Physical Features of High-Density Barium–Tungstate–Phosphate (BTP) Glasses: Elastic Moduli, and Gamma Transmission Factors

Abstract

We present elastic moduli, gamma radiation attenuation characteristics, and transmission factor of barium–tungstate–phosphate (BTP) glasses with the chemical formula (60-y)BaO-yWO₃-40P₂O₅, where y = 10 (S1)–40 (S4) in steps of 10 mole%. Different types of mathematical and simulation approaches, such as the Makishima-Mackenzie model, the Monte Carlo method, and the online Phy-X/PSD software, are utilized in terms of determining these parameters. The total packing density (V_t) is enriched from 0.607 to 0.627, while the total energy dissociation (G_t) is enriched by increasing the WO₃ content (from 52.2 (kJ/cm³). In the investigated glasses, increasing tungstate trioxide (WO₃) contribution enhanced Young’s, shear, bulk, and longitudinal moduli. Moreover, Poisson’s ratio is improved by increasing the WO₃ content in the BTP glasses. The 20BaO-40WO₃-40P₂O₅ sample possessed the highest values of both linear (µ) and mass attenuation (µm) coefficients, i.e., (µ, µm)_S4 > (µ, µm)_S3 > (µ, µm)_S2 > (µ, µm)_S1. Moreover, the 20BaO-40WO₃-40P₂O₅ sample had the lowest values of half (HVL) and tenth (TVL) layers, i.e., (half, tenth)_S4 < (half, tenth)_S3 < (half, tenth)_S2 < (half, tenth)_S1. The effective atomic number (Z_eff) of the studied glasses has the same behavior as µ and µm. Finally, the 20BaO-40WO₃-40P₂O₅ is reported with the minimum values of transmission factor (TF) for all the BTP investigated at a thickness of 3 cm. In conclusion, the sample with composition 20BaO-40WO₃-40P₂O₅ which has the maximum WO₃ reinforcement may be a beneficial glass sample, along with its advanced mechanical and gamma ray shielding properties.

1. Introduction

Radiology service has undergone enormous growth in terms of radiation procedures and personnel. It is widely known that most healthcare patients will stop by the radiology department. Besides computed tomography, the use of interventional procedures has risen in recent years. Nurses, surgeons, including orthopedics gemmologists, and other physicians are frequently present during radiation examinations [1,2]. Radiation workers and students in the medical field are exposed to unavoidable occupational radiation exposure [3,4,5]. However, radiation medical workers showed an understanding of the importance of radiation protection, but there is variation in the practice of radiation protection [6,7], and poor practice of using radiation protection tools was demonstrated [8,9]. The available lead shields are limited as they are challenging to use and carry due to heaviness and thickness. Therefore, medical radiation workers are not wearing lead shielding during procedures [10]. However, lead is the most popular shielding material; it has a few downsides that must be considered. Heaviness and musculoskeletal issues make it tough to use. Furthermore, it is a hazardous substance and raises biological and environmental problems [11]. Consequently, new shielding materials are needed to address the shortcomings of the lead apron and enhance radiation attenuation efficiency. Meanwhile, several investigations have been carried out to provide enhanced radiation protection techniques for the synthesizing and development of new shielding materials [12,13]. Recent investigations have stressed that glass shields [14,15,16,17,18,19,20] are one of the most ambitious materials that might be used as an alternative for conventional materials that are disadvantaged in certain ways. Researchers in the literature [21,22,23,24,25,26,27,28,29,30] are particularly interested in glass structures because of the high permeability they provide and the exceptional mechanical properties they possess. It has also been pushed to a position where it is emphasized and developed in daily radiation safety practice because of the non-toxic nature of glasses and the chemical compositions that may be synthesized at high densities. Glassy structures may be created using a wide range of chemical compositions. The unique optical, mechanical, structural, and radiation attenuation characteristics of each structure are enhanced because of this process.

Phosphate glasses have gained increased interest due to their potential applications in a variety of industrial and scientific fields, including radiation shielding, along with excellent physical characteristics, including high thermal expansion coefficients, low melting and softening temperatures, and high ultra-violet and far infrared transmission [31,32,33].

Barium oxide (BaO) is considered as a network modifier oxide in the glass structure [34]. Glasses containing phosphorus as a glass former and alkali and alkaline earth metals as modifiers have been found to be stable [35].

Tungsten trioxide (WO₃) is one of the oxides that, in a variety of P₂O₅ compositions, may combine to produce glass; these kinds of glass have high optical basicity and high refractive index [36,37,38]. A form of oxide known as WO₃ is introduced into glass compositions at different rates to boost the radiation-shielding properties of the glass. In this case, the relevance is derived from the monotonic impact that these WO₃ additive rates have had on the radiation shielding properties [36,37,38].

Since BaO has a relatively high density, we hypothesized that replacing barium oxide (BaO) with tungsten trioxide (WO3) would change the mechanical and gamma ray attenuation characteristics.

A group of BaO-WO₃-P₂O₅ glasses [38] with varying compositions was characterized to investigate the changes in radiation attenuation, mechanical, and gamma ray transmission characteristics that occur in conjunction with altering WO₃ additive ratios in a group of BaO-WO₃-P₂O₅ glasses [38]. These properties of four glass samples with varied structural features and WO₃ additive ratios were investigated systematically in this study. Accordingly, their elastic, mechanical, and radiation attenuation characteristics were extensively investigated.

In addition to providing a substantial contribution to the glass literature, the results of this work may contribute to a greater understanding of the role of WO₃ in the production and design of high-density glassy radiation shields.

2. Materials and Methods

2.1. High-Density Barium–Tungstate–Phosphate (BTP) Glasses

Through the current study, four barium–tungstate–phosphate glasses with the chemical formula (60-y)BaO-yWO₃-40P₂O₅, where y = 10–40 in steps of 10 mol%, were chosen [38]. The investigated glasses have the following criteria:

Table 1. Includes the sample codes, elemental weight fractions, density, and molar volume of the studied glasses.

Samples Code	Elemental Compositions (wt%)				Composition (mol%)			Density, ρ (g/cm3) ± 0.01 [38]	Molar Volume, Vm (cm3/mol) ± 0.01 [38]
	O	P	Ba	W	BaO	P2O5	WO3
S1	0.286015	0.158207	0.438403	0.117376	50	40	10	4.21	37.2
S2	0.291817	0.150655	0.333981	0.223546	40	40	20	4.18	39.4
S3	0.297091	0.143792	0.239075	0.320043	30	40	30	4.31	38.3
S4	0.301905	0.137526	0.152438	0.40813	20	40	40	4.5	40

.

(60-10)BaO-10WO₃-40P₂O₅ (S1) with density (ρ = 4.21 g/cm³ and molar volume (V_m = 37.2 cm³/mol)).

(60-20)BaO-20WO₃-40P₂O₅ (S2) with density (ρ = 4.18 g/cm³ and molar volume (V_m = 39.4 cm³/mol)).

(60-30)BaO-30WO₃-40P₂O₅ (S3) with density (ρ = 4.31 g/cm³ and molar volume (V_m = 38.3 cm³/mol)).

(60-40)BaO-40WO₃-40P₂O₅ (S4) with density (ρ = 4.50 g/cm³ and molar volume (V_m = 40.00 cm³/mol)), Table 1.

2.2. Elastic Moduli of Barium–Tungstate–Phosphate (BTP) Glasses

The mechanical elastic moduli of the proposed barium–tungstate–phosphate (S1–S4) glasses, including Young’s modulus (E^MM), bulk modulus (K^MM), shear modulus (S^MM), longitudinal modulus (L^MM), and Poisson’s ratio (σ^MM), have been investigated. This investigation has been achieved via the conventional Makishima-Mackenzie [39,40,41,42,43]. This model mainly depends on the functions of both total packing density (V_t) and the total dissociation energy per unit volume (G_t) of the chemical bonds in the glass samples, as [39,40,41,42,43]:

$$V_t=\left(\frac{1}{V_m}\right){\sum }_i\left(V_i{x}_i\right)$$

(1)

$$G_t={\sum }_i(G_i{x}_i) (\mathrm{k}\mathrm{J}/{\mathrm{cm}}^3)$$

(2)

where, (V_i) in Equation (1) and (G_i) in Equation (2) are the ionic radius and the average strength of each oxide in the glass composition for each sample. Via the values of (V_t) and (G_t), all elastic moduli can be given as [33,34,35,36,37]:

$$E^{MM}=2V_t{G}_t$$

(3)

$$K^{MM}=1.2V_t{E}^{MM}$$

(4)

$$S^{MM}=\frac{\left(3E^{MM}{K}^{MM}\right)}{\left(9K^{MM}-E^{MM}\right)}$$

(5)

$$L^{MM}=K^{MM}+\frac{4}{3}{S}^{MM}$$

(6)

Moreover, Poisson’s ratio (σ^MM) can be calculated as [39,40,41,42,43]:

$${\sigma }^{MM}=\left(\frac{E^{MM}}{2G^{MM}}\right)-1$$

(7)

2.3. Radiation Shielding Parameters and Transmission Factors (TFs) of Barium–Tungstate–Phosphate (BTP) Glasses

As a matter of fact, structural alterations in materials affect the lowering rate of energetic photons. Depending on the approach utilized, these alterations might be analyzed utilizing parameters or computed by assessing the complete material. Radiation transmission is characterized as a ratio between the intensity of the input radiation and output radiation, or secondary radiation, which is formed as a consequence of attenuation in the medium [44]. Monte Carlo simulation software, MCNPX [45], and a theoretical program, Phy-X/PSD [46], were utilized to calculate the gamma ray shielding properties and transmission factors (TFs) of the investigated glasses, respectively. For several well-known radioisotopes, such as ⁶⁷Ga, ⁵⁷Co, ¹¹¹In, ¹³³Ba and ⁹⁹Tc, there were individual TF values of each glass sample for various glass thicknesses. To quantify primary and secondary gamma radiation intensity, two detection zones (F4 Tally Mesh) [45] were set up in front of and behind the glass shield. Figure 1 depicts the MCNPX simulation setup for calculating the gamma ray transmission factor. Creating an adequate input file for a Monte Carlo simulation is the first step in creating a simulation environment that can be used for the investigation. We used a Lenovo^® ThinkStation-P620/30E0008QUS Workstation (Beijing, China) as our main processor throughout the Monte Carlo simulation.

3. Results and Discussions

3.1. Elastic Moduli of Barium–Tungstate–Phosphate Glasses

Relations (1) and (2) are used to calculate the values of the total packing density (V_t) and the total dissociation energy (G_t) of the suggested samples (S1–S4). These calculations have been performed via the (V_i) and (G_i) values of each glass oxide P₂O₅, BaO, and WO₃, as collected in

Table 2. Packing density factor (V_i), and dissociation/bond energy per unit volume (G_i) of the oxides BaO, WO₃, and P₂O₅.

Oxide	Vi (cm3/mol) [37,38]	Gi (kJ/cm3) [37,38]
BaO	13.1	40.6
WO3	21.3	67.8
P2O5	34.8	62.8

. Figure 2 and

Table 3. Total ionic packing density (V_t), total dissociation energy (G_t), Young’s modulus (E^MM), bulk modulus (K^MM), shear modulus (S^MM), longitudinal modulus (L^MM) and Poisson’s ratio (σ^MM) based on the Makishima-Mackenzie model of the studied glasses. The x_i is the mole fraction of component i of an oxide glass and V_m is the molar volume of the glass samples.

Parameters and Elastic Moduli	S1	S2	S3	S4
$V_t=\left(\frac{1}{V_m}\right){\sum }_i\left(V_i{x}_i\right)$ ± 0.001	0.607	0.594	0.633	0.627
$G_t={\sum }_i(G_i{x}_i)$ ± 0.001 (kJ/cm3)	52.2	54.92	57.64	60.36
$E^{MM}=2V_t{G}_t$ ± 0.01 (GPa)	63.426	65.291	72.961	75.631
$K^{MM}=1.2V_t{E}_{MM}$ ± 0.001 (GPa)	46.239	46.572	55.412	56.859
$S^{MM}=\frac{\left(3E_{MM}{K}_{MM}\right)}{\left(9K_{MM}-E_{MM}\right)}$ ± 0.001 (Gpa)	24.944	25.779	28.488	29.582
$L^{MM}=K_{MM}+\frac{4}{3}{S}_{MM}$ ± 0.001 (Gpa)	79.414	80.858	93.301	96.204
${\sigma }^{MM}=\left(\frac{E_{MM}}{2G_{MM}}\right)-1$ ± 0.001 (GPa)	0.271	0.266	0.281	0.278

show the changing of G_t and V_t parameters as a function of tungstate trioxide (WO₃) concentration in mol% of the S1–S4 glasses. Figure 2 shows that the value of (V_t) increases from 0.589 for the WO3-free sample (S1) to 0.605 for the WO3-rich sample. This can be explained as a result of increasing content of WO3 at the expense of P2O5, which energizes the glass structure. It can be further noticed that increasing WO3 beyond 10 mol% in the investigated glass network causes the overall packing density (V_t) to decrease slightly. This might be due to the peak of the largest band for W-O bond vibrations falling to a lower wavenumber. If we look deeply at Table 3 and Figure 3, we find that the (V_t) enhances from 0.607 to 0.627 for S1 and S4 glasses. The improving trend of (V_t) may be due to the larger ionic radius of WO3 compared to that of BaO. By the same trend, the (G_t) factory enhances from 52.2 to 60.36 (kJ/cm³) for S1 and S4 glasses, thus the trend of the (G_t) may be due to the WO₃ having the highest dissociation energy (67.8 kJ/cm³) compared to BaO (40.6 kJ/cm³) and P₂O₅ (62.8 kJ/cm³). The obtained values of (V_t) and (G_t) were applied in relation (3), and then Young‘s elastic modulus (E^MM) was calculated for all (S1–S4) glasses. In the next step, relation (4) was used to calculate the bulk modulus (K^MM) of the suggested glasses. Then, relations (5) and (6) were used to calculate both shear modulus (S^MM) and longitudinal modulus (L^MM), respectively. The obtained values of (E^MM), (K^MM), (S^MM) and (L^MM) are tabulated in Table 3 and plotted in Figure 3. As shown, the values of the (E^MM) were improved with an enhancement of tungstate trioxide (WO₃) concentration in glasses; the (E^MM) values varied from 63.426 GPa to 75.631 GPa for S1 and S4, respectively. This improvement may be related to the increase in the total dissociation energy and packing density with increasing in WO₃ concentration. Furthermore, as shown in Figure 3, the obtained values of the (K^MM) were enhanced from 46.239 Gpa to 56.859 GPa for S1 and S4 glasses. The values of the (S^MM) were improved from 24.944 GPa to 29.582 GPa, while values of the (L_MM) were increased from 79.414 GPa to 96.204 Gpa. In addition, via relation (7), Poisson’s ratio (σ^MM) of the investigated glasses was examined and its values were tabulated in Table 3 and graphed in Figure 4. The values of (σ^MM) were improved from 0.271 to 0.278 for S1 and S4 glasses. The trend of the elastic moduli of the current glasses may be related to the decrease in the amount of non-bridging oxygen (NBO) and vacancies as the WO3 concentration in glasses increases [39,40,41,42,43].

3.2. Radiation Shielding Features of Barium–Tungstate–Phosphate (BTP) Glasses

Another part of characterizing the explored glass group in this work was the measurement of the gamma ray shielding capabilities and transmission factors (TFs) of four individual glass samples (S1, S2, S3, and S4). The density of materials has a substantial effect on their gamma ray shielding characteristics owing to the increased possibility of interaction between the material and the gamma ray [47,48,49,50]. On the other hand, it is critical to observe the density variation of glassy materials to have a better understanding of the influence of integrated elements on the glass composition’s fluctuation. Figure 5 illustrates the variance in material densities of the tested glasses, S1, S2, S3 and S4. Between samples S1 and S4, there was a rise in glass density. The above-mentioned density increase may be explained by the fact that the WO₃ additive rate in the S1 sample has been continuously rising with each consecutive sample, leading to the maximum amount of WO₃ in S4 sample. As a consequence of the continuous WO₃ inclusion having the most impact on the S4 sample, the maximum glass density was determined to be 4.5 g/cm³. Furthermore, it was clearly observed that the net density difference between the S1 and S4 samples is 0.29 g/cm³. This variation may be explained by the elemental weight percent influence of W rising from 11 to 40 wt. percent in the glass composition, resulting in a net rise of glass density of 0.29 g/cm³. The initial phase of the recent investigation was the determination of linear attenuation coefficient (µ), which is a fundamental property of a candidate shielding material that can be determined for various photon energy values from low to high (MeV). The variation of the µ values regarding different energy values is illustrated in Figure 6 as a function of utilized photon energy values from 0.015 to 15 MeV. When an incoming photon interacts with the corresponding shielding matter, it might undergo several special interactions (i.e., photoelectric effect, Compton scattering, and pair production), with some having priority over others. For instance, the photoelectric effect (PE) is the most prominent of the few types of interactions found in the low-energy zone. As seen in Figure 6, linear attenuation coefficients have begun to decrease dramatically in the low-photon energy zone. This significantly declined trend in low energy is the result of the supremacy of the PEA procedure, which is α Z⁵ and (1/E3.⁵). Accordingly, the S4 sample had the highest linear attenuation coefficients in comparison to all other glass materials, namely S1, S2, and S3, examined. The majority of the cause for this circumstance is due to the maximum WO₃ contribution described above, as well as the WO₃ additive’s direct effect on the glass’ density. Compton scattering predominates in the medium energies, which are α Z and (1/E), whereas pair production prevails at high-photon energies, which are α Z². Figure 6 shows that the low-energy region has sharp discontinuities near element absorption edges. The sharp peaks are ascribed to K-absorption edges at 0.035 MeV and 0.06 MeV. The appearance of these edges is due to the presence of Ba and W, respectively. Following the determination of µ values in a variety of photon energies, another critical gamma ray shielding parameter, which is known as the mass attenuation coefficient (µ_m), was also determined for the same photon energy range. Figure 7 demonstrates the relationship between increasing gamma ray energy and corresponding µ_m values (cm²/g) for all S1–S4 samples. We noticed a remarkable similarity in behavioral attitudes, such as linear attenuation coefficients, over a broad variety of gamma ray energy ranges, including low-, intermediate- as well as high-energy photons. Compared to other examined glass samples, the S4 sample had the greatest µ_m values of all photon energies studied. One potential explanation for this circumstance is that the highest elemental concentration of WO₃ in the structure of S4 altered the behavior of mass attenuation coefficients, owing to the compound’s higher atomic number. Owing to the certain substitutions that have been implemented in the glassy matrix, this has resulted in a drop in the number of low-atomic-number elements, resulting in an increase in the incorporation of high-atomic-number elements, such as W. It broadly recognized that calculating shielding properties of the candidate materials may be performed in different useful ways, each of which enables the user to input a range of various types of data that may be useful in actual applications. Half value layer (HVL) as a shielding parameter may be considered as a part of the decision process not only for superiority but also for engineering aspects of the manufacturing process of the shielding materials. Therefore, the term half value layer clearly stresses the attenuation produced by shielding materials engaging with gamma rays on an atomic scale. The HVL measurements are very valuable for determining the needed shield thickness of a material at which gamma ray intensity is reduced by half. For that purpose, any shielding material capable of halving the strength of gamma radiation at thin layers is deemed an ideal shield for utilization purposes. In the recent investigation, we evaluated the HVL values for glass samples throughout an energy range of 0.015–15 MeV as attenuation coefficients. As shown in Figure 8, the observed behaviors of the investigated specimens varied substantially as the photon energy increased and, accordingly, HVL thickness increased. The half value widths are smallest in the region of low-photon energy, but they increase correspondingly as energy levels increase. The HVL values needed for the low-energy photons in all the glass samples studied are very thin, owing to the weak penetration properties of those photons. However, required HVL thickness values increased dramatically in the zone of high energy, as shown in Figure 8. According to our calculations, the S4 sample with the maximum WO₃ contribution exhibits the lowest HVL values across the entire photon energy range from low to high. Calculating the effective atomic number (Z_eff) of a compound may be a valuable technique for monitoring overall variations in the gamma ray attenuation qualities as a function of the atomic number variation in complex structures. In other words, the primary reason for calculating this value is because the structural changes generated by chemical alterations to the material define the atomic number that will be effective in the photon energy responsible. Figure 9 depicts the changes in Z_eff values as a function of photon energy. As previously stated, S4 has the highest WO₃ incorporation, which provided some considerable effects on previously described shielding metrics, such as linear and mass attenuation coefficients, as well as half-value layer values. The increase in overall atomic number with the incorporation of W (Z = 74) in the glass matrix was shown to result in a large rise in Z_eff in the lowest energy range. According to our findings, the S4 with the highest mass attenuation coefficients exhibits the highest Zeff values for the relevant photon energy. As a final stage of the characterization process, the gamma ray transmission factor (TF) values for the investigated glass samples were determined for several commonly used radioisotope energies, including ⁶⁷Ga, ⁵⁷Co, ¹¹¹In, ¹³³Ba, ²⁰¹Tl, ⁹⁹Tc, ⁵¹Cr, ¹³¹I, ⁵⁸Co, ¹³⁷Cs, and ⁶⁰Co. For samples with varied glass thicknesses, TF factors were determined. Figure 10 depicts the transmission factors (TFs) of studied glasses as a function of used radioisotope energy (MeV) at various glass thicknesses. The calculated transmission factors rise in proportion to the increasing radioisotope energy (from 0.0086 MeV to 1.3326 MeV). Our initial findings strongly indicated that, regardless of composition, the TF values in the low-energy zone were the lowest for glass samples of all thicknesses. Glass samples of varying thicknesses display a spectrum of reactions after being exposed to 0.1 MeV gamma rays. Maximum attenuation (also known as the lowest TF) values were recorded for all glass materials studied at a thickness of 3 cm. Due to the fact that the attenuation capacity of any shielding material is exactly proportional to its thickness, this situation may be attributed to the fact that increasing the shield thickness increases the attenuation potential of gamma rays reaching the shielding material’s structure. Furthermore, we compared the attenuation abilities of the analyzed glasses at 0.5 cm, 1.5 cm, 2.5 cm, and 3.0 cm glass thicknesses. Figure 11 illustrates various glass thicknesses as a function of the radioisotope energy (MeV) utilized to calculate the transmission factor (TF). As can be seen, all thicknesses display a decrease in TF values as the quantity of incoming gamma ray energy rises. When exposed to high-energy gamma rays, the S4 sample has shown exceptional transmission characteristics across all glass thicknesses utilized at the final stage of the TF characterization phase.

4. Conclusions

Four samples of barium–tungstate–phosphate (BTP) glasses with the chemical formula (60-y)BaO-yWO₃-40P₂O₅, where y = 10–40 in steps of 10 mol%, have been selected. Makishima-Mackenzie model, Monte Carlo code, and the newly online Phy-X/PSD software were applied to investigate the elastic moduli, gamma radiation attenuation characteristics, and transmission factors of the BTP glasses. According to our findings, the total packing density (V_t) was enriched from 0.607 to 0.627 for S1 and S4 samples. Similarly, the total energy dissociation (G_t) of the tested glasses was enriched by increasing the WO₃ content (from 52.2 (kJ/cm³) for S1 glasses to 60.36 (kJ/cm³) for S4 glasses). By increasing the tungstate trioxide (WO₃) in the investigated glasses, Young’s, shear, bulk, and longitudinal moduli were enhanced. Furthermore, Poisson’s ratio was improved by increasing the WO₃ content in the BTP glasses. The S4 sample possessed the highest values of both linear (µ) and mass attenuation (µ_m) coefficients. However, (µ, µ_m)_S4 > (µ, µ_m)_S3 > (µ, µ_m)_S2 > (µ, µ_m)_S1. Aside from this, the S4 sample had the lowest values of half (HVL) and tenth (TVL) layers in comparison to the other examined glasses. Therefore, (half, tenth)_S4 < (half, tenth)_S3 < (half, tenth)_S2 < (half, tenth)_S1. The effective atomic number (Z_eff) of the studied glasses has the same behavior as LAC and MAC. Finally, S4 achieved the minimum transmission factor (TF) values for all the BTP investigated at a thickness of 3 cm. However, the S4 sample exhibited superior radiation shielding characteristics.