Multidisciplinary Materials Chronicles

Figure 1. Simulation process geometry setup using FLAIR interface.

3. Results and Discussions

3.1.  Physical Properties

Figure 2 illustrates the variation in density and molar volume for glass compositions ranging from 50Te to 80Te. As depicted in Figure 2a, there is an upward trend in density for the glass samples from 50Te to 80Te, with values ascending from 4.858 to 5.251 g/cm³. Conversely, Figure 2b demonstrates a downward trajectory in molar volume for the same range of glass samples, decreasing from 31.24 cm³/mol to 29.80 cm³/mol. The increase in density is likely a consequence of the augmented Tellurium content, which escalates from 50 to 80 mol%. A reduction in molar volume is observed due to the inverse relationship between density and molar volume expressed by the equation ρ = M/V. This correlation implies that with the increment in glass density, there is a corresponding enhancement in material compactness, culminating in a diminished molar volume for the glass samples.

3.2. Shielding Properties

3.2.1. Macroscopic Cross-section

    Following the Beer-Lambert law, which is represented by the equation (1), the rate at which the intensity of radiation scattering and absorption that is transmitted via shielding materials (mixtures, alloys, and compounds) is measured expressed by [18]:

where I_o represents the intensity of incident photons, and I stands for the intensity of transmitted photons. With the help of Phy-X programs and the FLUKA Code, Table 2 illustrates the parameters that were determined by G_LAC and how they changed in response to the energy of the incoming photon. It can be seen from Table 2 that the results of the FLUKA simulations and the Phy-X analysis were in agreement for each sample. Additionally, the findings demonstrate that the G_LAC decreases as the amount of energy increases, which is a consequence of the high penetrating strength of radiation [19]. At the energy levels of 40 keV, sharp absorption edges were seen in Table 2 for all samples. This indicates the existence of Te elements, which are represented by the K-edge.

Figure 2. (a) Density and (b) molar volume change with sample concentration.

The results of a comparative study of G_LAC vs. energy for each of the samples are shown in Table 2. Since G_LAC is based on density, 80Te demonstrates the most outstanding G_LAC value due to its greater density. Table 2 also indicates that 50Te has the lowest G_LAC, another point of interest. According to the theory that the G_LAC lowers as density falls, this is compatible with the above idea.

3.2.2.  Mass Attenuation Coefficient

    To evaluate the mass-attenuation parameter (G_MAC), which is the ratio between the G_LAC and the density of the samples, equation (2) is used:

Figure 3 illustrates the G_MAC value calculated using FLUKA at several different energies. As a result of the fact that the mass attenuation coefficient is independent of density and is reliant on both the elemental composition and the atomic number of the element, it offers crucial insights into how the shielding qualities of a material may be adjusted by adjusting the nuclear configuration of a component. In addition, Figure 3 presents the calculated G_MAC values over a range of photon energies, as determined using the FLUKA simulation software. G_MAC, independent of material density, is a fundamental property that reveals the intrinsic ability of a substance to attenuate gamma radiation. It primarily depends on the elemental composition and the atomic number of the constituents within the material.

G_MAC is an invaluable metric for assessing how modifications in a material's elemental makeup can enhance its protective qualities in radiation shielding. The plot shows that the G_MAC decreases with increasing photon energy, which is consistent with the general behavior of photon attenuation in the matter. This trend reflects the dominant interaction mechanisms at different energy levels: the photoelectric effect at low energies, Compton scattering at intermediate energies, and pair production at high energies. The figure shows that the sample labeled as 80Te exhibits the highest G_MAC values across the studied energy spectrum. This suggests that the 80Te sample, with its higher proportion of Tellurium (which has a more significant atomic number than Molybdenum), presents a more effective gamma shielding material. The higher atomic number correlates with greater photon interaction cross-sections, thereby providing superior attenuation due to increased photoelectric absorption and other mechanisms. Such insights are crucial for designing materials for radiation shielding applications, particularly in fields where precise control over radiation exposure is necessary, such as nuclear medicine and diagnostics. By understanding the relationship between G_MAC and photon energy, researchers and engineers can better select and design materials that balance transparency with effective radiation absorption, ultimately leading to safer and more efficient use of nuclear technology.

Figure 3. Analysis of G_MAC for all samples versus photon energy.

3.2.3.  Half-Value-Layer (G_HVL)

When referring to the thickness of shielding materials capable of lowering radioactive quantities, the term G_HVL is used, expressed by equation (3) [20].

As seen in Figure 4, an inverse relationship exists between the G_HVL and G_LAC values. Furthermore, it is clear from Figure 4 that the G_HVL values progressively grow as the photon energy levels rise. This indicates that the shielding material must have a greater thickness to reduce the amount of Half-Value energy radiation [21]. Furthermore, it is evident from Figure 5 that a thickness that falls within the range of a few centimeters may significantly diminish the intensities of X-rays and γ- rays. The fact that the investigated glass samples 50Te, 60Te, 70Te, and 80Te had G_HVL values of 0.020, 0.018, 0.017, and 0.016 cm, respectively, at an energy of 50 keV, illustrates the relevance of the potential uses of these glasses.

Figure 4. Half-Value layers (G_HVL) using FLUKA code simulation for glass samples versus photon energy.

3.2.4.  Mean-Free-Path (G_MFP)

    During the process of a photon traveling through a substance, the photon may interact with either the atomic nuclei or the electrons of the material. Because of this interaction, the direction of motion of photons is altered to a large extent. G_MFP is the term used to describe the average route that photon travels through the material without encountering anything, being expressed by the equation (4) [22]. 

In Figure 5, we notice a rise in the average distance separating subsequent contacts. As the amount of energy grows, the G_MFP goes from a lower value to a larger one, eventually reaching a point where it is saturated and remains constant for all four samples. The 80Te sample has the most excellent density compared to other samples because Tellurium has a more significant molar fraction and a higher Z-number. As a result, the G_MFP of this sample is relatively low compared to different samples. 0.180, 0.164, 0.151, and 0.142 cm are the values of the G_MFP for our sample that was tested at an energy of 100 keV.

Figure 5. Mean-Free-Path (G_MFP) for all glass samples versus photon energy.

3.2.5.  Effective atomic number (Z_eff)

The value of the G_MAC that is obtained from the FLUKA simulation is used to assess the atomic cross section (σ_a) and the electronic cross section (σ_e) by using equations (5) and (6), respectively [23].

In addition, these values are then used to determine the effective atomic number (Z_eff) of the glass being investigated, given by the equation (7) [24].

Figure 6, illustrates the relationship between the effective atomic number (Z_eff) of the glass samples and photon energy. Z_eff is a measure of the overall shielding effectiveness of a material, representing an average atomic number that quantifies the composite effect of all the elements in the material on radiation attenuation [25]. The figure shows that Z_eff varies with photon energy, displaying a U-shaped curve typical of photon interaction processes. The increase in Z_eff with photon energy at low energies indicates the photoelectric effect being the dominant interaction mechanism. At intermediate energies, Z_eff decreases as Compton scattering becomes more prevalent. Z_eff rises again at the highest energies because pair production becomes the significant interaction process. This behavior reflects the increase in available electrons for photon interaction, which leads to a higher probability of photon attenuation by the material. In practical terms, a higher Z_eff at a given energy means that the material is more effective at blocking or attenuating photons at that energy level, which is crucial for designing materials for specific radiation shielding applications.

Figure 6. Effective atomic number (Z_eff) of glass samples versus photon energy.

Conclusion

    This study scrutinized glass compositions containing Tellurium and molybdenum oxide for their capabilities as radiation shielding materials. Through the application of FLUKA simulations and Phy-X/PSD analytical tools, the investigation focused on determining fundamental shielding properties, such as Gamma Mass Attenuation Coefficient (G_MAC), Gamma Linear Attenuation Coefficient (G_LAC), Mean Free Path (G_MFP), Half Value Layer (G_HVL), and Effective Atomic Number (Z_eff), across a photon energy range of 0.015 to 15 MeV. The research revealed a decline in G_LAC with an escalation in energy levels due to radiation's formidable penetrating prowess. An evident absorption edge was detected at the potential energy threshold of 40 keV for all glass samples, attributable to the K-edge absorption associated with tellurium elements. Notably, the 80Te sample distinguished itself by offering superior γ-ray shielding effectiveness, as suggested by its minimal G_HVL values. This heightened performance is ascribed to the more significant molar fraction of Tellurium and the consequent increase in the sample's effective atomic number (Z_eff) compared to the other samples evaluated. The G_MFP values demonstrated an initial decrease with rising energy levels, eventually reaching a plateau, indicative of a consistent saturation point across all four types of glass samples. The 80Te sample, with its maximal density, predictably exhibited a reduced G_MFP, underscoring its enhanced shielding efficacy.

Acknowledgments

H.M.H Zakaly thanks the Ministry of Science and Higher Education of the Russian Federation (Ural Federal University Program of Development within the Priority-2030 Program) is gratefully acknowledged.