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Article

Effect of Waste Iron Filings (IF) on Radiation Shielding Feature of Polyepoxide Composites

by
Mohammed T. Alresheedi
1 and
Mohamed Elsafi
2,*
1
Department of Electrical Engineering, King Saud University, Riyadh 11421, Saudi Arabia
2
Physics Department, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
*
Author to whom correspondence should be addressed.
Crystals 2023, 13(8), 1168; https://doi.org/10.3390/cryst13081168
Submission received: 30 June 2023 / Revised: 21 July 2023 / Accepted: 23 July 2023 / Published: 27 July 2023
(This article belongs to the Topic Recent Advances in Ionizing Radiation Shielding Materials)
(This article belongs to the Section Hybrid and Composite Crystalline Materials)
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Versions Notes

Abstract

:
In the present work, photon and neutron attenuation properties of polyepoxide composites produced by doping waste iron filings (IF) at different percentages (0%, 20%, 40%, and 60% iron filing percentage) were obtained using theoretical and experimental techniques. The experimental technique was performed using an HPGe detector with four different gamma lines (0.0595, 0.6617, 1.173, and 1.333 MeV) emitted from three gamma-ray sources (241Am, 137Cs, and 60Co). The theoretical techniques for shielding parameters calculation are estimated with Phy-X software and the XCOM program as well. The experimental and theoretical values of the mass/linear attenuation coefficient (M/LAC), half/tenth value layer (H/TVL), mean free path (MFP), lead equivalent thickness (LEth), and radiation shielding efficiency (RSE) have been determined and compared. A good agreement was achieved during the comparison. The shielding performance of the prepared composites increased with increasing the iron filing rate, where we can arrange the performance of shielding according to EP–IF60 > EP–IF40 > EP–IF20 > EP–IF0 at all different experimental and theoretical energies. The effective and equivalent (Zeff, Zeq) atomic numbers as well as the exposure buildup factor (EBF) at different depletion distances or mean free paths (MFPs) have been calculated for all EP–IF composites. The lowest EBF was for EP–IF60 while the highest EBF was for EP–IF0 through the discussed energy from 0.015 to 15 MeV. Finally, the fast neutron removal cross-section (FRNC) has been calculated for the prepared composites and the results showed improvement in FNRC with increasing the iron filing rate.

1. Introduction

Shielding has been used to protect against radiation emitted from some equipment, such as medical and industrial X-ray generating devices, medical radiation treatment devices, and in some facilities such as nuclear reactors and accelerators [1,2,3]. Spacecraft are also shielded to protect astronauts and spacecraft equipment from the influence of cosmic rays [4]. Radiation shielding is the use of physical barriers such as lead, aluminum, reinforced concrete, or others to attenuate radiation of all kinds, i.e., reduce the percentage of radiation to which a living or physical organism is exposed, with the aim of protecting from its effects and applying the requirements of global radiation protection [5,6,7].
The frequent use of radioactive sources in various fields is followed by radioactive contamination in the surrounding environment, making radiation shields an important matter in protection from these radiations. Recently, polymer-based shielding materials have been manufactured—as they are included as a matrix material that is easy to form, flexible, and has good mechanical and thermal properties—such as polyethylene, epoxy resins, and polyester resins [8,9,10]. Epoxy resin is a chemical that is characterized by the inability to be reshaped by heat after it has been converted into a solid. It consists of two components: a base (resin) and a hardener. It is highly adhesive and resistant to abrasion and chemicals, whether acids, alkalis, bases, or solvents. An insulating layer forms when it dries. It is used as a coating, mortar, or adhesive [11]. Epoxy resin has distinctive mechanical and physical properties that qualify it to be used in shielding applications, where it is used as a matrix material and some heavy particles are added to it, or it is used as a small part in the compound to improve its mechanical properties [12,13].
Iron filings are fine granules of iron that take a powder-like shape between them. Iron filings are considered a by-product because they are industrial waste from the process of filing, drilling, or scraping iron pieces, or as a result of polishing finished products [14]. The size of the particles or granules present in the iron powder does not exceed 0.1 mm in length and the smallest of them may reach a mundane length of a few micrometers. Iron filings are added to concrete mixtures to enhance their mechanical properties, including compressive strength, tensile strength, and fracture strength. Sand is also replaced by filings in proportions in cement mortar to form mixes that withstand compression [15,16,17]. Satyaprakash et al. [18] studied the mechanical properties of concrete in the case of sand replacement with filings and found that it improves compressive and tensile strength.
If we combine these resins as a matrix and iron filings as a filler material, we will obtain composites that have many applications and some important properties at the lowest cost. Madugu et al. [19] studied the physical and mechanical properties of iron filings additives to polyester fiber and found that these additives improve the physical and mechanical properties of the product. Abushammala and Mao [20] studied the electrical and mechanical properties of fiber epoxy composites reinforced by waste iron filings and concluded that the addition of Iron filings improves the electrical and mechanical properties of the composites.
In this work, a comprehensive study of the photon attenuation capability of epoxy resin composites reinforced by waste iron filings has been investigated. Four composites were fabricated, and the experimental and theoretical attenuation coefficients were studied at different broad energies, and the effective as well as the equivalent atomic number were calculated, in addition to calculating the exposure buildup factor for the fabricated composites.

2. Materials and Method

2.1. Materials

The study was conducted in this research on two main materials, which are polyepoxide (epoxy resins) and some waste of iron filings.

2.2. Epoxy Resin

Conbextra EP10 transparent epoxy resin was used. Its compressive strength is greater than 90 N/mm2, tensile strength is greater than 25 N/mm2, and flexural strength is greater than 60 N/mm2 when tested at 7 days. It has good chemical resistance and an average density of 1050 kg/m3. It was used as a matrix in the formation of vehicles because it has an effective cost, excellent durability, and excellent in-service performance. It is a completely liquid system consisting of a base and a hardener. The ingredients are supplied in the correct mixing ratios to form the composites whose attenuation properties are to be studied [21,22,23].

2.3. Iron Filings

A number of iron filings resulting from blacksmithing waste was collected, which increase with the increase in cutting and polishing. This quantity was ground and sifted through a 65 μ m diameter sieve. Before adding it to the epoxy, the shape of its particles was confirmed with an SEM “scanning electron microscope” [24] and the elements present and their ratio using EDX “energy dispersive X-ray” [25] analysis, as shown in Figure 1.

3. Methods

3.1. Composite Preparation

The composites were produced with 0%, 20%, 40%, and 60% iron filings (IF). Composites were coded as EP–IF0 (pure epoxy), EP–IF20 (80% epoxy and 20% iron filings), EP–IF24 (60% epoxy and 40% iron filings), and EP–IF60 (40% epoxy and 60% iron filings). Table 1 shows the composites code, weight percentages, and the measured density.

3.2. Radiation Shielding Measurements

In the experimental measurements, a 3 × 3 inches high purity germanium (HPGe) detector was used for attenuation coefficient determination of EP–IF composites at different gamma-ray energies emitted from 60Co, 137Cs, and 241Am radioactive sources. The 60Co emits two lines (1.173 and 1.333 MeV), the 137Cs emits one line with an X-ray line (0.662 MeV), and the 241Am emits a single line (0.0595 MeV). The detector was connected to a high voltage, multi-channel analyzer, amplifier, and an electronic unit, as shown in Figure 2. The MCA was connected to the detector to generate digital signal spectra. This spectrum was carried out using Genie-2000 software on a computer connected to the HPGe detector system [26].
The energy and the detector efficiency were calibrated before the detection measurements, where the three radioactive sources were used for calibration. After detector calibration, the point source was placed at the top of the collimator, as shown in Figure 2, without placing the EP–IF composite. The output signals appear as peaks, each peak representing the gamma line emitted from the source; by calculating the area under this peak, these peaks represent the initial intensities of photons ( I 0 ) or non-attenuated intensities. By placing the EP–IF composite between the detector and the collimator with the same measurement conditions, the attenuated or transmitted intensities ( I ) can be calculated by determining the peak area using Genie-2000 software. From these intensities (at the same line energy), we can determine the LAC (cm−1) of the EP–IF composite’s thickness ( t ) using Equation (1) in Table 2 [27,28,29,30,31,32]. From the experimental LAC values, the mass attenuation coefficient (MAC) can be determined using the ratio of the LAC and the density of the EP–IF composite ( ρ ), given by Equation (2).
XCOM is a widely used program to theoretically calculate gamma-ray attenuation coefficients, as well as interaction mechanisms for gamma-rays with an energy range from 1 keV to 100 GeV [33,34]. Attenuator coefficients such as mean free path (MFP), half-value layer (HVL), and tenth-value layer (TVL) are utilized to evaluate the radiation attenuation properties of EP–IF composites; these equations are tabulated in Table 2 [35,36,37,38,39,40]. The radiation shielding efficiency (RSE) of EP–IF composite that is used as a radiation shield is determined by using the initial (I0) and transmitted (I) gamma line intensities obtained from peak area evaluation [41]. The lead equivalent thickness (LEth) corresponding to the epoxy–IF thicknesses used in this work was evaluated using Equation (7) [42]. The effective atomic number and electron density are defined as the number of electrons per unit mass can be calculated using Equations (8) and (9), respectively, in Table 2 [43].
Equivalent atomic number (Zeq) and GP fitting parameters were determined to calculate the exposure buildup factor (EBF) results for epoxy–IF composites. The Zeff was calculated using Equation (10) [44]. The GP fitting coefficients of any shielding composite are given by Equation (11) [43]. The GP fitting parameters can be used to estimate the EBF values for any shielding micro composite, as shown in Equation (12) [44]. The GP fitting parameters are represented by b, c, a, d, and Xk. The possibility of a neutron passing through glass without interacting is described by the fast neutron removal cross-section FNRC ( ∑ R , cm−1), given by Equation (13) [45].

4. Results and Discussion

The MAC and LAC were experimentally determined according to the experimental section, and the data were compared with the theoretical results estimated from Phy-X online software. The results are presented in Figure 3 for four epoxy composites: Ep–IF0, Ep–IF20, Ep–IF40, and Ep–IF60. The results in Figure 3 show first the extent of the accuracy of the experimental results due to the presence of agreement between the experimental points with the theoretical lines of the four compounds. The second thing, which is normal, is that the values of both the MAC and the LAC decrease with increasing photon energy. This is because, at each region, one of the interactions is dominant over the other, since at low energies, the photoelectric absorption is dominant. Thus, at medium energies, the Compton interaction is the most dominant, while at higher energies, pair and triple production interactions are present. For example, at 0.0595, 0.6617, and 1.1732 MeV for Ep–IF20, the values of MAC were 0.2095, 0.0781, and 0.0639 cm2/g, and the values of LAC were 0.3427, 0.1301, and 0.1071 cm−1, respectively. Thirdly, with the increase in the percentage of iron filings in the epoxy composites, the difference in the MAC and LAC experimental and theoretical lines increases. This is because the results of the LAC depend on the density of the composite, since higher density results in a higher linear absorption coefficient (LAC). This is evident in Figure 4, for example, at an energy of 0.6617 MeV, the increasing percentages between the MAC and LAC values for Ep–IF0, Ep–IF20, Ep–IF40, and Ep–IF60 were 10.0, 32.9, 67.7, and 127.3%, respectively. These percentages are constant at all energies because the MAC is multiplied by a fixed amount (density).
In Figure 4, we plotted the relation between the LAC and photon energy separately without the MAC. The results showed the superiority of the composite with the highest percentage of iron filings (Ep–IF60) in the attenuation coefficient (at all theoretical and experimental energies), while the lowest attenuation coefficient at all studied energies was for Ep–IF0. The theoretical values were calculated from 0.015 to 15 MeV photon energies. At the lowest studied energy (0.015 MeV), the LAC values were 2.7791, 3.3486, 4.2140, and 5.6961 cm−1 for EP–IF0, EP–IF20, EP–IF40, and EP–IF60, respectively, while at the lowest studied experimental energy (0.0596 MeV), the determined values were 0.2323, 0.2785, 0.3427, and 0.4573 cm−1, respectively.
The LAC is affected by the density in a directly proportional manner, so the composites with the highest density have the highest rate of absorption or attenuation of the incident photons, as shown in Figure 5. In the studied epoxy composites, the density of present composites increases with the increase of the added iron filings; therefore, the higher concentration of the iron filings, give higher LAC in the studied composites as shown in Figure 6.
The experimental values of HVL, MFP, and TVL at energies 0.0596, 0.6617, 1.1732, and 1.3331 MeV, as well as theoretical values from energy 0.015 MeV to15 MeV, were determined for the epoxy–iron filing composites, as shown in Figure 7, Figure 8, and Figure 9, respectively. These parameters increase with increasing photon energy at all composites. The lowest HVL, MFP, and TVL at all discussed theoretical and experimental energies were for the Ep–IF60 composite, while the highest values were for the Ep–IF0 composite. The measured HVL values at 0.662 MeV were 7.7445, 6.6768, 5.3278, and 3.9859 cm, while the measured MFP values were 11.1730, 9.6326, 7.6864, and 5.7504 cm, as well as TVL values at the same energy were 25.7268, 22.1800, 17.6986, and 13.2409 cm for Ep–IF0, Ep–IF20, Ep–IF40 and Ep–IF60, respectively. These results briefly illustrate the importance of the manufactured composites in this work, as less than 4 cm is sufficient to attenuate or absorb half the intensity of the photons coming out of the cesium-137 source, and about 13 cm is enough to absorb one-tenth of the incident photons intensity.
If we turn to the low energies (the energy of americium-241 as an example of measured value), we will find that a thickness of 5 cm is sufficient to attenuate 90% of the incident rays. This result is distinguished in the applications of X-ray shielding and low gamma-ray energy, because these composites can be obtained at the lowest cost and in an easy preparatory way.
The radiation shielding efficiency (RSE) of the epoxy–iron filing composites was experimentally determined at 0.0596, 0.6617, 1.173, and 1.333 MeV within 3 cm thickness of all discussed composites. A higher RSE corresponds to the highest rate of iron filings added at all studied energies, as shown in Figure 10. In addition, RSE is inversely proportional to the increase in energy, so at the energy of 0.0594 MeV, the shielding efficiency is about 75%, while at the energy of 1.333 MeV, it was approximately 31% for the same composite (EP–IF60). The lead equivalent thickness (LEth) is one of the most essential factors that must be discussed for the studied composites because the main reference used as a shielding material is lead, but due to its high cost in addition to the toxicity it causes, we resorted to materials that are environmentally friendly and less expensive, even if they are thicker than the lead used. We determined the LEth for all fabricated reinforced epoxy composites at different experimental energies, as shown in Figure 11, and observed that at the highest energy (1.333 MeV), 3 cm of Ep–IF60 (40% epoxy + 60% iron filings) gives the same efficiency as 0.6 cm of lead. This means that if the required thickness of the prepared compounds to reduce the intensity of photons with energy of 1.333 MeV to 50% is 5.5760 cm, then it corresponds to 1.1152 cm of lead. Likewise, the thickness that reduces the intensity of these photons by 90% for Ep–IF60 is 18.5231 cm, which is equivalent to 3.705 cm of lead. Although there is a 5-fold difference in the thickness used, the cost of forming the epoxy mixture is lower, in addition to its safe use.
The effective atomic number (Zeff) of the epoxy–iron filing composites was determined experimentally at 0.060, 0.662, 1.173, and 1.333 MeV and theoretically at the range of 0.015–15 MeV, as shown in Figure 12. At the lowest theoretically calculated energy (0.015 MeV), we found that the composites containing the highest rate of iron filings had the lowest Zeff, while the free epoxy resin composite had the highest Zeff, which is due to the mass attenuation coefficient at this energy being higher in the free epoxy than the rest of the composites containing iron filings. At higher energy levels (starting from 0.02 MeV), and up to 15 MeV, we found that the Zeff increases with the increase in the rate of iron filings. At an experimental energy of 0.662 MeV, the Zeff values were 4.59, 4.94, 5.62, and 6.38 for EP–IF0, EP–IF20, EP–IF40, and EP–IF60, respectively.
In general, the maximum Zeff value in the composites was 10.03 (at the lowest energy), while the minimum value was 4.00 (at the highest energy). In all fabricated composites, the Zeff values have the highest values at low energy and gradually decrease to 0.15 MeV and become constant from 0.2 to 2 MeV; at higher energy levels, the behavior of the Zeff curve gradually increases with increasing photon energy. The equivalent atomic number (Zeq) and the R-ratio were calculated within a broad energy range (0.015–15 MeV), as shown in Figure 13. These parameters were calculated according to Section 2 equations to estimate the EBF of the epoxy–iron filing composites. The R value results are ≥ 1 , so it starts from 0.06 to 0.998 up to 0.15 MeV, then it stabilizes with a value of 0.999 to ≥ 1   MeV , then it gradually decreases to 0.6 at 15 MeV, and the R values have the same behavior for epoxy–iron filing composites. The behavior of Zeq displays nearly stable values from 8.5 to 9.5 from 0.015 to 1 MeV; at higher energy levels, the Zeq values decrease at 1.5 MeV and then stabilize at the values of 6.66, 7.08, 7.54, and 8.00 for EP–IF0, EP–IF20, EP–IF40, and EP–IF60, respectively.
Experimental results of the composites in Table 1 are shown in Figure 14. Figure 15 shows the EBF at 1,4, 8, 15, 25, and 35 mfp. The figure displays the same behavior of EBF for all epoxy/iron filing composites with different mean free paths, where the EBF increased from 1 with increasing energy to a maximum value at 0.1 MeV, and gradually decreased with increasing energy; in addition, the maximum value increases when raising the mfp value. For EP–1F60 composites, the EBF at the discussed lowest energy (0.015 MeV) was 1.121, 1.243, 1.316, 1.402, 1.481, and 1.521 at 1, 4, 8, 15, 25, and 35 mfp, respectively. At 0.1 MeV, the EBF at 1 mfp was 4.051, 4.036, 4.021, and 4.008 for EP–IF0, EP–IF20, EP–IF40 and EP–IF60, respectively.
In order to investigate the neutron radiation shielding property of iron filing-doped epoxy composites, the macroscopic cross-section (FNRC) for fast neutrons was calculated. The high number of interactions per unit of time means high values of FNRC and, in this case, the attenuation of fast neutrons occurs at higher rates. The calculated FNRC values for the produced EP–IF composites are given in Figure 15; it is clear from Figure 15 that the FNRC values increased as the iron filing ratio in epoxy increased. The highest value for FNRC was found at 0.113 cm−1 for the EP–IF60 (60% IF added) composite; when these values are compared with some studies in the literature, it is clear that they are higher than 0.093 cm−1 for ordinary concrete [40].

5. Conclusions

In this work, the radiation attenuation properties of the polyepoxide composites—which have many properties and are used in many different fields—and the effect of the waste iron filing (IF) ratio included in it were investigated. For this purpose, coefficients such as MAC, LAC, MFP, HVL, TVL, Zeff, EBF, and FNRC were experimentally and theoretically determined. Experimental parameters were measured using an HPGe detector for 0.0595, 0.662, 1.1731, and 1.3320 MeV lines, and theoretical parameters were calculated using XCOM software in the wide energy range from 15 keV to 15 MeV. According to the results obtained, the parameters experimentally and theoretically measured are in good agreement. The LAC values increased as the IF concentration in epoxy increased. From this result, the other parameters such as LEth, RSE, Zeff, Zeq, and FNRC values increased with increasing LAC values, while HVL, MFP, TVL, and EBF values decreased. It is obvious that the addition of IF to epoxy resin significantly improves the radiation shielding characteristics of epoxy when taking into account the results obtained for the parameters. This can be explained by the fact that as the IF ratio is increased, the amount of high atomic number components in polyepoxide chemical composition increases. Finally, it can be concluded that, at a very low cost, easy-to-manufacture environmentally friendly materials can be used as radiation shielding materials, especially at low energies (X-ray), and can be used for neutrons better than concrete.

Author Contributions

Conceptualization, M.E.; methodology, M.E.; software, M.T.A.; validation, M.E.; formal analysis, M.T.A.; investigation, M.T.A.; resources, M.E.; data curation, M.T.A.; writing—original draft preparation, M.E.; writing—review and editing, M.E.; visualization, M.T.A.; supervision, M.E.; project administration, M.T.A.; funding acquisition, M.T.A. All authors have read and agreed to the published version of the manuscript.

Funding

Authors would like to extend their gratitude to Researchers supporting project number (RSP2023R336), King Saud University, Riyadh, Saudi Arabia.

Data Availability Statement

All relevant data are within this paper.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. The EDX—analysis and SEM image of present iron filings.
Figure 1. The EDX—analysis and SEM image of present iron filings.
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Figure 2. Schematic diagram of the experimental technique.
Figure 2. Schematic diagram of the experimental technique.
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Figure 3. The theoretical and experimental MAC and LAC for epoxy–IF composites at a broad energy range.
Figure 3. The theoretical and experimental MAC and LAC for epoxy–IF composites at a broad energy range.
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Figure 4. The theoretical and experimental LAC for epoxy–IF composites at a broad energy range.
Figure 4. The theoretical and experimental LAC for epoxy–IF composites at a broad energy range.
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Figure 5. The experimental LAC as a function of density of epoxy–IF composites and photon energy.
Figure 5. The experimental LAC as a function of density of epoxy–IF composites and photon energy.
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Figure 6. The experimental LAC as a function of iron filing concentration in epoxy composites and photon energy.
Figure 6. The experimental LAC as a function of iron filing concentration in epoxy composites and photon energy.
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Figure 7. The experimental and theoretical HVL as a function of photon energy of epoxy–iron filing composites.
Figure 7. The experimental and theoretical HVL as a function of photon energy of epoxy–iron filing composites.
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Figure 8. The experimental and theoretical MFP as a function of photon energy of epoxy–iron filing composites.
Figure 8. The experimental and theoretical MFP as a function of photon energy of epoxy–iron filing composites.
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Figure 9. The experimental and theoretical TVL as a function of photon energy of epoxy–iron filing composites.
Figure 9. The experimental and theoretical TVL as a function of photon energy of epoxy–iron filing composites.
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Figure 10. The experimental RSE as a function of photon energy of epoxy–iron filing composites with 3 cm thickness.
Figure 10. The experimental RSE as a function of photon energy of epoxy–iron filing composites with 3 cm thickness.
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Figure 11. The experimental LEth as a function of photon energy of epoxy–iron filing composites with 3 cm thickness.
Figure 11. The experimental LEth as a function of photon energy of epoxy–iron filing composites with 3 cm thickness.
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Figure 12. The theoretical and experimental Zeff values for EP–IF composites at different broad energy ranges.
Figure 12. The theoretical and experimental Zeff values for EP–IF composites at different broad energy ranges.
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Figure 13. The R-ratio and Zeq values at different energies used for EBF calculations.
Figure 13. The R-ratio and Zeq values at different energies used for EBF calculations.
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Figure 14. The EBF of EP–IF composites as a function of photon energy with different mfp.
Figure 14. The EBF of EP–IF composites as a function of photon energy with different mfp.
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Figure 15. FNRC for the EP–IF composites.
Figure 15. FNRC for the EP–IF composites.
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Table
Table 1. Compositions of fabricated epoxy–iron filing composites.
Table 1. Compositions of fabricated epoxy–iron filing composites.
Composite CodeComposition (wt %)Density (g·cm−3)
Epoxy ResinIron Filings
EP–IF010001.100 ± 0.009
EP–IF2080201.329 ± 0.014
EP–IF4060401.677 ± 0.007
EP–IF6040602.273 ± 0.011
Table
Table 2. Equations used in this study.
Table 2. Equations used in this study.
Equation NumberParameterEquationRemarks
(1)Linear attenuation coefficient L A C = − 1 t   l n   I I 0 t: thickness of absorber composite
(2)Mass attenuation coefficient M A C = L A C ρ ρ : density of absorber composite
(3)Mean free path M F P ,   c m = 1 L A C
(4)Half value layer H V L ,   c m = l n 2 L A C
(5)Tenth value layer H V L ,   c m = l n 10 L A C
(6)Radiation shielding efficiency R S E ,   % = 1 − I I 0 × 100  
(7)Lead equivalent thickness L E t h = L A C E P − I F L A C P b . t E P − I F
(8)Effective atomic number Z e f f = σ t σ e where the total atomic cross-section σ t = M A C × N N A
The electronic cross-section
σ e = 1 N A ∑ i f i N i Z i M A C i
(9)Electronic density N e = N A N Z e f f ∑ i n i NA, Avogadro’s number
(10)Equivalent atomic number Z e q = Z 1 l o g R 2 − l o g R + Z 2 l o g R − l o g R 2 l o g R 2 − l o g R 1   where Z1 and Z2 represent the element’s atomic number that corresponds to the ratio R1 and R2, respectively, and
R = M A C C o m p o t o n M A C T o t a l
(11)GP fitting parameter P = P 1 l o g Z 2 − l o g Z e q + P 2 l o g Z e q − l o g Z 1 l o g Z 2 − l o g Z 1  
(12)Exposure buildup factor B E , X = 1 + b − 1 K − 1 . K x − 1           f o r     K ≠ 1
or
B E , X = 1 + b − 1 . x           f o r       K = 1 		K E , X = c x a + d . t a n h x X k − 2 − t a n h − 2 1 − t a n h − 2             f o r     x ≤ 40   m f p ,

where X is the depth of penetration and E is the initial gamma energy
(13)Fast neutron removal cross-section F N R C = ∑ R = ∑ i ∑ R / ρ i w i ∑ R / ρ i is the removal cross-section of the ith component
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Alresheedi, M.T.; Elsafi, M. Effect of Waste Iron Filings (IF) on Radiation Shielding Feature of Polyepoxide Composites. Crystals 2023, 13, 1168. https://doi.org/10.3390/cryst13081168

AMA Style

Alresheedi MT, Elsafi M. Effect of Waste Iron Filings (IF) on Radiation Shielding Feature of Polyepoxide Composites. Crystals. 2023; 13(8):1168. https://doi.org/10.3390/cryst13081168

Chicago/Turabian Style

Alresheedi, Mohammed T., and Mohamed Elsafi. 2023. "Effect of Waste Iron Filings (IF) on Radiation Shielding Feature of Polyepoxide Composites" Crystals 13, no. 8: 1168. https://doi.org/10.3390/cryst13081168

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