluate the impact of WO3 on TeO2–Na2O glass systems in view of the feature of mechanical, optical, and photon attenuation. The rising values of elastic moduli suggest that increasing WO3 on TeO2–Na2O glass systems makes the glassy structure more stable. Incorporating WO3 into TeO2–Na2O glass systems results in an increased energy band gap, rising from 2.83 to 2.95 eV. This phenomenon, in turn, leads to a decrease in the refractive index, dielectric constant, and optical dielectric constant values from 2.444 to 2.411, 5.975 to 5.811, and 4.975 to 4.811, respectively. While the linear attenuation coefficient (LAC) of the examined glass systems (W5, W10, W15, and W20) displayed a comparable pattern, the LAC value of glass sample W20 stood out as the highest among them. However, due to the addition of WO3 on the TeO2–Na2O glass system, at a lower energy region from 0.0284 to 0.06 MeV, there was a little variation among the mass attenuation coefficients of these glass systems studied herein, but a negligible variation was found from 0.662 to 2.51 MeV. The studied glass sample W20 with the highest amount of WO3 (20 mol%) on the TeO2–Na2O glass system displayed the lowest half-value layer. However, glass samples W5, W10, and W15 exposed 1.29, 1.07, and 1.03 times higher values of mean free path than W20. In addition, the values of the half-value layer were compared with the literature data of WO3–MoO3–TeO2, BaO–Li2O–B2O3, and CaF2–BaO–P2O5 glass systems. Studied glass sample W20 showed the maximum shielding performance from energy 0.284 to 2.51 MeV.

This study provides insights into the effects of Bi2O3 on the physical, mechanical, and gamma ray shielding properties of Bi2O3–BaO–B2O3–ZnO–As2O3–MgO–Na2O glasses. The higher Bi2O3 concentrations result in increased density and molecular weight of the glasses. The molar volume also increases with higher Bi2O3 percentages, accompanied by a decrease in the average distance between boron atoms and a reduction in polaron radius and inter-nuclear distance. Electronegativity decreases and electronic polarizability increases with increasing Bi2O3 concentration, indicating higher electron-donating capacity and greater susceptibility to external electric field distortion. The elastic moduli exhibit a downward trend with increasing Bi2O3 concentration, indicating a decreased degree of elastic behaviour. The decrease in cross-linking is further supported by the reduction in Poisson’s ratio. The decrease in values of the hardness also indicates a decline in the stiffness and connectivity of the glass network. The linear attenuation coefficients (LACs) of three different glasses were obtained using Phy-X software in 0.015–15 MeV energy range. Also, the effective atomic numbers are calculated for the selected glasses. The LAC has the highest values for Bi21, indicating that the addition of Bi2O3 causes an improvement in the LAC.

A series of polyepoxide resins doped by lead oxide with low concentrations were fabricated in order to study the impacts of low PbO concentrations on the fabricated composites’ physical- and radiation-shielding properties. The epoxide resin was reinforced with the PbO compound with concentrations 0, 5, and 10 wt%. The density measurements affirmed that by elevating the PbO concentration between 0 and 10 wt%, the composites’ density increased from 1.103 to 1.185 g·cm−3. This low-density increase was echoed in the fabricated composites’ radiation-shielding properties, where the Monte Carlo simulation code affirmed a linear attenuation coefficient increase by factors of 230%, 218%, 24%, and 10%, respectively, at 59, 121, 356, and 662 keV. The half-value layer, mean free path, and transmission factor indicated a linear attenuation coefficient enhancement.

In a variety of applications using ionizing radiation, it is essential to ensure the safety of both individuals and equipment. To this end, excellent radiation shielding materials, including glasses and rare earth elements, such as Dy2O3, are currently being researched. The goal of this study is to explore the effect of Dy2O3 on the radiation-shielding properties of the SiO2–PbO–B2O3–Dy2O3 glass system; for clarity, it is abbreviated as Dy-X. Dy2O3 is a good choice for use as a modifier in radiation shielding glasses since it has high density. Additionally, Dy2O3 has good thermal stability and can be added to glass matrices without substantially affecting their physical features. The influence of increasing the amount of Dy2O3 present in the glasses from 0 to 5 mol% on the linear attenuation coefficient (LAC) and effective atomic number (Z eff) was studied using glasses with five distinct compositions and densities. In order to achieve this, the Phy-X program was utilized. The results demonstrate that Dy5 (with a composition of 55B2O3–25PbO–20SiO2–5Dy2O3) has the highest LAC value of the prepared glasses, while Dy0 has the lowest. We investigated the influence of Dy2O3 on Z eff at 0.284 MeV. The results show that the Z eff values increase with increasing Dy2O3 content. The Z eff values were found to be 27.35, 27.94, 28.52, 29.09, 29.65, and 30.20 for Dy0, Dy1, Dy2, Dy3, Dy4, and Dy5, respectively. From the Z eff results, we observed that increasing the Dy2O3 content in the samples leads to an improvement in the shielding ability of the glass system. We compared the LAC of the Dy-X glasses with six glass systems at 0.662 MeV. All Dy0–Dy3 glasses have lower LAC values than all the TeO2–Li2O–ZnO glasses, but Dy4 has an LAC value greater than those of three of these glasses.

Epoxy resins with varying amounts of MoO3 were theoretically investigated for their radiation shielding ability at low energies (between 0.0395 and 0.344 MeV). The quantity of MoO3 varied from 0 to 30%, and relevant shielding parameters were obtained and analyzed from Phy-X software. The half value layer (HVL) of the resins demonstrated that increasing MoO3 content improved the space-efficiency of the prepared samples at all tested energies, leading to the Mo4 sample, the epoxy resin with the greatest MoO3 content having the smallest HVL. Additionally, the mean free path of the materials has an inverse relationship with their density, which increased with additional MoO3. The tenth value layer ratio between Mo1 and Mo4 illustrated how the introduction of Mo has a much greater effect on thickness reduction at lower energies than at higher energies due to photoelectric phenomena. The Z eff and N eff parameters showed how the epoxy samples benefitted from the introduction of MoO3 at different energies.

The radiation attenuation characteristics of WO3-Li2O-ZnO-P2O5 glasses have been examined using Phy-X software. The linear attenuation coefficient is correspondingly increased with the inclusion of WO3, which indicates the existence of a reducing tendency in the photon transmission correlating with an increment in the WO3 content in the glasses. When density is increased, there is a considerable reduction in the half-value layer (HVL), which is most noticeable between 80 and 100 keV. Because the HVL reaches high values at 100 keV for the samples, it can be deduced that the HVL steadily increases as the energy increases. Additionally, increasing the amount of WO3 in the glasses causes the mean free path (MFP) to decrease. The MFP for the glasses was compared with that of different heavy concretes, and the comparison demonstrated that the chosen systems have the potential to be used for the fabrication of protection masks that are utilized during diagnostic radiation treatment. We determined the ratio between the tenth value layer for the free-WO3 sample and the sample with 10 mol% and we found that the ratio is higher than 1, which suggests that the tenth value layer is decreased with the addition of WO3 to the glasses.

Bi2O3–PbO–CdO–B2O3 glass samples were prepared via melt quenching. The substitution of Bi2O3 for B2O3 resulted in a continuous increase in density from 4.334 to 5.742 g/cm3. The molar volume (V m) gradually increased from 37.197 to 38.429 cm3/mol when the Bi2O3 level increased from 10 to 25 mol%. With the addition of Bi2O3 from 10 to 25 mol%, Young’s, bulk, shear, and longitudinal modulus reduced from 40.80 to 35.07 GPa, 22.92 to 19.97 GPa, 16.95 to 14.52 GPa, and 45.53 to 39.33 GPa, respectively. These glasses are bendable rather than elongated and can withstand longitudinal stress over shear stress. Radiation protection qualities were investigated using EpiXS software, which is based on the ENDF/B-VIII EPICS2017 library, between 122 and 1275 keV. The mass attenuation coefficients are substantially higher at low energies. The radiation shielding properties of Bi2O3–PbO–CdO–B2O3 glasses were improved by replacing B2O3 with Bi2O3. Quantifying this improvement is critical in developing compact radiation shielding employing this glass system.

The Bi2O3–ZnO–PbO–B2O3 (BiZPB) glasses are prepared using the melt-quenching technique. As the concentration of lead oxide increases, the band gap energy (E g) decreases from 2.864 to 2.671 eV. The BiZPB glasses exhibit remarkable stability under thermal stress, as indicated by the thermogravimetric analysis graph, with only a marginal 0.5% loss in their initial mass. The decrease in the glass transition temperature (T g) of BiZPB glasses, with an increase in the PbO concentration, can be attributed to the specific influence of PbO on the glass structure and properties. The radiation shielding performance for the prepared glasses is evaluated using Phy-X software. The transmission factor (TF) for the 10B2O3–10ZnO–40PbO–40B2O3 glass sample is almost zero at 0.122 MeV, which means that this glass sample can attenuate almost all the photons with an energy of 0.122 MeV, whereas the TF values for this sample with thicknesses of 0.5 and 1 cm are 88 and 77%, respectively., it can be observed from the TF values that the prepared glasses have good attenuation performance against low energy (0.122, 0.245, and 0.344 MeV), while they have weak shielding performance against high energy radiation. The addition of PbO causes a reduction in TF, which means that the addition of an extra amount of PbO into the glasses results in an enhancement in the radiation shielding competence of the samples. The average half-value layer (HVL̅\bar{{\rm{HVL}}}) is also calculated. The results demonstrated that HVL̅\bar{{\rm{HVL}}} is at its lowest between 0.248 and 0.411 MeV, ranging between 0.396 and 0.513 cm.

In this study, we developed flexible composites using silicone rubber (SR) or polydimethylsiloxane as the matrix and WO3 and BaO nanoparticles as filler to analyze their radiation-shielding performance. The linear attenuation coefficient (LAC) values for the prepared composites were reported to range from 0.059 to 1.333 MeV by using the experimental method. At 0.059 MeV, the SR with 40% of BaO NPs possesses the highest LAC, followed by SR with 20% of BaO and WO3 NPs. The SRs S-2 and S-4 that contain WO3 and/or BaO exhibit continuously greater LAC values than the sample S-1. Numerically, the LAC for S-2 (with 40% of BaO NPs) is 1.6 times greater than that for S-1 (free BaO and WO3) at 0.662 MeV, while the LAC for S-2 is 1.47 times more than that for S-1 at 1.275 MeV. We examined the impact of the thickness of the prepared composites on the attenuation performance by studying the transmission factor (TF) at two different thicknesses (1 and 2 cm). For S-1 and S-2, the TF decreases due to the increase of the thickness from 1 to 2 cm. The TF for S-1 with a thickness of 1 cm is 75% at 0.059 MeV, while it is 56% (for 2 cm). We evaluated the percentage decrease in the TF at 0.059 MeV for every SR as the thickness changes from 1 to 2 cm. For S-3, S-4, S-5, and S-6, the percentage decrease in the TF is extremely significant varying from 98% to 99%. This suggests that increasing the thickness of these SR samples from 1 to 2 cm has a major effect on the shielding capabilities they possess, particularly at low energies.

In this study, four tellurite–germanate glasses containing zinc, lithium, and bismuth with varied Bi2O3 and TeO2 amounts were investigated. The mechanical qualities of sample glasses were investigated and associated with their structural properties. Furthermore, the radiation-shielding capabilities of N1–N4 glasses were evaluated at 0.662 MeV using EPICS2017. The radiation-shielding characteristics were compared with the radiation-shielding parameters published in the literature for various glass systems. When TeO2 was replaced with Bi2O3, Young’s and bulk moduli of the material decreased. The L values of glasses were higher than their S values (14–13 GPa), indicating that they can tolerate longitudinal stress better than shear stress and can be bent rather than elongated readily. The MACs calculated were comparable to those obtained using WinXcom. The tenth-value layer (TVL) of all of the sample glasses was higher than that of the bismuth aluminosilicate glasses. All of the borate glass systems containing bismuth, sodium, and antimony had lower TVLs than N1–N3 glasses. The half-value layer was more in the N4 glass with the greatest Bi2O3 content than those in 50 and 60 mol% PbO-containing strontium borate glasses.

We focused on the analytical solution of strong nonlinearity and complicated timefractional evolution equations, including the Sawada-Kotera equation, Ito equation, and Kaup-Kupershmidt equation, using an effective and accurate method known as the Aboodh residual power series method (ARPSM) in the framework of the Caputo operator. Therefore, the Caputo operator and the ARPSM are practical for figuring out a linear or nonlinear system with a fractional derivative. This technique was effectively proposed to obtain a set of analytical solutions for various types of fractional differential equations. The derived solutions enabled us to understand the mechanisms behind the propagation and generation of numerous nonlinear phenomena observed in diverse scientific domains, including plasma physics, fluid physics, and optical fibers. The fractional property also revealed some ambiguity that may be observed in many natural phenomena, and this is one of the most important distinguishing factors between fractional differential equations and non-fractional ones. We also helped clarify fractional calculus in nonlinear dynamics, motivating researchers to work in mathematical physics. [ABSTRACT FROM AUTHOR]

This study presents the results of an investigation into the physical, optical, and mechanical characteristics of glasses prepared from a mixture of ZnO, MgO, B2O3, and PbO. It was found that increasing the concentration of PbO in the glasses led to an increase in both the density (ρ) and molar mass (M). The addition of PbO also affected the packing arrangement of oxygen atoms in the glass network, resulting in changes to the oxygen molar volume (V o) and oxygen packing density. Furthermore, the investigation found that the optical basicity (Ʌ th) of the glass elevated with increasing PbO concentration. Finally, the behavior of the average electronegativity (χav) and electronic polarizability (αo−2{\alpha }_{{\rm{o}}}^{-2}) with respect to the concentration of PbO in the glasses is discussed, whereby the addition of PbO affected the glasses’ mechanical characteristics as follows: (i) the addition of PbO increased the complexity of the glass network by enhancing the average cross-link density (nc̅\bar{{n}_{{\rm{c}}}}) and the number of bonds per unit volume of the glasses (n b); (ii) the glasses’ Young’s modulus (E), bulk modulus (B), and shear modulus (G) declined as the mol percent of the PbO increased; (iii) the longitudinal modulus (L) reduced but remained greater than G; (iv) the glass network cross-linking reduced the Poisson ratio (σ); (v) the glasses’ fractal bond connectivity (d) values indicated a three-dimensional network; and (vi) lead oxide hardened the glass, suggesting that a stronger structure manifests. These findings collectively demonstrate that PbO improves the rigidity and interconnectivity of glass. The gamma radiation-shielding characteristics of the glasses were evaluated using the Phy-X software in the 0.015–15 MeV energy range. The radiation-shielding properties of the studied glasses can be compared with other materials by introducing a new parameter known as the radiation coefficient ratio (R). It is observed that Q4 glass sample had superior shielding performance.