1 Introduction

X-ray photons are created when an inner orbital electron is ejected and when atomic orbital electrons move from high to low energy levels ^[1,^2]. The property of the atomic number dependence of the absorption of X-ray photons was quickly applied for medical diagnostic purposes. After the discovery of X-ray diffraction by Max von Laue in 1913, major fields of materials analysis have developed. XRF spectroscopy isolates narrow energy bands from polychromatic beam characteristic radiation produced in the sample using either the diffracting power of a single crystal or a proportional detector. The first of these methods is called wavelength dispersive spectrometry and the second is energy dispersive spectrometry ^[3]. The increase in the use of nuclear energy in all branches of human activities has been linked to the production and use of radioactive materials which has led to an increase in danger associated with these activities ^[4]. To gain a high level of security and be safe from exposure to radiation of all kinds, the radioactive materials in laboratories or in fields must be surrounded by protective shields to avoid the danger caused by these radiations. The shielding materials must meet some requirement, e.g. dealing with all kinds and levels of radiation, have a high resistance to the effect of radiation and with low intrinsic radioactivity, in addition to their abundance, easy to be manufactured and cost-effectiveness ^[5]. The deformation pattern of the crystal will be increased when increasing the relative formation and this leads to an increase in the recrystallization velocity of nuclei growth and the linear velocity of growth as well. If both velocities are evenly increased when the relative formation increases then the effect of relative formation will vanish. The grain size of re-crystallized will decrease when the relative formation increases, hence we can conclude that; the velocity of recrystallization of nuclei growth will be more greatly increased than the linear velocity of new grain growth ^[6]. X-ray machines have three principal uses as diagnostic, therapeutic, and non-medical radiographic devices. An X-ray tube is usually housed in a heavy lead casing with an aperture through which the primary, or useful, beam emerges. Typically, the beam passes through metal filters (e.g., Al, Cu) to remove unwanted, less penetrating radiation and is then collimated to reduce its width. The housing, supplied by the manufacturer, must conform to certain specifications to limit the leakage radiation that emerges from it during operation. For diagnostic X-ray tubes, regulations require that manufacturers limit the leakage exposure rate at a distance of 1 m from the tube’s target to 0.1 Rh^-1 when operated continuously at its maximum rated current and potential difference ^[7]. The production of tomographic images is reconstructed by transforming the X-ray attenuation coefficient distribution in a patient body. The final image is produced as a result of a whole chain of processes and is affected by many factors including the technical parameters of the scanner, the type of projection system, and finally the type of reconstruction algorithm applied ^[8]. The formation of exciting micro beams (X-ray or ion beams) provided elemental mapping down to the few parts per million concentration regime, enhancing the applicability of the ion beam, and X-ray spectrometry was interesting in measuring MCA for glass systems ^{[9 - 18]}. Recently have interest in using glass samples of ZrO₂, CaO, Na₂O, P₂O₅, B₂O₃, and Bi₂O₃, oxides was within the goal of many to test of these compounds in terms of shielding against nuclear radiation ^[19,^20]. Other researchers used the Monte Carlo simulation (MC) technique is an effective method to simulate particle transport and interactions with matter and to generate the mechanical and radiation parameters for different shielding materials ^[21]. Used different sulphate compounds with AlSO₄, BaSO₄, KAlSO₄, and Na₂SO₄ to study the radiation shielding behavior of such materials ^[22]. Devoted his interest in nano-materials and the extent to which these materials repel radiation especially neutrons ^[23]. Applied gamma spectroscopy using HPGe detector for photon attenuation measurements ^[24]. In this work, FLUKA version 4 - 3.0 and Flair GUI were used to estimate the photon radiation coefficients for a group of sulfuric materials such as FeSO₄, CuSO₄, NiSO₄ and ZnSO₄. Shielding efficiency and quality were also given. Results for low-energy photon regions will be confirmed with the experimental one.

2 Theortical framework of radiation shielding parameter calculations

Photon attenuation coefficient μ, describes the attenuation rate that accounts for the total number of atoms in a cm³ volume of material and the possibility of X-rays or gamma rays being scattered or absorbed from the nucleus or an electron of a material. Table I shows all the mathematical relationships, the Photon attenuation coefficient μ, mass attenuation coefficient (MAC), half value layer (HVL), tenth value layer (TVL) and mean free path (MFP) for the attenuation of photons. These characteristic values are often calculated to show the shielding properties quality of any material against X-rays or gamma rays.

3 FLUKA Simulations

FLUKA is a general-purpose Monte Carlo (MC) package. It has many applications for the interaction and transport of nucleons and photons. It uses the best mathematical models and a precision, microscopic approach ^[25]. FLUKA has a wide range of applications, design shielding, radiation protection, dosimetry, and radiation detector simulation. The 2021.2.9 latest version of FLUKA was published in January 13th, 2023 which was requested and downloaded from the FLUKA site. FLUKA needs a helper code called Flair. Flair is a user-friendly interface for FLUKA code to simplify the editing of FLUKA input cards, running FLUKA, and visualization of the output results. It is fully based on Python language. A Powerful and user-friendly graphical interface For FLUKA is the FLAIR code ^[24,^25]. The latest FLAIR-2.3-0c version was published in 24th-Mar-2023 and can be requested and downloaded from flair site. In this work simulation was done using the following FLUKA and flair parameters:

Figure 1 The simulation set up for FLUKA code. 

Results and discussions

Figures 2-5 show the (XRF) measurements for pure elements (Fe, Cu, Ni, Zn) and sulphate compounds respectively. These figures clearly indicate that kα of X-ray energy peaks for pure elements with higher intensity. It has been observed that for compound samples intensity of these kα of X-ray energy peaks was decreased, due to the decreased fraction of elements (Fe, Cu, Ni, Zn) in sulphate compounds. These have been shown in Figs. 3-6 respectively.

Figure 2 The Experimental Set-up. 

Figure 3 Shows the X-ray fluorescence plots for Iron sulphate. 

Figure 4 Shows the X-ray fluorescence plots for Copper sulphate. 

Figure 5 Shows the X-ray fluorescence plots for Nickel sulphate. 

Figure 6 Shows the X-ray fluorescence plots for Zinc sulphate. 

Because of the grain form and crystal structure of atoms, the mass attenuation coefficient (MCA) for sulphate compounds was calculated using Table I. It was determined that the (MCA) for sulphate compounds increased with larger molar mass except for Iron sulphate. It can be seen in Fig. 7 and Table III.

Figure 7 The Experimental and theoretical plot between mass attenuation coefficient (MCA) and molar mass of sulphate compounds 

The Fig. 8 shows SEM image which is composed of uniformly distributed uneven granular structure.

Figure 8 The SEM Image For FeSO₄ 

Results of Monte Carlo FLUKA simulation

Figure 9 represents the MCA calculated for the (0.0001 - 100 MeV) photon energy range. The right figure is the zoom part for the (0.0001 - 0.01 MeV) low energy. It should be mentioned that the lower part has 5 peaks at energies 0.0002, 0.0005, 0.001, 0.0024, and 0.009 MeV. The compound FeSO₄ precedes all at 0.001 MeV photon energy. For the energy range from about 0.04 up to 0.1 MeV one can find ZnSO₄ can have the highest value while the FeSO₄ has the lower values. Based on the MCA calculations, we generate the HVL and The TVL values according to Table I. Results are summarized in Fig. 10. Results show that for about 600 keV the HVL has a value less than (1 cm). As the photon energy increases up to 100 MeV the HVL can have (10 cm). In many areas such as A and B the FeSO₄ can reach good values than other compounds.

Figure 9 MAC of the introduced samples the right figure represents the low energy part. 

Figure 10 The HVL and the TVL for photon energy range (0.1 keV - 100 MeV). 

For the energy range 0.01 up to 100 MeV the photon attenuation coefficient for the samples record the overlapping values while the MFP record (1-10 cm) for the interesting energy region (0.1-100 MeV) as shown in Fig. 11.

Figure 11 Represent the attenuation coefficient and mean free path for photon energy range up to 100 MeV. 

For proton and alpha charge particles, the stopping power was calculated for the introduced compounds as shown in Fig. 12. Calculations were done using SRIM 2008.04 contributions supported freely by E. Dabich and J. F. Ziegler et al. 1984-2008. For proton, the compounds CuSO₄ and FeSO₄ have a peak value at 0.08 MeV while for Ni and Zn sulphate the maximum value is seen at 1 MeV proton energy. The situation is different for the alpha projectile it has stopping power peak at 0.08 keV for all samples.

Figure 12 Represents the proton and alpha stopping power up to 10 MeV. 

The proton and alpha 0.01-10 MeV ranges were calculated using the SRIM 2008.04 code Fig. 13. For proton, it is found that Cu and Fe have higher values than Zn and Ni sulphate but for the alpha particle range, Zn and Cu sulphate have the highest values than the other one.

Figure 13 Represents the proton and alpha particle ranges for energy up to 10 MeV. 

Figure 14 shows a plot of Zeff and Zeq for the current samples in the range 0-15 MeV. Thus, the sample FeSO₄ possesses the lowest Zeff and Zeq because Fe has the lowest atomic weight 55.845 than other samples.

Figure 14 Represent the Zeff and Zeq of FeSO₄, ZnSO₄, NiSO₄, and ZnSO₄ samples. 

The thermal fast neutron effective removal cross-section (∑k‍ in units of cm^-1) is revealed in the bar illustration for all samples in Fig. 15. In addition, the calculated ∑‍R for the studied samples shows that S3 has the peaked value. Moreover, the lowest calculated value of ∑‍R is for sample S4 has values of 0.25 and 0.096 cm^-1 for thermal and fast neutron respectively.

Figure 15 Fast and thermal neutron removal cross-section for S1-S4 Samples. 

Conclusions

The full peak area for standard pure metals Fe, Cu, Ni, and Zn were calculated using the Origin 6.8 program. The accurate densities of such metals were well determined. Results show that these intensities reduced sharply for the selected sulphate compounds FeSO₄, CuSO₄, NiSO₄ and ZnSO₄ it should be mentioned that it is as low as possible when using iron sulphate. It is clear from the Scanning Electron Microscope SEM image investigation that, for Iron sulphate the granular shape of the surface particles and their distribution have a strong effect on the attenuation of X-rays, so the intensity decreased to less than 1000 compared to the metal one. The Monte Carlo using FLUKA code helps to know the wide energy range of MCA. And the extracted other factors like (HVL) and (TVL) shows the trends of the studied samples to the incident photon radiations. Calculations for proton and alpha particles stopping power and ranges let us know CuSO4 and FeSO4 have a peak value at 0.08 MeV while for Ni and Zn sulphate the maximum value is seen at 1 MeV proton energy. In the case of the alpha projectile, it has a stopping power peak near 0.08 keV for all samples and the function has Gaussian trends than the proton particles. The calculation of the removal cross-section can explain that; the priority of the introduced samples can be arranged as S3, S1, S2, and S4 these arrangements are according to the heights of shielding efficiency for thermal and fast neutron modes.