1 Introduction

Nuclear energy plays a significant role as a low-carbon energy source, providing a reliable main source of power in many countries. However, safety and waste disposal remain ongoing challenges [1]. The uncontrolled release of radiation from this technology poses a significant public health concern. As is known, the danger of these radiations lies in their ability to trigger developmental irregularities, leading to birth defects, genetic damage, malignancies, and declining fertility and fitness [2]. Therefore, nuclear scientists have developed many materials as a shield against these radiations, including concrete, mortars, glasses, and polymers [3,4,5,6,7,8,9]. Additionally, there is recent research about using natural raw materials as a radiation shield. Minerals are one of these natural raw materials such as halloysite [10, 11], barite [12, 13], chambersite [14], magnetite, limonite, hematite [13], garnet [15], serpentine [16, 17], and quartz [18]. Hence, the importance of applied mineralogy, as a branch of geology, appears in some recent studies to characterize the application of different minerals as barriers to attenuate the radiation or restrict the radioactive wastes generated from nuclear facilities [19]. According to global initiatives for sustainability, the use of minerals and rocks, in their native status, in radiation attenuation is preferred over concrete, which remains the most predominant material to mitigate the effects of radiation leaks [20,21,22,23,24]. This preference can be attributed to several factors: lower cement usage (compared to the concrete industry) resulting in energy and cost savings, as well as reduced maintenance requirements. Additionally, it allows for the utilization of abundant mineral resources that might not have other uses, effectively repurposing them for nuclear waste storage. Notably, hematite and barite are the most commonly used minerals for γ-ray shielding due to their high density [25,26,27]. They also show efficiency in fast neutron shielding through a moderation process involving inelastic collisions of fast neutrons with barium and iron in barite and hematite, respectively [27, 28]. Employing 137Cs and 60Co at 0.662 and 1.33 MeV, respectively, Akkurt et al. studied the γ-ray attenuation of barite and found good agreement between their experimental findings and the XCOM calculations [12]. Furthermore, various γ-ray shielding parameters have been measured for barite and hematite at different photon energies produced from 133Ba and 152Eu using HPGe detector [13]. The results confirmed that both barite and hematite minerals can efficiently shield γ-rays, with barite exhibiting superior performance. However, few studies, have discussed the radiation attenuation capacity of hematite and barite in their native status [12, 13]. Moreover, these reports, lack data on the fast neutron attenuation of these minerals. Additionally, no theoretical or simulation studies have yet confirmed the experimental findings.

In the Western Desert of Egypt, specifically in the Bahariya Oasis, hydrothermal solutions during the Middle Eocene led to the formation of barite and hematite [29]. Baharia Oasis holds significant, yet unexploited, reserves of these minerals, with hematite alone estimated at around 270 million metric tons [30]. As a result, the hematite served as the main raw material for steel manufacturing at the Egyptian Iron and Steel Company (EISC). However, mining operations for hematite ceased after the government's decision to liquidate EISC in January 2021 due to the high expenses associated with its maintenance and operation, leading to the abandonment of millions of tons of ore. Accordingly, the hematite and barite minerals became like mining wastes with no utilization. Recently, there has been a general approach in the scientific community toward exploiting different types of waste to achieve sustainable development [31,32,33,34,35,36,37,38,39]. Also, this abundance suggests their potential as stable underground repositories for nuclear waste or as wall-lining tiles in radiotherapy and nuclear reactor facilities.

On the other hand, theoretical and simulation software, such as Phy-X/PSD, NXcom, XCOM, WinXCom, and Monte Carlo simulations, have been successfully verified by experimental investigations of radiation attenuation in various materials [40,41,42,43,44,45,46,47,48,49,50,51]. Additionally, some researchers have relied solely on this software to characterize the radiation-shielding properties of other materials [52,53,54,55,56,57,58,59,60,61,62,63,64]. Therefore, this study aims to comprehensively evaluate the gamma-ray, thermal neutron, and fast neutron shielding capabilities of hematite and barite from the Bahariya Oasis. We will achieve this through theoretical and simulation studies of thermal neutrons, fast neutrons, and gamma-ray attenuation. Specifically, the NGCal and NXcom programs will be used for theoretical calculations of thermal and fast neutrons, respectively. Meanwhile, the MCNP-5 code (Monte Carlo simulation code) will be employed for gamma-ray and thermal neutron simulation studies, with validation provided by the XCOM program. Finally, the radiation attenuation of these minerals will be compared to those of commonly used radiation shielding materials.

2 Materials and Methods

2.1 Material Characterization

Hematite and barite samples were derived from Bahariya oasis, the Western Desert in Egypt. The collected sample of barite was characterized by its pale brown-yellow color, glassy luster, and high specific gravity. In contrast, hematite displayed various shades of red, such as dark red, along with an earthy texture and a lower specific gravity than barite. In addition to its earthy luster, a distinguishing feature of the hematite sample was its tendency to leave a residue of its color on the hand. The density and elemental composition of both samples were determined to serve as input data for theoretical and simulation programs used to characterize their radiation attenuation capabilities. As described in [65], the density was characterized. Elemental analysis was performed using X-ray fluorescence (XRF) based on ASTM D7348 and E1621 [66, 67].

2.2 γ-Ray Attenuation (MCNP-5 and XCOM)

2.2.1 MCNP-5 Simulation

The Monte Carlo simulation code (MCNP-5) is a valuable means to simulate the attenuation parameters of different attenuating materials like concretes [68], glasses [69, 70], polymers, and building materials. MCNP-5 simulation was accomplished via an input file describing material densities, chemical composition, radiation source location, working energies, geometry, and detector. These aforementioned factors were introduced to the input file through many cards like surface, cell, material, source (SDEF), importance, tally, cutoff, and physical. The nuclear library ENDF/B-VI.8 was attached to the MCNP-5 code to support it by the cross-section of interactions required to evaluate the shielding parameters. In the created input file, F4 tally was applied to estimate the average flux per unit cell and the average track length (ATL) that is required to evaluate the linear attenuation coefficient (LAC, cm−1) of the investigated materials. Additionally, the input file contains a cell card that describes each simulation factor (i.e., outer shielding material, collimators, detector, source, and the investigated materials) by a unit cell. Every cell has its density, importance, and cell number. To identify every cell, it should be surrounded by some surfaces which are introduced in the surface card, where every surface has a definite shape and dimensions. For example, the outer shielding material which protects the geometry from the surrounding radiations has a cylindrical shape with a diameter of 25 cm, thickness of 5 cm, and height of 40 cm made of lead. Inside the outer lead cylinder, collimators, samples, and the detector were installed, as illustrated in the 3D representation for the MCNP-5’s input file (Fig. 1). All information about the sources used was introduced to the SDEF card, where the source placed in the center of the outer cylinder POS (0 0 0) emits radiation along Z direction AXS (0 0 1) with energies (ENG) varied between 0.015 and 15 MeV including 0.662 MeV (for Cs-137), 1 MeV, and 1.332 MeV (for Co-60). Additionally, the distribution and emission probability for the radioactive source were introduced to the SDEF card. According to the input file, two lead collimators with narrow apertures were used to collect the γ-ray flux released from the source and absorb the dispersed radiation from both the source and the sample. Between the γ-ray source and investigated samples, the first collimator (7 cm × 7 cm) with a vertical central aperture with a diameter of 1 cm is located. At a distance of 2 cm from the collimator’s upper surface, the source was located inside a hole in the first collimator. Furthermore, the second collimator (7 cm × 3 cm) with a central vertical slit of 1 cm diameter was placed between the sample and the detector. The cutoff card was set at 108 historical emissions. After running the simulation on, an output file is created automatically containing the ATL of γ-photons over the various cells and the relative error in the simulation process which ranges between ± 0.5%. Then, the ATL was used to calculate the LAC for the investigated samples. After that, based on the LAC and the density of the investigated samples, the mass attenuation coefficient (MAC, cm2/g) was evaluated. Additionally, the half-value layer (HVL, cm), transmission factor (TF, %), radiation protection capacity (RPC, %), and equivalent thickness of lead (ETPb, cm) were evaluated based on the simulated LAC according to equations in Table 1.

Fig. 1
figure 1

3D-geometry of the simulation by MCNP-5 code

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Table 1 Equations used to determine simulated parameters of γ-attenuation
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2.2.2 XCOM

In addition to the MCNP-5 simulation, the XCOM program was used to verify the simulated μ values. Utilizing the NIST database within XCOM, we calculated the MAC values according to the “Mixture Rule” using the following equation[71]:

$$ MAC\left( {\mu_{m} } \right) = \mathop \sum \limits_{i} w_{i} (\mu_{m} )_{i} $$
(1)

where \({w}_{i}\) and \(({\mu }_{m}{)}_{i}\) denote the fractional weight and mass attenuation coefficient per element, respectively. Furthermore, Table 2 summarizes different relationships for calculating mean atomic mass, number (<A>, <Z>)mean electron density (<N>), and effective atomic number (Zeff). Zeff takes into account both single and energy-dependent values for photon interaction (PI) and photon energy absorption (PEA). The single Zeff value was determined based on various parameters such as elemental weight fraction [72], fractional electronic content [73,74,75,76], or atomic percentage [77, 78].

Table 2 Equations utilized to determine the γ-ray attenuation parameters according to different expressions
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2.3 Thermal Neutrons (NGCal Software)

The NGCal software (http://ngcal.com [83]), a free online tool developed by Gökçe et al., calculates the attenuation behavior of thermal neutrons based on the material’s macroscopic cross-section (Σth in cm−1). Σth represents the probability of a neutron being absorbed per unit path length. This software can assess the attenuation performance of materials against thermal (25.4 meV) and fast (4 MeV) neutrons, as well as gamma rays (0.002–20 MeV). Material composition and density are required for calculations.

2.4 Fast Neutrons (NXcom Program)

The macroscopic effective removal cross-section (ΣR) describes the probability of a fast neutron undergoing its first collision within a material, effectively removing it from the group of penetrating neutrons per unit length. The NXcom computer program [84] assesses this removal process for fast neutrons and the attenuation coefficient for gamma rays in various materials (concrete, composites, etc.). Similar to the XCOM program, NXcom requires the elemental composition of a sample as input data and applies the mixture rule to calculate ΣR for each sample as follows[85].

$$ \Sigma_{R} = \mathop \sum \limits_{i} w_{i} (\Sigma_{R} )_{i} , $$
(2)

where \({\rho }_{i}\) represents the density of the ith constituent element as in the mixture (\({\rho }_{i}\hspace{0.17em}=\hspace{0.17em}\rho \cdot {w}_{i}\); \(\rho \) represents mixture density), and \({w}_{i}\) denotes the fractionated weight of the ith constituent element.

3 Results and Discussion

3.1 Material Characterization

Table 3 summarizes the elemental composition and density of materials investigated for their radiation shielding effectiveness using simulations and theoretical calculations. The results reveal that barite (4.20 g/cm3) boasts a higher density compared to hematite (2.90 g/cm3). The elemental analysis of barite indicates a primary composition of barium sulfate (BaSO₄), explaining its high concentrations of sulfur (11.83%) and barium (51.93%). Hematite, on the other hand, is composed of Fe₂O₃, leading to its high iron content (61.06%). Interestingly, both minerals contain a significant amount of oxygen, with hematite having a slightly higher proportion.

Table 3 Elemental composition (%) by XRF and densities (g/cm3) of studied samples
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3.2 γ-Ray Attenuation

3.2.1 Mass Attenuation Coefficient (MAC, cm.2/g)

MAC is the most crucial parameter for radiation shielding, as other parameters are derived from it. Figure 2a–c demonstrates excellent agreement between the simulated MAC values obtained using the MCNP-5 software and those calculated using XCOM, across the energy range of 0.015–15 MeV. This consistency is further supported by the perfect correlations (R2 = 1) observed in Fig. 2a, b for both hematite and barite. The high degree of similarity between the MCNP-5 simulations and XCOM calculations suggests that the simulation process yields highly accurate results. Figure 2c illustrates the simulation findings. The maximum mass attenuation coefficients for hematite and barite occur at the lowest energy level (E = 0.015 MeV), with values of 36.63 cm2/g and 38.35 cm2/g, respectively. As photon energy increases, the MAC values steadily decrease, mainly due to the prevalence of photoelectric absorption. A significant peak (7.38 cm2/g) appears in the MAC of barite at 0.05 MeV, which is attributed to the presence of Ba in its composition. Both materials exhibit similar MAC within the 0.662–3.00 MeV energy range, indicating comparable attenuation behavior. However, pair production becomes the dominant interaction process at higher energies (E > 3 MeV), leading to some variation in the MAC with increasing gamma-ray energy.

Fig. 2
figure 2

Comparison of simulated and calculated MAC for barite (a) and hematite b within 0.015–15 MeV. c Shows the variation of simulated MAC across this energy range for studied samples

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3.2.2 Linear Attenuation Coefficient, LAC, (µ, cm.−1)

Figure 3 illustrates the decreasing trend of linear attenuation coefficient (μ) with increasing photon energy (0.015–15 MeV) for hematite and barite. This trend is due to the weakening influence of the photoelectric effect at higher energies. However, a distinct barium K-edge peak disrupts this trend for barite at 0.05 MeV. In the mid-energy range (0.3–3 MeV), Compton scattering becomes the dominant interaction process, leading to a gradual decline in μ. Beyond 5 MeV, pair production takes over as the primary process, resulting in minimal changes in μ for both materials [86]. Notably, barite exhibits consistently higher μ values than hematite.

Fig. 3
figure 3

Variation of simulated μ (cm−1) values with the photon energy from 0.015–15 MeV for the studied samples

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3.2.3 Half-Value Layer (HVL, cm)

Figure 4 depicts the relationship between photon energy and HVL for hematite and barite. As expected, HVL increases with energy for both materials due to the diminishing influence of photoelectric absorption. A sharp dip in barite’s HVL at 0.05 MeV corresponds to the Barium K-edge. In the intermediate range (0.1–5 MeV), Compton scattering prevails, leading to a gradual HVL rise. Beyond 5 MeV, pair production stabilizes HVL for both materials. Significantly, barite consistently displays lower HVL values than hematite throughout the entire energy range, indicating its superior performance in gamma-ray attenuation. For instance, between 0.015 and 15 MeV, hematite’s HVL values range from 0.01 to 9 cm, while barite's range from 0.004 to 5.20 cm. This suggests that barite consistently demands less thickness to achieve equivalent shielding compared to hematite.

Fig. 4
figure 4

Variation of simulated HVL (cm) values with the photon energy from 0.015–15 MeV for the studied samples

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3.2.4 Mean Free Path (MFP, cm)

Figure 5 compares the mean free path (MFP) of hematite and barite with photon energy, mirroring the trend observed for HVL. Notably, barite exhibits consistently lower MFP values throughout the entire energy range (0.015–15 MeV). Barite’s MFP ranges from 0.01 to 7.01 cm, while hematite’s spans from 0.01 to 12.98 cm. A significant increase in MFP for both materials occurs between 0.1 and 5 MeV due to the dominance of Compton scattering. At energies ˃ 5 MeV, the influence of pair production leads to a decrease in the rate of change of MFP.

Fig. 5
figure 5

Variation of simulated MFP (cm) values with the photon energy from 0.015–15 MeV for the studied samples

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3.2.5 Transmission Factor (TF, %)

Figure 6 illustrates the dependence of photon transmission factor (TF%) on photon energy. Both hematite and barite exhibit increasing TF% with energy. The lowest TF% (highest attenuation) for both materials occurs at low energies, indicating efficient absorption due to the photoelectric effect. As the energy rises (up to 5 MeV), TF% increases, suggesting a dominance of Compton scattering and a higher probability of photon escape or scattering [86]. At the highest energies (8–15 MeV), both materials show the highest TF% (lowest attenuation), signifying reduced effectiveness against high-energy photons. Notably, barite consistently displays lower TF% values than hematite, demonstrating its superior ability to attenuate photons across the entire energy spectrum.

Fig. 6
figure 6

Variation of simulated TF (%) values with the photon energy from 0.015–15 MeV

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3.2.6 Radiation protection capacity (RPC, %)

Figure 7 (MCNP-5 simulations) compares the radiation protection capabilities (RPC%) of hematite and barite across different photon energies. While both materials exhibit a decrease in RPC% with increasing energy, hematite generally offers lower protection compared to barite. The only exception is the very low energy range (0.015–0.030 MeV) where both achieve 100% RPC. Barite demonstrates superior performance with higher and more stable RPC% values (100–99.42%) between 0.015–0.100 MeV, while hematite’s peak RPC% (100%) is within a narrower range (0.015–0.050 MeV). The observed differences in RPC% can be explained by the varying influence of photoelectric interaction and Compton scattering on different energy photons. Beyond 0.100 MeV, both materials show a decrease in RPC% due to Compton scattering. At even higher energies (> 5 MeV), the impact of pair production leads to minimal changes in RPC values[86].

Fig. 7
figure 7

Simulated values of RPC (%) at different energy ranges from 0.015–15 MeV

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3.2.7 Equivalent Thickness to Lead (ETPb, cm)

The thickness of hematite and barite needed to equal 1 cm of lead shielding (ETPb) was calculated for photon energies (0.015–15 MeV) as shown in Fig. 8. In this energy region, hematite required 4.08–70.36 cm, while barite needed 2.92–13.88 cm. The higher µ value of Pb compared to hematite and barite leads to the elevated ETPb values. At the lowest energy (0.015 MeV), ETPb for hematite and barite was 11.95 and 7.89 cm, respectively. ETPb increased at 0.03 MeV and 0.1 MeV due to lead’s L-edge and K-edge effects, which require more hematite or barite to achieve the same level of shielding as lead [81. Between 0.3–1.332 MeV, ETPb decreased to 14.33–6.66 cm for hematite and 4.10–2.95 cm for barite. For energy levels from 3–15 MeV, ETPb increased for hematite (4.57–8.33 cm) and barite (3.13–4.5 cm) due to pair production cross-section correlated with Z2. The highest ETPb for barite (13.88 cm) was observed at 0.03 MeV, while hematite reached its maximum value of 70.36 cm at 0.10 MeV. These results signify the superior shielding capabilities of barite over hematite.

Fig. 8
figure 8

Variation of simulated EtPb (cm) values with the photon energy from 0.015–15 MeV for the studied samples

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3.2.8 Effective Atomic Number (Zeff), Electron Density (Neff), and Their Derivatives

Table 4 summarizes the calculated parameters for barite and hematite. Notably, barite exhibits higher density, mean atomic number (<Z>), and effective atomic number (Zeff). Based on these preliminary calculations, barite suggests superior efficiency in shielding gamma rays compared to hematite.

Table 4 Density (ρ), mean atomic mass<A˃, mean atomic number<Z˃, mean electron density<N˃, as well as single-valued Neff and Zeff calculated by various empirical equations
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Although a single Zeff value has its uses, it is overly simplistic for many applications. For these cases, energy-dependent Zeff values are required. Table 5 shows the maximum (Max.) and minimum (Min.) values of these energy-dependent effective atomic numbers and effective electron densities, categorized for photon interaction (PI) and photon energy absorption (PEA). Notably, the values of average atomic number (<Z>) consistently align with the minimum Zeff, PI across all samples, indicating the dominance of the Compton scattering process (Tables 4 and 5).

Table 5 Minimum and maximum values of energy-dependent effective atomic numbers and electron densities
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Figure 9a, b reveal a high degree of similarity in the variation of Zeff, PI and Zeff, PEA with energy. Therefore, we focus on Zeff, PI (Fig. 9a). Notably, barite (Fig. 9a) lacks the intermediate constant Zeff, PI region. Additionally, a dip appears above 1 MeV, but the minimum remains above <Z>, indicating Compton scattering is not dominant [80]. Finally, Zeff, PI in barite systematically increases more than hematite at higher energies, confirming its superior shielding.

Fig. 9
figure 9

Variations of Zeff, PI (a), and Zeff, PEA (b) with photon energy (MeV)

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3.3 Thermal Neutron Attenuation

Σth results obtained from the NGCal online software for the investigated samples are confirmed by the MCNP-5 simulation code, as shown in Table 6. The computations illustrate that the thermal neutron attenuation of hematite (0.894 cm⁻1) is higher than that of barite (0.288 cm⁻1) by 210%. The NGCal result matches the MCNP-5 simulation results within about ± 10% difference. The superiority of hematite can be attributed to its higher ratio of iron with a larger absorption cross-Sect. (2.56 barns) compared to barium, in barite, which has a lower absorption cross-Sect. (1.30 barns) [87]. Additionally, hematite has a higher hydrogen (H) content (0.60%) compared to barite (0.13%). Hydrogen has a relatively high absorption cross-section of 0.3326 barns.

Table 6 The macroscopic cross-section of thermal neutrons Σth (cm−1) of samples
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3.4 Fast Neutron Attenuation

Table 7 illustrates the weight percentage (wt.%) of each element in the samples and their corresponding removal cross-sections for fast neutrons (ΣR). Oxygen significantly contributes to the ΣR of both barite and hematite, with a higher overall ΣR for barite. For hematite, hydrogen and iron are the major contributors to ΣR, while barium and sulfur play the most significant role in barite. This higher total ΣR value for barite’s constituent elements indicates its superior performance in attenuating fast neutrons compared to hematite.

Table 7 Elemental contribution to macroscopic removal cross-section (ΣR, cm⁻1) of fast neutrons in studied samples
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3.5 Radiation Attenuation Comparison

Table 8 compares the gamma-ray attenuation of the studied samples (hematite and barite) with previously studied materials (concrete, minerals, etc.) using theoretical or simulation methods. Table 8 lists the samples, their descriptions, and gamma-ray linear attenuation coefficients at common comparison energies (0.662, 1.173, and 1.332 MeV). Also, Table 8 illustrates that the barite offers the highest gamma-ray shielding at all three energies. Hematite exhibits superior gamma-ray attenuation to most materials except BRC, BC, WM, H7, HBC7, PVC − C30, and N0 while performing similarly to Nd4.

Table 8 Comparison of linear attenuation coefficients for γ-rays in different materials
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4 Conclusion

The present study’s findings lead to the following conclusions:

  1. 1)

    Both theoretical calculations (XCOM) and simulations (MCNP-5) demonstrated superior gamma-ray shielding performance for barite compared to hematite. This was evident across all parameters (μ, MAC, HVL, MFP, TF, RPC, ETPb, Zeff, and Neff). The good agreement between theory and simulation supports this conclusion. This advantage can be attributed to barite's higher density (4.20 g/cm3) compared to hematite (2.90 g/cm3).

  2. 2)

    Hematite displayed a 210% higher effectiveness in attenuating thermal neutrons compared to barite, as verified by the MCNP-5 simulation results. This can be explained by the higher absorption cross-section of Fe in hematite (2.56 barns) compared to Ba in barite (1.30 barns). Additionally, hematite has a higher hydrogen content (0.60%) than barite (0.13%).

  3. 3)

    Calculations using NXcom indicated that barite outperforms hematite in shielding fast neutrons. This is due to barite's higher density and barium content, which enhance the probability of inelastic fast neutron collisions.

  4. 4)

    Based on their performance, both hematite and barite have the potential to be used as natural radiation shielding materials, offering an alternative to common shielding materials.