Determination of gamma-ray transmission factors of WO₃–TeO₂–B₂O₃ glasses using MCNPX Monte Carlo code for shielding and protection purposes

1 Introduction

Photon–matter interaction, which allows us to examine the interior structure of a material, is a commonly used concept in the medical sector for the purposes of diagnosis and therapy [1,2]. Although the sort of energy created by the radioisotopes used for diagnosis and treatment is advantageous for research, it has, on the other hand, harmful effects on biological tissues [3,4]. For the best protection conditions against the hazardous consequences of ionizing radiation, it is essential to comprehend all the quantifiable shielding properties of materials that may absorb the given radiation energy [5]. Meanwhile, lead (Pb) is one of the most traditional materials used for shielding purposes in various radiation fields. However, Pb is a toxic element that has detrimental biological effects when it enters the body by breathing and skin absorption. Therefore, various ongoing research aim to extend the design of shielding materials made without Pb and Pb-based compounds. In recent years, various types of alternative materials such as polymers, glasses, concrete, building supplies, ceramics, etc. have all been used due to the enormous scientific motivation provided by these drawbacks of Pb. The development of radiation shielding materials with innovative and environmentally advantageous properties has been pursued. The removal of Pb from the design of glass materials, which are vital components of nuclear medicine units [6–10], is one of the primary objectives of researchers. It has been shown earlier [11–15] that glasses containing oxide-based additions possess intriguing shielding properties. In the meantime, it is difficult to achieve a glassy structure without a glass modifier. Hereby, borate is one of the most often used and effective materials for producing glass (B₂O₃). Strong tungsten–oxygen (W–O) bonding and a strong polarization capacity make tungsten-oxide (WO₃) a fascinating material for application in glass technology [16]. To improve their mechanical and shielding characteristics, glasses often include WO₃ such as telluride, borate, and phosphate glasses [16–19]. The telluride glass systems, particularly binary TeO₂–WO₃ glasses, on the other hand, are the subject of the most popular research [19,20]. Tellurite’s glass formation and thermal stability may be improved by adding ZnO [21]. As a result, researchers are focused on expanding the spectrum of shielding glass material groups and developing the ideal glass structure for this use. The creation of radiation shielding materials made of glass is the subject of extensive investigation. Glass systems like ZnO–TeO_2, B₂O₃–P₃O₄–ZnO, and WO₃–ZnO–PbO–B₂O₃ that include zinc oxide as one of its components have been studied recently for their radiation shielding characteristics [21–23]. Recent studies have examined how the addition of WO₃ to the synthesis and nuclear safety features of the telluride glass system might significantly modify the nuclear shielding properties [24–26]. Particularly, if the radiation shielding parameters could be defined for each energy value generated by radioisotopes used in nuclear medicine, it would be simpler to decide the structure that can be employed for shielding and give the maximum degree of protection [27]. Radiation shielding operates on the attenuation principle, which states that a barrier material will stop or deflect particles while decreasing the efficacy of waves or rays. Moreover, it is crucial to investigate the tenth value layer, half value layer, effective atomic number, exposure build-up factor (EBF), and energy absorption build-up factor (EABF) of the sample glasses in terms of better understanding the overall attenuation behaviours of the shielding materials. To expand the earlier work [28], the unstudied shielding parameters of the WO₃–TeO₂–B₂O₃ composite system, whose structural, physical, and optical aspects have been thoroughly studied, but only a few of its shielding parameters have been explored, are reviewed in detail. Moreover, transmission factor (TF) values are determined for some well-known radioisotopes’ energies, which ranged from 0.0086 to 1.3325 MeV, to investigate the shielding capabilities using the Monte Carlo method. The results of this investigation may be utilized in future investigations or to assist researchers with similar scientific goals.

2 Materials and methods

2.2 Shielding parameters and gamma TFs

To achieve the goals of this study, six glasses containing tungsten trioxide, tellurium dioxide, and boron trioxide (WO₃–TeO₂–B₂O₃) were chosen from previous research [28]. As a means of keeping the photon energy range explored in this work at a much higher level, the gamma-ray energies of various radioisotopes (0.0086–1.3325 MeV) are utilized to determine TFs. However, the unexplored shielding characteristics of the glasses were assessed with the aid of the Phy-X/PSD (Photon Shielding and Dosimetry) software [11]. The gamma TFs were calculated using MCNPX 2.7.0 general-purpose Monte Carlo simulation program. The TFs of glasses (i.e., S1–S6) having diverse chemical compositions of WO₃–TeO₂–B₂O₃ were comprehensively evaluated and compared using several evaluation parameters [29–32]. During the computation of TFs for a wide number of radioisotopes, as shown in Table 2, each input file has been designed considering the elemental mass fractions, densities, and other related parameters of the glasses that are essential for an input determination. Figure 1 depicts the layout of the MCNPX simulation used to determine the gamma-ray transmission coefficient. The TF of the absorber was calculated by dividing the total radiation flux (F) by the radiation flux (I) after absorption process by attenuator material. To estimate the TF of the investigated glasses, the average gamma-ray flux in the F4 tally mesh was multiplied by the average gamma-ray flux in the uniform detection field. Two detecting fields, one in front and one behind the glass, were used to convert this formulation into MCNPX code. This formulation was translated into MCNPX [33] code by using two detecting fields, one in front of the glass and one behind the glass. Both the main gamma-ray intensity in front of the glass and the attenuated gamma-ray intensity behind the glass were measured and detected instantly.

Table 2

Gamma ray energies of nuclear-type radioisotopes

Radioisotopes	Gamma-ray energy (MeV)
67Ga	0.0086, 0.0093, 0.1840
57Co	0.0144, 0.1221, 0.1365
111In	0.0230, 0.1710, 0.2450
133Ba	0.0532, 0.0796, 0.0810, 0.2764, 0.3029, 0.3560, 0.3838
201Tl	0.0710, 0.1350, 0.1670
99mTc	0.1405
51Cr	0.3201
131I	0.2843, 0.3645, 0.6370, 0.7229
58Co	0.5110, 0.8108
137Cs	0.6617
60Co	1.1732, 1.3325

Figure 1

2-D and 3-D illustration of designed MCNPX setup (2-D and 3-D views are obtained from MCNPX Visual Editor VisedX22S).

3 Results and discussions

The direct contribution of structural changes to the absorption qualities of glass materials may be examined by calculating the radiation absorption characteristics of glass materials in accordance with specified parameters [34–45]. The term effective atomic number (Z _eff) is of great interest for radiation researchers due to its role during the absorption process of initial photons in the material. It is worth mentioning that the gamma-ray radiation scattering and absorption are related to the Z _eff values of the investigated glass samples. As seen in Figure 2, Z _eff values changed as a function of incoming photon energy (MeV). As the photon energy increased, it was obvious that the Z _eff values for the glass samples also altered. In the low-energy zone, the photoelectric effect predominates due to the photon–matter interaction. Consequently, the low-energy photons on the absorbing layer interact with the electrons in the orbit of the material medium, contributing their whole energy to this interaction and achieving complete absorption. In response to an increase in photon energy, electrons in this orbit are ejected, and photons with decreasing energy are released to generate secondary and subsequent collisions. In this situation, Compton scattering is the most prominent photon–matter interaction in the mid-energy region. Due to the k-absorption edge of Te (i.e., 0.31 keV), the Z _eff values reached their maximum at 0.3 MeV on the graph. On the other hand, Z _eff value exhibits a progressive rise when energies above 2.0 MeV are considered (Table 3). For the photon-exposed sample glasses, the effective electron number (N _eff) changes in the same way as Z _eff does [46–48]. The effective atomic number (Z _eff) and the effective electron density (N _eff) both show contradictory tendencies in their relationship with the energy of the incident photon (MeV), with values beginning to diverge in opposite directions around 0.04 MeV. For the photon-exposed sample glasses, the effective electron number (N _eff) changes in the same way as Z _eff does. This is mostly due to the correlation between the effective atomic number and the effective electron number. As is well known, the number of electrons a nucleus contains is proportional to its atomic number. As the atomic number grows, so does the number of electrons, which is the primary reason that elements with a high atomic number are better in their ability to absorb photons. The photon that reaches the atomic orbit contacts several times with a large number of electrons and is absorbed more efficiently and in less time as a consequence. The effective atomic number (Z _eff) and the effective electron density (N _eff) both show contradictory tendencies in their relationship with the energy of the incident photon (MeV), with values beginning to diverge in opposite directions around 0.03 MeV. The Z _eff values (Figure 2) converge until 0.08 MeV, after which they diverge with a significant rise in the value difference. They continue in the same sequence until the very end, when S6 shows the highest values, followed by the remaining glasses in descending order until S1 reports the lowest values. At 0.04 MeV, the N _eff values diverge, making it simpler to discern the S6–S1 values in decreasing order. Before proceeding, they momentarily swap to S1–S6 decreasing values (Figure 3). In Figure 4 one can see that the photon’s energy level correlates with the atomic equivalent number Z _eq. This pattern is most notable for the rapid rise at 0.03 MeV, which is followed by a less abrupt increase at 0.07 MeV, with S1 having the lowest value and the other glasses rising steadily until S6 has the highest value. Meanwhile, the terms EBF and EABFs are crucial for assessment of photon absorption process considering the interacted and un-interacted photons with the absorber material. In this study, both the EBF and the EABF were calculated, and the results are presented in Figures 5 and 6 as a function of energy (MeV) over a range of mean free paths (from 0.5 to 40 mfp). Consistent increases in these quantities are seen for increasing photon energies, with the largest increases occurring at 0.04, 0.06, 0.08, 0.1, and 15 MeV. However, the EBF and EABF values alter significantly when the energy is increased up to 15 MeV, although they are less visible at shorter penetration depths. In general, with denser materials and a broader spectrum of incoming X-rays or gamma rays, larger mfp values result in photon accumulation. Energy ranges serve as the basis for EABF and EBF values. High values are visible in high energy, while low values are visible in low energy. This is caused by pair production at high energies, which results in the total absorption of photons, and the dominance of photoelectric processes at low energies. The energy of incident photons is decreased throughout this process, yet they are not entirely absorbed. Consequently, multiple scattering is generated by this mechanism, which leads to an accumulation of photons in the medium. Based on our results, S6 has the highest EBF and EABF values, while S1 has the lowest. To estimate the effective atomic number (Z _eff) of the studied glasses, it is necessary to establish the radiation shielding parameters such as atomic cross-section (ACS) and electronic cross-section (ECS). Figure 7 illustrates the variation of the ACS as a function of the photon energy entering the system, whereas Figure 8 depicts the variation of the ECS. Out of the six glasses tested, S1 sample had the maximum attenuation of gamma rays, indicating that it is the most effective gamma-ray shield. To calculate the effective atomic number (Z _eff) of the examined glasses, it is essential to know the radiation shielding parameters such as ACS and ECS. As can be seen in both figures, as the photon’s energy rises, both the ACS and ECS values decrease. Moreover, in every glass sample, the ACS values were greater than the ECS values. This is due to the fact that the likelihood of full atomic interaction in any given material is far greater than the probability of full electrical contact with incoming photons in any given material. In the last part of this study, the values of the gamma-ray TF were determined for each of the glass samples that were evaluated for a range of radioisotope energies between 0.0086 and 1.3325 MeV. Two different methods were used determine the glasses’ TF values. The TF factors of samples S1–S6 with varied glass thicknesses were measured first. These samples were put through a series of tests. Figure 9 depicts the TF of the examined glasses as a function of the radioisotope energy (MeV). Transmission increases as the energy of the radioisotope increases from 0.0086 to 1.3325 MeV. This is due to an increase in the number of photons capable of penetrating the opposite side of the material. Moreover, as shown in Figure 9, although transmission values reach their maximum at low glass thicknesses, TF values tend to decline as glass thickness increases. This indicates that the number of photons that travel through the glass at low thicknesses is higher, whereas this rate decreases as the thickness increases. At around 0.1 MeV, however, a distinct separation becomes apparent. Glass samples of varying thicknesses respond to gamma rays in different ways. As the energy level grows, these distinctions become more prominent. For all the analysed glass samples, the maximum attenuation values (and the lowest transmission values) were obtained at a thickness of 3 cm. This effect demonstrates that an increase in shield thickness will result in a greater attenuation of incoming gamma rays. Figure 10 depicts TFs as a function of radioisotope energy for various glass thicknesses (MeV). At different glass thicknesses, such as 0.5, 1.5, 2.5, and 3 cm, the TFs of all glass samples are changed.

Figure 2

Variations of effective atomic number (Z _eff) with photon energy (MeV) for all S1–S6 glasses.

Figure 3

Variations of effective electron density (electrons/g) with photon energy (MeV) for all S1–S6 glasses.

Figure 4

Variations of equivalent atomic number (Z _eq) with photon energy (MeV) for all S1–S6 glasses.

Figure 5

Variation of EBF of investigated glasses at different mean free path values.

Figure 6

Variation of EABF of investigated glasses at different mean free path values.

Figure 7

Variations of atomic cross-section with photon energy (MeV) for all S1–S6 glasses.

Figure 8

Variations of electronic cross-section with photon energy (MeV) for all S1–S6 glasses.

Figure 9

TFs of investigated glasses as a function of used radioisotope energy (MeV) at different glass thicknesses.

Figure 10

Comparison of the TFs as a function of used radioisotope energy (MeV) for different glass thicknesses.

4 Conclusion

The aim of the research was to broaden the scope of a previous study conducted on WO₃–TeO₂–B₂O₃ glasses in order to gain a better understanding of the effects of varying quantities of WO₃ additive by calculating crucial gamma-ray absorption parameters and analysing its contribution to the absorption properties in a more comprehensive manner. Accordingly, some critical gamma-ray attenuation properties such as Z _eff, N _eff, Z _eq, EBF, EABF, ACS, ECS, and TFs of six different glass samples were determined in a wide-range photon energy. In transmission tests using the MCNP code, the gamma-ray transmission ratios of the glasses investigated with a broad variety of radioisotopes were also evaluated. As WO₃ concentration and molar volume increase, it has been observed that sample density decreases. In addition to confirming previously published gamma-ray absorption values, the findings of this investigation also demonstrated that the decrease in density caused by the higher WO₃ ratio in the TeO₂/WO₃ translocation had a detrimental effect on all those parameters. The glass sample S1 (ZnO–B₂O₃–TeO₂), which has the highest proportion of TeO₂, is found to have the best shielding composition among the samples investigated in this investigation. According to the findings of this investigation, the density of the oxide type added to the glass composition plays an essential role in defining its absorption properties. Among the various translocated oxides, the percentage increase in the composition of the low-density oxide has the potential to generate a disadvantage by reducing the absorption capabilities.