1 Introduction

With the increasing use of nuclear applications in our daily lives, the possibility of exposure to ionizing radiation has also increased. The use of nuclear applications outside science and industry, particularly in the medical field, has increased the possibility that even people who do not work with radiation may be exposed to ionizing radiation above levels considered normal. Therefore, the exponential increase in the use of ionizing radiation has led to an acceleration of such radiation protection studies [1,2,3,4].

The three protective measures used in the effective implementation of the ALARA (as low as reasonably achievable) principle, which is the basic principle for working with ionizing radiation, and in radiation protection in general, are time, distance, and shielding. As their names suggest, the less time spent with the radioactive source, the farther away from the source, and the better the source is shielded, the farther away from the lethal effects of radiation [5, 6]. Of these three measures, shielding has a growing research potential, and scientists are constantly working on new types of materials and their shielding properties [6,7,8,9]. Although these studies initially focus on the shielding properties of the material against radiation, the structural properties of the material according to the area where it will be used are also very important. It may be desirable to have a lightweight material that shields against radiation, or it may be desirable to have a material that is both lightweight and strong enough to be a construction material. In addition, it may be desirable for the material to be able to provide good shielding against more than one type of radiation, or it may be desirable to have a material that provides protection against radiation, is resistant to radiation damage, and can be worn in a different area of application. The fact that there are so many applications means that new materials are constantly being investigated. Another point to mention is some of the undesirable properties of lead, which is traditionally used against ionizing radiation [4, 5, 7]. Although the use of lead is an effective method of shielding, the highly toxic nature of lead is its most undesirable feature. Furthermore, the high density of lead makes it a very heavy material, another undesirable characteristic. It should also be noted that lead is not a good construction material when these two undesirable characteristics and its mechanical properties are taken into account. The use of lead, for which alternatives are currently being studied even on Earth, is seen as a very distant option in space travel and studies that have accelerated in the last 20 years and are expected to progress to the colonization of another planet in the coming years.

Aluminum oxynitride (AlON), the subject of this study, has attracted a lot of attention in the field of materials in recent years with its mechanical and other properties [10,11,12,13,14,15,16,17,18]. AlON or more commonly known as transparent aluminum is a composition of Al2O3 and AlN. AlON stands out as a unique single spinel-phase solid solution within the Al2O3–AlN mixture, characterized by the composition Al(64 + x)/3O(32-x)Nx, where x ranges from 0 to 8. Studies point to the significance of AlON when x equals 5, leading to the formulation of Al23O27N5 as the most stable and stoichiometric phase. This particular phase adopts a cubic crystal structure, resulting in isotropic optical properties [15, 19]. Since the AlON is a ceramic metal, the material shows excellent mechanical properties like strength, resistivity to chemicals and also transparency from the ultraviolet to mid-infrared wavelengths range. A complete set of mechanical and optical properties of AlON are given in detail in Salifu et al. [20] and Ramisetty et al. [21]. Transparent aluminum already finds itself useful areas such as transparent armor, missile domes, IR windows, opto-electronics, military aircraft, LEDs with its exceptional properties [15, 17,18,19,20].

Along all the properties which AlON have, its most striking feature, and the reason it is the subject for this paper, is its transparency. Although it is a type of ceramic, it can be used like glass because it is transparent-to-visible light. This would make AlON a very advantageous material for shielding if it also had good shielding properties against gamma radiation. Lead-equivalent glasses are used in many medical applications, from radio-pharmaceutical production to nuclear imaging and radiotherapy. They are also used in spacecraft and on the International Space Station (ISS), where cosmic radiation is intense. AlON, which does not contain toxic components such as lead and whose mechanical properties are highly suitable for use in such situations, could represent a breakthrough in both of these areas. To our knowledge, no study assessing the gamma shielding properties of AlON has been conducted yet.

In this study, the properties of AlON such as linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), half-value layer (HVL), tenth-value layer (TVL), mean-free path (MFP), effective atomic number (Zeff), and effective electron density (Neff) were investigated to determine the radiation shielding properties of the material via Monte Carlo simulations and theoretical calculations. The study is organized as follows: In Sect. 2, the methodology of the study is given, in Sect. 3, the above-mentioned properties are determined, and the results obtained are discussed. The fourth and last section summarizes the results and concludes the study.

2 Methodology

This study investigates the attenuation properties of the most stable state of AlON, represented as \({\text{Al}}_{{23}} {\text{O}}_{{27}} {\text{N}}_{5}\), through Monte Carlo simulations and theoretical analysis. The investigation employs the Geant4 and XCOM programs, respectively [22,23,24,25]. XCOM is a photon cross-section database that quickly calculates mass attenuation coefficients for elements, compounds, and mixtures. Conversely, Geant4 is a C++ based Monte Carlo simulation toolkit that is ideal for simulating complex nuclear and particle physics experiments.

This study investigates the attenuation parameters, including LAC, MAC, TVL, HVL, and MFP, for an \({\rm Al}_{23}{\rm O}_{27}{\rm N}_{5}\) sample [26, 27]. Additionally, Zeff and Neff values are explored over a wide energy range [28, 29]. Table 1 shows how to calculate these parameters for a given sample.

Table 1 Common attenuation parameters for photon and calculation method
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The first equation, known as the Beer–Lambert law, can be used to calculate linear attenuation coefficients for both photons and neutrons [8, 27]. The variables x, I, and \(I_0\) represent the thickness of the sample, the number of unaltered photons that passed through the sample, and the initial number of photons that arrived at the sample, respectively.

The calculation of mass attenuation coefficients for a given sample using XCOM involves inputting parameters such as the atom ratio. On the other hand, Geant4 requires an experimental setup that closely resembles the real one to obtain meaningful results. This necessitates the inclusion of all relevant components in the setup. In this study, an experimental setup was designed using Geant4 to investigate the attenuation properties of AlON. The experimental setup includes a rectangular AlON crystal, a detector positioned behind it, and a narrow beam gamma source integrated into the simulation. The unaltered photons are counted after passing through the AlON sample. The basic design of this setup is shown in Fig. 1.

Fig. 1
figure 1

Setup of attenuation experiment that prepared in Geant4

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In Fig. 1, the lead shield is represented by the blue cubic shape and acts as a collimator. The detector is represented by the white cylindrical shape on the right. The sample investigated for its attenuation properties is represented by the rectangular red shape. For demonstration purposes, \(10^5\) primaries were used, and it is clear from Fig. 1 that the narrow beam reaches the sample. The energy range investigated is between \(10^{-3}\) MeV and \(10^{5}\) MeV, based on XCOM’s standard energy interval. The following section systematically presents the results on the attenuation properties of transparent aluminum.

3 Results and discussions

In order to compare the theoretical calculation of XCOM with the simulation results of Geant4, we began by investigating the linear attenuation coefficients (LACs) of transparent aluminum oxynitride. Figure 2 shows the LACs of AlON in the range of \(10^{-3}\) MeV and \(10^{5}\) MeV. Both XCOM and Geant4 provide almost identical values in this range, with the only visible difference occurring around \(10^{-1}\) MeV, which is the transition area of photoelectric effect and Compton scattering. Also, as shown in Fig. 3, the comparison for MACs indicates a very good agreement between theoretical calculation and simulation, with the difference being hardly noticeable.

Fig. 2
figure 2

Linear attenuation coefficients comparison for aluminum oxynitride (XCOM and Geant4)

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Fig. 3
figure 3

Mass attenuation coefficients comparison for aluminum oxynitride (XCOM and Geant4)

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Fig. 4
figure 4

Mass attenuation coefficients (MACs) for AlON, ordinary concrete and lead

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Upon closer examination of Fig. 4, it is evident that the MAC values decrease rapidly between 0.001 and 0.08 MeV due to gamma-matter interaction, specifically the photoelectric effect, which is dependent on \(Z^{4-5}\). The subsequent region, ranging from 0.1 to 6 MeV, exhibits a slower decrease in MAC values compared to the previous one. In this region, the Compton effect is highly dominant, and the change in the MACs depends on the atomic number Z. The remaining region, where the pair production mechanism is dominant and the MACs depend on \(Z^2\), is decreasing very slowly, almost linearly [30].

Fig. 5
figure 5

Linear attenuation coefficients (LACs) for AlON, ordinary concrete and lead

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Figure 5 displays a comparison of the linear attenuation coefficients (LAC) of AlON, concrete, and lead. As expected, they exhibit a similar trend with respect to the mass attenuation coefficients (MAC). The LAC values decrease rapidly in the photoelectric effect (PE) region, slowly decrease in the Compton scattering (CS) region and then, follow an almost linear trend in the pair production (PP) region. The LAC values range from 0.6 to \(1.1 \times 10^4\) \({\rm cm}^{-1}\) in the PE region, 0.09 to 0.6 \({\rm cm}^{-1}\) in the CS region, and 0.07 to 0.1 \({\rm cm}^{-1}\) in the PP region.

One crucial aspect of gamma radiation is the half-value layer, which simply represents the thickness needed to block half of the gamma rays. As illustrated in Fig. 6, there is a clear contrast in trends between MACs and HVLs. HVLs exhibit an increasing pattern as energy levels increase. Specifically, the values show a rapid escalation in the range of \(1.0 \times 10^{-3}\) MeV to \(1.0 \times 10^{-1}\) MeV, a gradual increase from \(1.0 \times 10^{-1}\) MeV to \(1.0 \times 10^{1}\) MeV, and minimal variation in the subsequent energy range. The HVLs of aluminum oxynitride span from \(7 \times 10^{-5}\) to \(1 \times 10\) cm in the PE region, 1.2 to 8.3 cm in the CS region, and 6.7 to 9.7 cm in the PP region. A comparative analysis shows that lead exhibits the highest effectiveness among the three materials, followed by AlON, with ordinary concrete ranking third.

Fig. 6
figure 6

Half-value layer (HVLs) for AlON, ordinary concrete and lead

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Figures 7 and 8 show the trends in TVL and MFP values, respectively. Both these parameters indicates a consistent pattern with HVLs. It is evident from both figures that the PE region, characterized by a rapid increase, spans from \(1.0 \times 10^{-3}\) MeV to \(1.0 \times 10^{-1}\) MeV. The CS region demonstrates a gradual increase from \(1.0 \times 10^{-1}\) MeV to \(1.0 \times 10^{1}\) MeV, while the PP region lies within the range of \(1.0 \times 10^{1}\) MeV to \(1.0 \times 10^{5}\) MeV. Additionally, the order “lead > AlON > concrete” holds true for both figures, signifying that AlON is superior to concrete but falls short of the efficacy of lead.

Fig. 7
figure 7

Tenth-value layer (TVLs) for AlON, ordinary concrete and lead

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Fig. 8
figure 8

Mean-free path (MFPs) for AlON, ordinary concrete and lead

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Figures 9 and 10 illustrate the effective atomic number (\(Z_{\rm eff}\)) and effective electron density (\(N_{\rm eff}\)), respectively, for AlON. In this part of the investigation, the MACs for AlON are theoretically determined using the XCOM database, employing the final two equations as outlined in Table 1. The energy range remains consistent, spanning from \(10^{-3}\) MeV to \(10^{5}\) MeV. It is noteworthy that these figures exhibit more than three distinct regions with varying trends. A gradual increase is observed in the interval from \(10^{-3}\) MeV to \(10^{-2}\) MeV, followed by a rapid decrease between \(10^{-2}\) MeV to \(10^{-1}\) MeV. Subsequently, a nearly linear trend persists up to \(10^{1}\) MeV, followed by another gradual increase spanning \(10^{1}\) MeV to \(10^{2}\) MeV. The remaining region displays a linear trend extending to the conclusion of the investigated energy range.

Fig. 9
figure 9

Effective atomic number (\(Z_{\rm Eff}\)) for AlON

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In Fig. 9, the minimum value of \(Z_{\rm Eff}\) occurs approximately at 10, while its maximum value is observed around 12. Regarding the \(N_{\rm Eff}\) values in Fig. 10, they extend up to \(10^{23}\), given the relation between \(N_{\rm Eff}\) values and the Avogadro Number. In this instance, the minimum value of \(N_{\rm Eff}\) is approximately \(3.0 \times 10^{23}\) \(\frac{{\rm electron}}{g}\), and the maximum value is around \(3.5 \times 10^{23}\) \(\frac{{\rm electron}}{g}\).

Fig. 10
figure 10

Electron density (\(N_{\rm Eff}\)) for AlON

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Following the investigation of attenuation parameters and the shielding mechanism of transparent aluminum, our research was expanded to explore practical applications of glasses employed in shielding gamma rays. To conduct an evaluation, we compared the shielding properties of Aluminum Oxynitride with several commercially available glasses, considering both those containing lead and those without lead content. The selected commercial glasses encompass RS-253, RS-253-G18, RS-323-G19, RS-360, and RS-250, with corresponding minimum densities of 2.50, 2.52, 3.26, 3.60, and 5.18 \(g/cm^3\), respectively [31]. It must be noted that AlON has a density of 3.67 \(g/cm^3\) [19, 20]. To facilitate a comprehensive comparison between AlON and the mentioned glasses, LACs and HVLs were assessed across three gamma energy levels. These energy levels hold particular relevance in medical applications, notably in diagnostics and treatment. The obtained results are presented in Figs. 11 and 12.

Fig. 11
figure 11

Comparison of commercial shielding glasses and transparent aluminum in terms of LAC

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Both figures illustrate that aluminum oxynitride (AlON) surpasses RS-253 and RS-253-G18 across all energy levels. It is important to highlight that these two glass types lack any lead content. RS-323-G19 exhibits superior performance compared to AlON at lower energies but performs less effectively at higher energy levels. In the case of the remaining two glasses, AlON demonstrates comparability with RS-360 at higher energies. Notably, RS-323-G19, RS-360, and RS-250 contain lead content.

Fig. 12
figure 12

Comparison of commercial shielding glasses and transparent aluminum in terms of HVL

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It is noteworthy that, in its undoped state, aluminum oxynitride inherently outperforms ordinary concrete in impeding gamma rays and surpasses commercially available lead-free glasses. Moreover, it demonstrates comparability with lead-containing glasses, particularly at higher energy levels. The transparent-to-visible light characteristic of AlON renders it a significant material for applications in the medical and aerospace applications. Finally, despite its glass-like appearance, AlON exhibits mechanical properties comparable to concrete, positioning it as a versatile construction material for various applications.

4 Conclusion

This study investigates the radiation attenuation characteristics and shielding mechanisms of aluminum oxynitride. Systematic investigations are conducted on key parameters, including the linear attenuation coefficient (LAC, \(\mu\)), mass attenuation coefficient (MAC \(\mu _m\)), half-value layer (HVL), tenth-value layer (TVL), mean-free path (MFP), effective atomic number (\(Z_{\rm Eff}\)), and effective electron density (\(N_{\rm Eff}\)), covering an energy range from \(10^{-3}\) MeV to \(10^{5}\) MeV. The determined values for these parameters range as follows: \(9x10^{-2} - 9x10^{3} 1/cm\) (LAC), \(2x10^{-2} - 2x10^{3} cm^2/g\) (MAC), \(7x10^{-5} - 9x10^{0} cm\) (HVL), \(7x10^{-4} - 3x10^{1} cm\) (TVL), \(9x10^{-5} - 1x10^{1} cm\) (MFP), \(8x10^{0} - 1x10^{1}\) (\(Z_{\rm Eff}\)), and \(2x10^{23} - 3x10^{23} electron/g\) (\(N_{\rm Eff}\)). Comparative analyses with ordinary concrete and lead reveal that aluminum oxynitride (AlON) outperforms concrete but falls short of the shielding effectiveness demonstrated by lead. Furthermore, comparisons with commercial lead-equivalent glasses indicate that AlON surpasses lead-free alternatives and competes favorably with lead-containing glasses, particularly at higher energy levels. These findings suggest the potential utility of AlON, especially in nuclear medicine applications, providing lead-free gamma ray protection. Aluminum oxynitride could potentially be applied as a construction material, specifically in areas associated with radiation within hospitals and facilities dedicated to nuclear medicine production.