An exploration of the physical, optical, mechanical, and radiation shielding properties of PbO – MgO – ZnO – B 2 O 3 glasses

: This study presents the results of an investigation into the physical, optical, and mechanical characteristics of glasses prepared from a mixture of ZnO, MgO, B 2 O 3 , 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 a ﬀ ected 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 ( χ av ) and electronic polarizability ( − α o2 ) with respect to the concentration of PbO in the glasses is discussed, whereby the addition of PbO a ﬀ ected 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 ( n ̅ 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 ﬁ ndings 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 coe ﬃ cient ratio ( R ). It is observed that Q4 glass sample had superior shielding performance.


Introduction
Radiation can be detected in the everyday surroundings of humans, which is produced by both natural and artificial sources.The sun exemplifies a natural radiation source since it releases ultraviolet rays that can cause burns to human skin, with both rocks and ground soil having the potential to release radiation into the atmosphere.For example, X-rays are a commercial radiation source that can be used to examine the skeletal system for broken bones, while magnetic resonance imaging is used to diagnose additional health issues.However, at sufficiently high doses, both ionizing and non-ionizing radiation are considered dangerous.In order to protect against the risks associated with radiation, nuclear researchers and engineers have thus focused on understanding the nature of radiation and its potential for application [1][2][3].
In order to safeguard both workers and the surrounding environment from the harmful effects of radiation, the nuclear energy sector follows the strictest international regulations.Radiation exposure can be decreased through a number of straightforward measures.First, by creating physical barriers made of lead, concrete, or steel; for example, nuclear reactors are enclosed inside a structure composed of multiple concrete and steel layers, while concrete-and steel-encased water tanks are employed to store nuclear fuel.Second, by minimizing the amount of time spent in close proximity to a radiation source, which will ultimately result in reduced radiation exposure.Finally, by increasing the distance between workers and the radiation source [4][5][6].
The goal of radiation protection is to safeguard health, given that exposure to radiation can be harmful to human organs and tissues.The energy and kind of radiation, as well as the degree to which tissues are sensitive, all play a role in determining how the radiation will affect the human body.When exposed to radiation, damage may range from inflammation and skin irritation to abnormalities, stunted growth, the loss of key bodily functions, and the development of cancer.Therefore, one of the challenges that nuclear engineers encounter is producing adequate radiation-shielding components that can protect humans from radiation while limiting ionizing radiation's undesirable consequences [7][8][9][10].Lead and concrete are the two most frequently utilized materials in the radiation-shielding process; nevertheless, both have certain drawbacks, such as their extreme weight, while lead is also an extremely toxic substance.Consequently, radiation protection materials' specialists are focused on the production of substitutes for lead and concrete.In the context of lead-free options for the reduction or absorption of undesirable radiation, various shielding materials such as glass, iron, ceramics, alloys, and polymers incorporating nanomaterials have been the subject of significant interest [11][12][13][14][15].
Across the range of shielding options, glass is often regarded as one of the most favorable materials for use in radiation protection applications due to its favorable optical qualities, affordable production, and the potential to modify its density through the addition of heavy components.Glass is available in a wide range of forms and dimensions, each characterized by a unique set of properties that influence the specifics of the technical applications that include glass in their implementation [16][17][18][19][20].
One of the most common kinds of glass is the form containing B 2 O 3 , which is utilized in a broad range of settings including scientific and optical applications.This is because B 2 O 3 -containing glass possesses exceptional physical features such as a low melting point and a straightforward formation process.Recent results from a variety of studies suggest that such glass has a low density due to the low density of B 2 O 3 .On the other hand, the density of glass containing B 2 O 3 can simply be increased, which will enhance its ability to shield photons [21,22].Utilizing heavy metal oxides represents one of the most popular methods for increasing the density of glass containing B 2 O 3 , and one that has received significant attention in the literature.The presence of PbO has a major impact on the capacity of glass to absorb photons, and when added to a glass containing B 2 O 3 , the optical-and radiation-shielding characteristics both improve [23][24][25].As a result, the inclusion of a B 2 O 3 oxide mixture, as well as PbO or any other heavy material, has a strong likelihood of producing glass systems with the potential to be employed as face or eye shields to protect those utilizing radiation in the process of therapeutic treatments.
In addition to the significance of utilizing PbO in order to enhance the optical qualities of glass containing B 2 O 3 , the utilization of MgO to modify the structural properties of glass is of considerable relevance; whereby the incorporation of MgO has the potential to enhance the chemical durability and resistance of B 2 O 3 -based glasses.This characteristic is necessary for a broad range of applications, including those in which the glass will be employed in corrosive environments.
Since the significance of the glass system comprising B 2 O 3 , with varying proportions of PbO and other oxides such as MgO, is now established, as well as its widespread applicability in various medical and industrial settings, it is thus pertinent to investigate different types of glasses' radiation-and mechanical-shielding capabilities.Therefore, the present research not only explores the physical, mechanical, and gamma ray shielding properties of the PbO-MgO-ZnO-B 2 O 3 glass system, but also its radiation attenuation qualities.

Preparation of samples
The melt-quenching approach was employed throughout the manufacturing process of glasses composed of PbO-MgO-ZnO-B 2 O 3 [26,27] in order to guarantee that the finished product would be of the optimum quality.Initially, oxides of the highest possible AR grade were placed on an electronic scale (accuracy: 0.001 g), which was then used to determine their weight.A reliable combination was generated using an agate mortar due to its ability to reduce the size of various substances to a fine particle.The mortar was utilized to ensure a comprehensive crushing of the weighted compounds.After thoroughly combining all of the ingredients, the mixture was poured into an alumina crucible in a muffle furnace that was heated to and then maintained at 1,050°C throughout the entire operation.The objective of the agitation was to ensure that the components were evenly distributed.Next, an annealing furnace was employed to maintain a graphite mold at 300°C during the annealing procedure, into which the molten substance was poured until it was completely full.The amount of internal stress in a material may be reduced by annealing, which also helps to prevent the material from breaking.After leaving the samples to rest for 2 h, the temperature of the surrounding was allowed to return to normal before the samples were carefully collected for further analysis.The samples were photographed so that a visual evaluation could be carried out regarding their form, size, and color, as seen in Figure 1.The density of each of the samples, with the samples coded as follows: Q1

Physical properties
The Archimedes principle was used at room temperature to estimate the density (ρ) of the current glass samples.Three separate runs of this experiment were conducted, with benzene serving as the immersion liquid on each occasion, and the density values were calculated using the following relation [28,29]: where W a and W b are the weight of the existing glass samples in air and benzene, respectively, and 0.8765 g cm −3 is the density of benzene at ambient temperature.Molar volume (V m ) refers to the volume of glass per mole of its constituent atoms or molecules.Using the following formula, it was possible to calculate the glass sample's V m from the molar mass (M) [26]: In a glass system containing boron atoms, the average boron-boron separation ( ) − d B B refers to the average dis- tance between neighboring boron atoms, thus providing a measure of the spacing between boron atoms.The impact of doping on existing samples may be inferred from the [26,29]: where V m b is the volume that accommodates one mole of boron atoms.If X B is the mole fraction of B 2 O 3 oxide [26], then Dopant concentration refers to the amount or concentration of a foreign element or dopant introduced into a glass material.Dopants are intentionally added to modify the properties of the glass, such as its optical, electrical, or mechanical characteristics.The inter-nuclear distance refers to the average distance between neighboring atoms within the glass structure.A polaron is a quasi-particle that arises in certain materials due to the interaction between an electron or hole and the surrounding lattice, with the polaron radius referring to the average size of polarons present in the material.The dopant concentration (N), inter-nuclear distance (r i ), polaron radius (r p ), and field strength (F) were obtained as follows [26,29]: where Z is the oxidation state of dopant ions.

Oxygen packing density (OPD), optical basicity, electronegativity, and electronic polarizability
The oxygen molar volume refers to the volume occupied by one mole of oxygen atoms in the glass system and is influenced by factors such as the size of the oxygen atoms and their arrangement.The glasses' V o was calculated as follows [26,29]: where n is the number of oxygen atoms in each formula unit.
OPD is a measure of how closely packed the oxygen atoms are within the glass structure, representing the fraction or percentage of space occupied by oxygen atoms in relation to the total volume of the glass system.A higher OPD indicates that the oxygen atoms are more densely packed, while a lower density suggests that the oxygen atoms are more spread out.The packing density of oxygen is influenced by factors such as the size of the oxygen atoms, their arrangement, and the presence of other atoms or molecules in the glass matrix.The Ʌ th value of a glass is a measure of its constituent ions' ability to accept or donate electrons and is related to the glass's chemical and physical properties.OPD and Ʌ th were determined through the following formulas [29]: where Ʌ i and x i are the optical basicities, and the equivalent proportion of each oxide (Ʌ 1 ( Electronegativity is a measure of an element's potential to attract electrons in a chemical bond, whereby the lower the electronegativity, the greater the ability of the element to donate electrons.The glasses' χ av was calculated as follows [30]: Electronic polarizability is a measure of how easily the electron cloud of an atom or molecule can be distorted by an external electric field.It is related to the size and shape of the electron cloud, and the strength of the bonds holding it together.The glasses' − α o 2 was calculated as follows [31][32][33]:

Mechanical properties
The glasses' n ̅ c was calculated as follows [24]: where n f is the coordination number of the cations present in the sample.n b was calculated as follows [24]: According to the Makishima-Mackenzie theory [34,35], the mechanical properties of glasses are dependent upon the atomic packing density (V t ) and the inter-atomic bonding energy (G t ) of the glass.The atomic packing density provides information regarding the arrangement and spacing of atoms within the glass structure, where a higher packing density suggests that the atoms are more densely packed, which can influence the glass's mechanical properties.The inter-atomic bonding energy provides information about the strength and stability of the atomic bonds within the glass.It is closely related to mechanical properties, as stronger bonds generally contribute to higher mechanical strength and deformation resistance.Considering these parameters, the Makishima--Mackenzie theory provides insight into how the atomic arrangement and bonding within a glass system contribute to its mechanical behavior.
V t was calculated as follows: G t is calculated as follows: where V i and G i are the atomic packing densities and interatomic bond energies of the glasses' components, respectively [36].The glasses' E, B, G, L, σ, d, and hardness (H) were calculated as follows:

Gamma ray-shielding properties
The gamma radiation-shielding characteristics of the glasses were evaluated using the Phy-X software in the 0.015-15 MeV energy range [37,38].The effective atomic number (Z eff ) represents one of the nuclear factors to be assessed in order to construct and select appropriate shielding glass systems.The Z eff of the Q1-Q4 glass samples was estimated as follows: where f i is the fractional abundance of the element i having mass attenuation coefficient as MAC i .
The half value layer (HVL), which specifies the thickness necessary to reduce the radiation to 50% of the initial level, is a helpful parameter that can be utilized during the planning and selection of any radiation attenuation medium, whereby the greater the sample's attenuation qualities, the lower its HVL.
The following formula was applied for the determination of the HVL from the linear attenuation coefficient (LAC): 3 Results and discussion

Physical properties
Following an exhaustive investigation of the glasses' physical characteristics, the results are displayed in Table 1.An in-depth examination of the data led to the observation that an increase in the concentration of PbO from 45 to 60 mol% increased both the ρ and M. In the glass network, a denser form of PbO replaced a less dense form of B 2 O 3 .
The current glass network was depolymerized when intermediate oxide (PbO) was introduced, which resulted in the transformation of trigonal BO 3 into tetrahedral BO 4 , as well as the production of non-bridging oxygens (NBOs).In addition, the atomic mass of PbO is higher than that of B 2 O 3 , which is a factor that contributed to the general rise in density that occurred with elevated PbO concentration (Figure 2).As can be seen in Figure 2, when the percentage of lead oxide in the glasses grew, their molar volume reduced from 29.138 to 28.137 cm 3 .It is interesting to note that the d B-B , which indicates a compression in the glass network, dropped from 3.339 × 10 −8 to 3.079 × 10 −8 m when there was an increase in PbO concentration.The larger molecular mass of PbO may cause the rise in ion concentration, which increased from 9.302 × 10 21 to 12.884 × 10 21 ions cm −3 as the PbO concentration rose.Moreover, the polaron radius and the inter-nuclear distance both shrunk from 1.916 × 10 −8 to 1.721 × 10 −8 m and from 4.755 × 10 −8 to 4.270 × 10 −8 m, respectively.These alterations could be associated with the increased density of the glass network.There was a correlation between the increased ion concentration and the expansion of the inter-nuclear distance.Finally, the overfilling of PbO in the network increased the binding strength between the Pb ions and oxygen, which caused an increase in the field strength around the Pb ion concentration from 5.449 × 10 15 to 6.753 × 10 15 cm 2 .

OPD, optical basicity, electronegativity, and electronic polarizability
The oxygen molar volume and OPD in the PbO-MgO-ZnO-B 2 O 3 glasses were modified by adding PbO.The findings reveal that the oxygen molar volume rose from 17.140 to 20.098 cm 3 mol −1 as the quantity of PbO in the glass network increased, while the OPD fell from 58.343 to 49.757.This signifies that the glass network's oxygen molar volume increased because oxygen atoms occupied more space in the network.However, because oxygen atoms are not as tightly packed, the OPD reduced.Figure 3 illustrates the variation in these parameters with different mol percent of PbO in the glass composition.The opposite behavior of these parameters is explained, since the density and molar volume of the glasses influence these parameter values.The results suggest that the addition of PbO affects the packing arrangement of oxygen atoms in the glass network, leading to changes in both the oxygen molar volume and the OPD.
The addition of PbO into the PbO-MgO-ZnO-B 2 O 3 glass matrix led to an increase in the glass's Ʌ th from 0.858 to 0.972 as more PbO was added, thus indicating that the oxygen atoms in the glass network have a higher negative charge when PbO is present.This trend is explained by the PbO being an amphoteric oxide, which thus can function as both an acid and a base.When PbO is added to the glass network, it replaces some of the acidic oxide (B 2 O 3 ), leading to an increase in the Ʌ th .This behavior also describes the amplifying ability of oxide ions to transport electrons to neighboring cations.
The behavior of electronegativity and electronic polarizability is discussed here with respect to the mol percent of PbO in the glasses fabricated from a mixture of PbO, MgO, ZnO, and B 2 O 3 , with Figure 4 showing the changes in these parameters.In this case, as the mol percent of PbO in the glasses increased, the electronegativity decreased from 2.224 to 2.122, thus suggesting that the samples were donating more electrons with increasing PbO concentration.Moreover, the electronic polarizability increased from 2.057 to 2.393, indicating that the electron cloud in the glasses became more susceptible to distortion by an external electric field.The opposite behavior of electronegativity and electronic polarizability can be explained by the increase in optical basicity and the number of NBOs.

Mechanical properties
The value of n ̅ c increased from 2.444 to 3.000 when the concentration of PbO was enhanced.When the value of n ̅ c rose, there was also an increase in the network complexity.The value of n b , which indicates the degree to which a network is linked as it increases, should be raised to 1.023 × 10 23 cm −3 from its previous value of 1.156 × 10 23 cm −3 .Both of these values could result from an increase in the number of NBOs when the concentration of PbO rises.The longer link length and larger ionic radius of PbO compared to B 2 O 3 may have contributed to the formation of excessive free volume, which in turn led to a decline in the packing density values (V t ) from 0.476 to 0.441 cm 3 mol −1 .When PbO was added to a network, the dissociation energy (G t ) increased from 7.952 to 8.048 kcal cm −3 as a direct consequence of the addition.The density, composition, and molar volume of the samples affect these values directly.
The mechanical properties are presented in Table 2 and depicted in Figure 5.As a result of a rise in the proportion of lead oxide present in the glass's composition from 45 to 60%, the glass's E, which is a measure of stiffness, decreased from 31.631 to 29.676 GPa.Both the B and G decreased in value with a rise in the mol percent of PbO from 18.004 and 14.016 GPa to 15.657 and 13.424 GPa, respectively, in comparison to their initial values.In spite of the longitudinal modulus (L) decreasing from 36.696 to 33.556 GPa, the values remained higher than the corresponding shear modulus (G).Therefore, the Q1-Q4 coded samples can bear greater longitudinal stress than shear stress and can be bent more quickly than extended, while withstanding shear stress more effectively than longitudinal stress.Moreover, the samples are more capable of bending than extending, which would be logical given their shape.The inter-atomic bonding energy and material connections offered by elastic moduli may be employed to acquire a macroscopic perspective of a material's stiffness, where the elastic modulus decreases with the number of unit bonds that comprise each glass unit formula, and the average strength of these bonds is linked to the values of the cation-anion forces.Thus, the value of the elastic modulus decreases.The introduction of additional components into the glass matrix leads to the development of new interion ions, which in turn drive the expansion of the network, with this process referred to as network growth.As a direct result, it is shown that a decrease in the elastic modulus is associated with a decrease in both the average bond strength and the number of bonds.

Sample
Mechanical properties comparing the transverse strain to the longitudinal strain.It was possible to draw the conclusion that the glass network comprises cross-links since the Poisson's ratio in the current glasses reduced from 0.208 to 0.185 during the course of the experiment.The fractal bond connectivity, as represented by the letter d, enables the cross-linking that occurs within the glass structure to be seen.The d values of the current glass samples varied from 3.114 to 3.430, demonstrating that the structure was a network composed of three dimensions.As a consequence of increasing the amount of lead oxide in the glass, the hardness of the glass samples rose from 2.547 to 2.628, indicating that the structure became more robust.This demonstrates that the incorporation of PbO results in an increase in the glass's hardness, while suggesting that the selected glasses had improved interconnectivity and stiffness.

Gamma ray-shielding properties
The linear attenuation coefficient (LAC) is one of the most useful factors for examining the radiation-shielding features and predicting the glass's ability to shield the incoming photons.LAC calculations of the Q1-Q4 glass samples were conducted through the Phy-X software, with the findings plotted in Figure 6.Obviously, the shape of the LAC curve is determined by the primacy of the basic gamma photon interaction processes in a selection of energy regions.Low photon energies are those where the photoelectric process dominates.The likelihood of this occurring per atom relies on the energy (E −3.5 ) and the atomic number (Z n ), where the exponent n ranges from 4 to 5. Figure 6 reveals that at low energies (in the 377-513 cm −1 range at 0.015 MeV), the glasses consequently had reasonably high LAC.According to Figure 6, the LAC declined as the energy increased, with the exception of around 0.1 MeV when a sudden change in the LAC occurred.This was close to the lead's K-absorption edge, which manifested at 88 keV.Another process, known as Compton scattering (CS), becomes more significant when the energy approaches 0.6 MeV, with the mechanism more prevalent between 0.6 and several MeV.All the samples had the same attenuation levels between these energies, as seen by the LAC curve.This is attributable to the likelihood of CS relying linearly on Z, whereas the LAC was mostly unaffected by the PbO content (all samples with various PbO weight fractions had comparable LAC).For instance, the LAC for the Q1 and Q2 glasses were 0.321 and 0.393 cm −1 with a difference of 0.072 cm −1 at 1 MeV, respectively, representing the highest and lowest concentrations of PbO.It is important to note that the most common interaction type for high-energy gamma rays is pair production (PP), and that the likelihood of PP relies on Z 2 .This accounts for the minor increase in LAC at high energies (E > 5 MeV).
The impact of the alteration of the lead oxide used for producing samples on the LAC of the glasses can be examined in Figure 6.Due to PbO's greater density compared to B 2 O 3 , it was observed that adding PbO to the glasses dramatically affected their LAC.As a result, for all energies, the LAC had an increasing order from Q1 to Q4.
The mass attenuation coefficient (MAC) for the Q1-Q4 glass system at the energy range under consideration was also investigated, with the findings presented in Figure 7.It should be underscored that those samples with high MAC values can better attenuate the incident photons.As a result, materials engineers will frequently focus on the production of novel glass materials that have a rather high MAC.From Figure 7, the MAC had high values between 0.015 and 0.15 MeV, with the maximum MAC occurring at 0.015 MeV (equal to 80.33, 84.03, 87.36, and 90.37 cm 2 g −1 for the Q1-Q4 glass samples, respectively).The high MAC reported in this energy range can be demonstrated according to the Kabsorption edge of Pb.The MAC showed a sharply declining trend in the energy range of 0.1 to approximately 1 MeV and then became nearly constant up to 6 MeV.When the energy was greater than 6 MeV, the MAC value increased as the energy rose.This trend in the MAC can be explained according to the domination of the photoelectric effect (in the low energy range), and CS and PP (for the high energy range).Based on Figure 7, the Q1 glass sample had the minimum MAC value at all energies, while the Q4 glass sample had the highest MAC value, thus suggesting that the addition of PbO improves the MAC.This outcome can be attributed to lead having a comparatively high atomic number compared to boron (Z = 832 and 5 for Pb and B, respectively).This finding shows that the Q4 glass sample had superior photon attenuation competence and that the chosen glass system required a significant amount of PbO to improve this attenuation competence.
Figure 8 depicts the fluctuation of Z eff with photon energy for the four glass samples and demonstrates how the Z eff is affected by both energy and the sample's composition (i.e., the amount of PbO and B 2 O 3 ), with all glasses having the maximum Z eff over an approximate 0.015-0.1 MeV energy range.According to Figure 8, the glasses' Z eff rose sharply at 0.1 MeV, followed by rapid falls as the energy was increased up to 0.6 MeV.The Z eff values tended to remain stable in the range of 0.5 to a few MeV (CS area), but they slowly increased above 4 MeV.The data shown in Figure 8 demonstrate that the Z eff increased when PbO was raised from 45 to 60 mol%, suggesting that PbO improves the photon-shielding properties.This increase in Z eff is due to an increase in the mole fraction of an element with a higher atomic number (Pb, Z = 82).It should be noted that greater Z eff values for a material indicate that photon absorption is more likely because more electrons are available for interaction.Therefore, it can be concluded that the Q4 glass sample (with 60 mol% PbO) possessed the best attenuation properties, which is consistent with the previous findings.Figure 9 describes the impact of changing the PbO percentage on the HVL for the produced glasses at various photon energies, where the HVL data demonstrate a correlation between the PbO concentration and the glass sample's ability to shield gamma photons.The HVL decreased as the glasses' PbO level increased, indicating that the sample's tendency to absorb gamma photons was favorably impacted.Additionally, this finding indicates that a decrease in the thickness of the glass shield was caused by an increase in the PbO percentage.Numerically, at 0.04 MeV, the HVL decreased from 0.015 to 0.011 cm due to the change in PbO from 45 to 60 mol%.Moreover, it decreased from 0.038 to 0.028 cm at 0.1 MeV, from 0.478 to 0.361 cm at 0.3 MeV, and from 2.162 to 1.765 cm at 1 MeV.Additionally, Figure 9 shows that the HVL increased as the energy levels increased, indicating that lower-energy photons can lose their energy over a greater distance than higher-energy photons.This finding suggests that in order to shield greater numbers of photons, and particularly those with high energy, the requirement is for a thicker sample of glass.
The tenth value layer (TVL) was also determined, with the results summarized in Figure 10.The TVL profile was similar to the HVL profile for the four glasses, with the only difference in the magnitude, since each of these two parameters represents the required thickness to shield the photons to certain levels.The TVL commenced with small values (although higher than the HVL values) and varied in the 0.004-0.006cm range at 0.015 MeV, while it was found that the HVL at this energy was within the 0.001-0.002cm range.The TVL had a higher value than the HVL since it requires a greater thickness to reduce a larger percentage of the penetrating radiation.At 0.03 MeV, the TVL increased to 0.017-0.023cm.In general, the TVL for the studied glasses was lower than 0.1 cm for energies below 0.06 MeV and was lower than 1 cm when the energy was below 0.3 cm.It is important to mention that the TVL for the energy of 0.2 MeV was approximately 0.5-0.6 cm, and became in the order of 1.2-1.5 cm at 0.3 MeV.Therefore, a significant difference in the TVL was found between the two successive energies of 0.2 and 0.3 MeV, since as the energy increased, the photons easily penetrated the samples, and thus the thickness needed to be increased to stop or attenuate the higher energy photons.For the energy of 0.5 MeV, the TVL was in the order of 2.8-3.5 cm, so it was necessary to utilize a glass characterized by a thickness below 4 cm if radiation with an energy of 0.5 MeV was used.However, if the energy was greater than 0.5 MeV, then the thickness needed to be increased to 5-6 cm (if the energy was around 1 MeV), while the thickness needed to be in the order of 10 cm for the energy of 2 MeV.For energies above 5 MeV, the thickness had to be increased to greater than 11 cm in order to achieve safe protection.Therefore, to provide sufficient protection, the thickness of the glass to be utilized in practical applications is dependent upon the energy of the radiation.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), which represents the ratio between the LAC for two known materials.For instance, if the R is calculated for two samples A and B, and it is found that the R for sample A is higher than that for sample B, then it can be concluded that sample A is more effective in shielding the photons.Therefore, if the R for A and B is 20, it can be stated that sample A is 20 times better than sample B in terms of shielding the photons.The ratio between the LAC for the Q4 glass sample was determined with lead, iron, RS-520 glass, RS-360 glass, and RS-253-G18 glass, with the R for these materials plotted in Figure 11.The R was higher than one for all materials used for the comparison, except for the lead, where it was less than one.For RS-520, the R was approximately 1.3 for energies below 0.4 MeV, and therefore, the Q4 glass sample was 1.3 times more effective than the RS-520 glass in attenuating the photons, while the R was around 1.15 for energies above 0.4 MeV, which means that the attenuation performance of Q4 was close to the attenuation properties for the RS-520 glass at high energies.Moreover, the R for Al revealed that the Q4 glass sample had superior shielding performance than the Al, especially at an energy close to the K-absorption edge of Pb (in the low energy region).The R for the lead showed that the material had a higher attenuation performance than the Q4 glass sample, where the R at any energy was in the order of 0.4.

Conclusion
The investigation of the studied glasses' physical characteristics revealed that an increase in the concentration of PbO led to a rise in their density, molecular weight, and ion concentration.The increase in binding strength between Pb ions and oxygen resulted in elevated field strength around the Pb ion concentration.The oxygen molar volume increased while the OPD decreased, thus indicating changes in the packing arrangement of the oxygen atoms.Furthermore, the optical basicity of the glasses increased as more PbO was added, leading to an increase in the negative charge of oxygen atoms in the glass network.The behavior of electronegativity and electronic polarizability with respect to the mol percent of PbO in the glasses was opposite, with the electronegativity decreasing and the electronic polarizability increasing.The mechanical characteristics of the Q1-Q4 coded glasses depend on their composition, particularly the mol percent of PbO.When PbO is incorporated into a material, the elastic, bulk, and shear moduli all decrease while the material's hardness increases.To what extent the glass network is cross-linked may be inferred from Poisson's ratio and the fractal bond connectivity metric.The radiation-shielding properties of the prepared glasses were reported, whereby it was found that the addition of PbO could enhance the attenuation competence of the glasses, since the LAC and Z eff increased with the addition of PbO.According to the LAC data, the Q4 glass sample (60 mol% PbO) possessed the optimum attenuation properties.From the HVL results, a decrease in the thickness of the glass shield was noticed due to the increased PbO percentage.The TVL values were found to be higher than the HVL counterparts, since a greater thickness was required to reduce a larger percentage of the entering radiation.Through a comparison of the radiation-shielding properties of the sample glasses with other materials, the results demonstrated that the Q4 glass sample was 1.3 times more effective than the RS-520 glass in attenuating the photons, while the attenuation performance of Q4 was close to the attenuation properties for the RS-520 glass at high energies.

Figure 1 :N
Figure 1: Image of the samples.

Figure 2 :Figure 3 :
Figure 2: Density and molar volume versus the mol percent of PbO.

Figure 5 :
Figure 5: Mechanical parameters versus the mol percent of PbO.

Figure 11 :
Figure 11: The radiation coefficient ratio for selected materials.

Table 1 :
Physical parameters of the prepared glasses