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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]

In this work we investigated new different glass compositions 20PbO–20BaO–(60 − x)B2O3–xZnO (x = 0, 5, 10, 15 and 20 mol%) to study the radiation shielding capability of these glass composites. The shielding ability was measured experimentally using narrow beam method (which including HPGe detector, point sources and lead collimators). The accuracy was verified by XCOM software, the linear attenuation coefficient (LAC) of the produced glasses was ascertained using both methods. We noticed that the B40Z20 glass composite (contain 20 mol%) has the highest LAC at the four examined energies (0.060, 0.662, 1.173 and 1.333 MeV) since the LAC enhances as the ZnO content increases from 0 to 20 mol%. The based shielding parameters such as HVL and RSE or called radiation shielding efficiency were determined experimentally. The HVL reduces as the glasses' density (or, more accurately, the amount of ZnO) increases. At 0.06 MeV, the HVL have the following values: 0.041, 0.039, 0.038, 0.036 and 0.035 cm for the glasses with density of 3.582, 3.739, 3.897, 4.055 and 4.212 g/cm3 respectively. [ABSTRACT FROM AUTHOR]

A novel glass system B2O3–SiO2–Bi2O3–TeO2–BaO–ZnO doped with Eu2O3 (x = 0–4 mol%) is fabricated through melt-quench technique and coded as BiTeEu-x. Density and refractive index measurements done on the glasses resulted in the increase up to 5.4377 gcm−3 and 1.99, respectively, for 4 mol% addition of Eu2O3. Vickers micro-indentation measurements done on synthesized glasses gave increasing microhardness values with Eu3+ doping due to higher bond strength of Eu–O bond compared to Te–O bond. The Phy-X/PSD simulation software utilized for obtaining radiation shielding parameters produced highest range of mass attenuation coefficient (63.878–0.036 cm2/g) and lowest range of half-value layer (0.002–3.551 cm) for the same glass proving its superiority in radiation attenuating capacity. This article addresses the theoretical analysis of photon buildup occurring inside the fabricated glasses in 0.015–15 MeV energy range with respect to different penetration depths. Neutron shielding ability of BiTeEu-4 glass was found to be impressive with fast neutron removal cross section (FNR) value of 0.10362 cm−1. [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.