Abstract
Fast neutron and gamma-ray attenuation characteristics of Inconel-600, -601, -625, and − 718 superalloys, stainless steel-304, and lead were studied using MCNPX Monte Carlo code, WinXCom, XMuDat, and Auto-Zeff computer programs. The µm, HVL, MFP, σa, σe, Zeff and Neff, and ΣT were calculated for 192Ir, 18F, 137Cs, and 60Co gamma sources and 1 MeV fast neutrons. The difference between the MCNPX and calculated results was less than ± 2%. Above and below 511 keV photon energy, respectively, Inconel-600 and Inconel-625 have the highest mass attenuation coefficient among Inconel alloys. The thickest HVL and MFP values were achieved for the Inconel-601 superalloy. The σa and σe values decreased as photon energy increased. The Zeff values were approximately constant with photon energy increase. The Zeff of the Inconel-601 was the lowest, while that of Inconel-625 was the highest. In the studied gamma-ray energies, the Neff value variations were insignificant. The stainless steel-304 material was found to have the highest ΣT, while Inconel-600 had the highest value between Inconel superalloys. Calculated data indicates that Inconel-600 is the superior candidate for shielding gamma rays among Inconel superalloys.
Keywords: Gamma-ray and fast neutron shielding, Inconel Superalloy, MCNPX, WinXCom, XMuDat, Auto-Zeff.
Subject terms: Engineering, Materials science, Physics
Introduction
Considering the wide applications of X- and gamma rays and neutrons in medical diagnosis and therapy, industry, agriculture, and so on, the study and estimation of radiation attenuation characteristics from radiological measurements and radiation protection point of view are identified1,2.
In principle, any material can be used for radiation shielding if it has a sufficient thickness to absorb the incident radiation to a safe level. The radiation shielding material commonly used is concrete because it is inexpensive and adaptable for any construction design3–5. There are, however, many drawbacks associated with the usage of concrete, such as considerable variability in its composition and water content. This variation results in uncertainty in calculations for shield design predictions of the radiation distribution and attenuation in the shield. Water content has the disadvantage of decreasing the density and structural strength of concrete. However, concrete has many disadvantages and can be damaged by many processes, such as the expansion of aggregates, freezing of trapped water, fire or radiant heat, bacterial corrosion, leaching, physical and chemical damage, and considerable variability in its composition and water content6–8. In addition, for polymers, gamma and neutron radiation can cause structural changes, which can be harmful. Chemical bonds can be broken in high-energy radiations. As a result, their mechanical and thermal properties can be altered. Additionally, low melting point and density and low content of high atomic number elements in polymer composite materials are their crucial drawbacks9,10. Many of the pointed drawbacks for concretes are also true for many rocks, such as feldspathic and compact basalt, volcanic rock, igneous rocks, sandstone, limestone, and gypsum6,7.
Materials with high-temperature operating properties are needed in nuclear reactors, rocket motors, spacecraft, gas turbines, etc11. Materials used for radiation shielding in a reactor environment must have high radiation absorption capacity, a combination of strength and metallurgical stability, and high resistivity against temperature, chemical corrosion, etc12,13. Materials with a stronger crystal structure, such as superalloys, can endure these effects and can serve better shielding, mechanical, and chemical performances. Superalloys have shown better strength for creep-rupture at temperatures up to 700 ℃. Moreover, the sufficiently high density (over 9 g cm− 3 for some alloys) and good shielding characteristics for gamma rays and neutrons make it a good choice to be used in many applications at nuclear reactors14.
Ni-based superalloys have the advantage of resisting many severely corrosive environments. They resist pitting and crevice corrosion in high-temperature situations15. Inconel superalloys are one of the primary candidates capable of meeting the structural material requirements of very high-temperature applications. Inconel-600, -601, -625, and − 718 are well-known for their high resistance to corrosion and temperature and are used for heat tubing in steam generators and high-temperature applications in nuclear power plants16,17.
A minimal number of research articles have been published about the radiation attenuation properties of Inconel superalloys. Sayyed et al.18 evaluated the radiation shielding features of Co and Ni-based superalloys, including Inconel-625 and − 718 and some other alloys, using the MCNP-5 code and Phy-X/PD program. Calculated data indicated that Inconel-718 is suitable for the shielding of fast neutrons. Radiation and fast neutron shielding properties of Nickel-based Superalloys of Inconel-600, -718, and − 725 were estimated theoretically by Sriwongsa et al.19 using WinXCom software program at photon energy ranging of 1 keV–100 GeV. They found that Inconel-725 had excellent radiation shielding properties and is comparable with standard commercial concretes. Aygun Z. and Aygun M11. evaluated the radiation shielding potentials of Inconel-617 and Incoloy-800HT by EpiXS and Phy-X/PSD codes. They observed that Inconel-617 has a higher shielding ability than Incoloy-800HT. Gamma-ray and neutron shielding properties of Inconel-600, -601, -617, -625, -625LCF, and − 686 were estimated by Ravangvong et al.20 using the WinXcom program at the energy range of 1 keV – 100 GeV. Their study indicated that Inconel-686 and Inconel-600 were the best gamma-ray and fast neutron shielding mediums, respectively.
This research aims to estimate the gamma-ray and fast neutron shielding characteristics of Inconel-600, −601, −625, and − 718 superalloys using MCNPX, WinXCom, XMuDat, and Auto-Zeff software for 192Ir, 18F, 137Cs, and 60Co gamma sources and 1 MeV fast neutrons. Then, the obtained results will be compared with stainless steel-304 and Pb mediums.
Materials and methods
Gamma-ray shielding simulation
The MCNPX code version 2.6.0 is used to investigate the shielding properties of interested materials: Inconel alloys, stainless steel-304, and Pb. MCNPX code is a special type of nuclear code based on the Monte Carlo method that can transport different nuclear particles through materials22. To obtain the precise values of the mass attenuation coefficients and their related quantities, measurements should be made in good geometry conditions. Cylindrical geometries were employed for the modeling of samples. Four sections of sub-cylinders of 1 cm diameter and 0.25 cm thickness were considered for samples setting in front of sources in tandem (no distance between sub-cylinders). To eliminate the impact of scattering and bone sample thickness, the data average obtained from each of the thicknesses was reported as the final result.
The monoenergetic and collimated beams, which emit gamma rays perpendicular to the front face of the samples, were considered as a radiation source. For this purpose, a disk source of 1 cm diameter was defined in the data card of the MCNPX code with ERG, PAR, POS, and DIR commands for the energy and type of particle, position, and direction of the source, respectively.
The percentages by weight of the elements in the aforementioned samples (Inconel alloys, stainless steel-304, and Pb) and their densities were derived from literature for samples’ material specification11,18–20,22.
A small cylinder of 5 cm × 6 cm was considered as detector volume. It is set inside the cylindrical lead shield with a 19 cm thickness at 50 cm from the source (density = 11.34 g cm− 3; atomic number = 82). Two 15 cm × 7 cm lead cylinders with 0.6 cm and 1 cm holes were used as the collimators. The rest of the free space around the material cells in the MCNPX numerical model is considered void. Tally F4 was used to estimate the average flux on a cell (detector) volume for only one incident gamma photon. Also, it was used the tally energy card (En card) to modify the tally F4 output into energy bins. This tally calculates the average flux at the detector volume for only one incident gamma photon. The simulations were performed with 1–10 million histories. All simulated results were reported with < 0.5% statistical uncertainty provided by the code itself. The relative error is defined as a division of the standard deviation of the population (histories) to the sample mean.
Only the gamma rays with the highest branching ratio were considered for each source. Photons of 317 (83%), 511 (97%), 662 (85%), 1173, and 1332 (100%) KeV energies were assumed for 192Ir, 18F, 137Cs and 60Co, respectively23,24. Default energy cut-off values of electrons and photons (1 KeV) were used in simulations21. Figure 1 indicates the simulated geometry in the MCNPX code. Particle track illustration and a 3-D view of geometry were given in Fig. 1, as well. Figure 1b shows that the modeled configuration almost eliminates the scattered photons from getting to the detector. Also, Fig. 1c indicates good collimation and shielding of the source, samples, and detector. MCNP/MCNPX Visual Editor computer code of version X_24E was used for plotting geometry and particles’ tracks.
Fig. 1.
Geometry of modeled configuration. (a) Sizes are not on the scale, (b) particle track displaying (2-D view), and (c) 3-D view of geometry.
Gamma-ray attenuation theory
The mass attenuation coefficients of samples (µm) for studied gamma rays were derived by the transmission factors in various thicknesses of samples using Lambert’s law described as25:
 |
1 |
Where I0 and I denote the incoming and outgoing intensities of photons through the attenuator, t is sample thickness, and µ denotes the linear attenuation coefficient. The mean free path (MFP) is defined as the inverse of the linear attenuation coefficient. The half value layers (HVL) are calculated by dividing Ln2 by the linear attenuation coefficients of materials. In addition, the mass attenuation coefficients are calculated by dividing the linear attenuation coefficient of each sample by its density.
On the contrary, mass attenuation coefficients of samples were calculated using WinXCom and XMuDat programs data by Eq. (2), in which wi and µm, i are the percentage by weight and mass attenuation coefficient of the ith element in the sample, respectively26:
 |
2 |
The effective atomic and electronic cross-sections (σa and σe) of samples are determined from the simulated and calculated values of µm using the following relations25,26:
 |
3 |
 |
4 |
Where Ai and Zi are the atomic mass and atomic number of the ith element, and NA is Avogadro’s number. Also, fi denotes the fractional abundance of the ith element concerning the number of atoms such that f1 + f2 + f3+…+fi = 1. The effective electronic cross sections (σe) are only computable from the µm, i values of WinXCom and XMuDat programs, and in this research, the WinXCom program was selected for this purpose.
Also, the Zeff values for MCNPX code and WinXCom and XMuDat programs are obtained by the following equation27:
 |
5 |
Accordingly, the effective electron densities (Neff) of samples are calculated from Eq. (6)27:
 |
6 |
WinXCom, XMuDat, and Auto-Zeff software
The theoretical values of mass attenuation coefficients of different elements and compounds have been calculated by Hubbell and Seltzer28 and Boone and Chavez29, and they were presented in the form of various computer programs such as WinXCOM30 and XMuDat31. The WinXCom program employs the Hubbell and Seltzer28 database, while the XMuDat program can produce mass attenuation coefficient values based on both Hubbell and Seltzer28 and Boone and Chavez29 data. In this study, to compare and validate the simulation results, the XMuDat computer program was used to calculate the gamma-ray attenuation properties as well. The Boone and Chavez29 data source was chosen in the XMuDat program in this research. XMuDat is a program to be used for the calculation of various photon interaction coefficients. Six absorbing materials can be set up individually and simultaneously. Each material can be composed of components chosen from the elements and further from several compounds and mixtures of dosimetric interest. This program provides the data for mass attenuation, mass energy transfer, and mass energy absorption coefficients in a photon energy range of 1 keV to 50 MeV31. The WinXCom program is a web application database presented by NIST, USA that provides cross-sections and mass attenuation coefficients for the elements and several compounds or mixtures in the photon energy range of 1 keV to 100 GeV. It is even possible to define mixtures of already defined compounds or mixtures. The substance definition list comes with a predefined list of the first hundred elements in the periodic table (Z = 1−100)30.
In addition, the Auto-Zeff software was used to determine the effective atomic numbers. This software is a useful tool in Visual Basic, which readily facilitates the rapid calculation of energy-dependent effective atomic numbers, average atomic numbers, and spectral-weighted mean atomic numbers. This software surpasses the dubious power-law approach in which effective atomic number is determined by exploiting the smooth correlation between atomic cross-section and atomic number32. It has been demonstrated that the implementation of power-law approaches results in a significant overestimation of effective atomic numbers and, even when used relatively, inaccurate comparisons between different media33–35.
In this software, photon interaction cross section matrices are constructed for energies spanning 10 keV to 10 GeV and elements Z = 1–100. Coefficients for composite media are constructed via linear additivity of the fractional constituents and contrasted against the pre-calculated matrices at each energy, thereby associating an effective atomic number through interpolation of adjacent cross section data. Uncertainties are of the order of 1–2% for this user-friendly software. The results are significantly more accurate than normal power-law predictions in this software. The accuracy of the software has been validated against other published theoretical calculations and experimental measurements over a broad energy range. The very good agreement demonstrates that the use of this software is a valid and efficient alternative to direct measurement27,36–39.
Fast neutron total macroscopic cross-section
If a narrow beam attenuation experiment is met for the fast neutrons, the number of detected neutrons will fall off exponentially with absorber thickness. In this case, the fast neutron total macroscopic cross-section, ΣT, is calculated through the following relation40:
 |
7 |
Where I0 and I denote fast neutrons’ incoming and outgoing intensities through the attenuator, t is sample thickness.
The same setup for gamma-ray was applied for fast neutron shielding simulation. Tally F4 was used to obtain the average flux in a cell (detector volume) for incident fast neutrons. Also, it was used the tally energy card (En card) to modify the tally F4 output into energy bins. Neutrons with a kinetic energy level close to 1 MeV were considered as the fast neutrons with mean fixed energies41. The monoenergetic and collimated neutron beam with 1 MeV energy emitting neutrons perpendicular to the front face of the samples was also considered a radiation source.
Results and discussion
Gamma-ray attenuation properties of samples
Simulated and calculated values of mass attenuation coefficients are given in Table 1 for the interested samples at the studied gamma-ray energies.
Table 1.
Percentage composition of studied materials and their densities.
| Sample | Density (g cm− 3) | Element | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B | C | Al | Si | P | S | Ti | Cr | Mn | Fe | Co | Ni | Cu | Nb | Mo | Pb | ||
| Inconel-600 | 8.47 | – | 0.10 | – | 0.33 | – | 0.01 | – | 15.50 | 0.65 | 8.00 | – | 75.09 | 0.33 | – | – | – |
| Inconel-601 | 8.11 | – | 0.10 | 1.00 | 0.50 | – | 0.02 | – | 25.00 | 0.50 | 8.88 | – | 63.01 | 1.00 | – | – | – |
| Inconel-625 | 8.44 | – | – | 0.20 | – | – | – | 0.20 | 21.50 | – | 2.00 | 2.50 | 61.00 | – | 3.60 | 9.00 | – |
| Inconel-718 | 8.19 | 0.01 | 0.07 | 0.50 | 0.32 | 0.01 | 0.01 | 0.90 | 19.00 | 0.32 | 17.00 | 0.91 | 52.50 | 0.27 | 5.13 | 3.05 | – |
| Stainless steel-304 | 8.00 | – | 0.04 | – | 0.50 | 0.02 | 0.02 | – | 19.00 | 1.00 | 70.17 | – | 9.25 | – | – | – | – |
| Lead | 11.35 | – | – | – | – | – | – | – | – | – | – | – | – | – | – | – | 100.00 |
Differences between simulated and calculated (WinXCom and XMuDat) results of mass attenuation coefficients, the relative deviation (RD), were given in Table 2. The relative deviation (RD) is calculated according to the following relation:
 |
8 |
Table 2.
Mass attenuation coefficients (× 10− 2 cm2 g–1) of samples.
| Sample | Density (g cm− 3) | Energy (keV) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | ||||||||||||
| A | B | C | A | B | C | A | B | C | A | B | C | A | B | C | ||
| Inconel-600 | 8.47 | 10.97 | 10.98 | 10.97 | 8.48 | 8.51 | 8.49 | 7.46 | 7.50 | 7.47 | 5.60 | 5.63 | 5.60 | 5.24 | 5.28 | 5.25 |
| Inconel-601 | 8.11 | 10.84 | 10.89 | 10.88 | 8.43 | 8.47 | 8.45 | 7.43 | 7.46 | 7.43 | 5.58 | 5.61 | 5.58 | 5.22 | 5.26 | 5.23 |
| Inconel-625 | 8.44 | 11.14 | 11.18 | 11.17 | 8.48 | 8.51 | 8.49 | 7.43 | 7.46 | 7.43 | 5.55 | 5.58 | 5.56 | 5.20 | 5.23 | 5.20 |
| Inconel-718 | 8.19 | 10.98 | 11.03 | 11.02 | 8.44 | 8.48 | 8.46 | 7.41 | 7.45 | 7.42 | 5.55 | 5.58 | 5.56 | 5.19 | 5.23 | 5.20 |
| Stainless steel-304 | 8.00 | 10.60 | 10.63 | 10.63 | 8.29 | 8.33 | 8.31 | 7.31 | 7.35 | 7.32 | 5.50 | 5.53 | 5.51 | 5.15 | 5.18 | 5.16 |
| Lead | 11.35 | 35.63 | 36.03 | 36.26 | 15.39 | 15.62 | 15.58 | 10.84 | 11.01 | 10.99 | 6.06 | 6.18 | 6.15 | 5.53 | 5.62 | 5.59 |
A: MCNPX, B: WinXCom, and C: XMuDat.
It is apparent from Table 1 that the calculated (WinXCom and XMuDat) results are very close to each other compared to the simulated data. The percentage differences between the WinXCom and XMuDat results range from − 0.56 to 0.63%. Table 1 illustrates that above and below 511 keV photon energy, respectively, Inconel-600 and Inconel-625 have the highest mass attenuation coefficients compared with other Inconel alloys and stainless steel-304. This is due to the high mass densities of Inconel-600 and Inconel-625 and the high ratio of high atomic number elements in their elemental composition.
As given in Table 2, the RD values range from − 1.85% to − 0.07% and − 1.76–0.04% for MCNPX-WinXCom and MCNPX-XMuDat results, respectively, and they were found to be less than ± 2% (good agreement) for all the studied materials. At photon energies below 662 keV, high differences are observed between the mass attenuation coefficients of lead and other materials. For 1173 and 1332 keV photon energies, the mass attenuation coefficient of Inconel alloys and stainless steel-304 are close to the mass attenuation coefficient of lead compared to the other studied photon energies. The mass attenuation coefficient is heavily dependent on the atomic number, particularly in the energy regions dominated by photoelectric absorption, where higher-Z materials like lead (Z = 82) are expected to perform much better. However, at higher energies (above 662 keV), Compton scattering becomes the dominant interaction process, leading to a reduced dependence on atomic number. It should be noted that lead still has a greater mass attenuation coefficient because mass attenuation coefficients are influenced by both atomic number and material density (approximately 11 versus 8 g.cm− 3 for lead and Inconel alloys, respectively).
Figure 2; Table 3 show the energy dependence of the half value layers (HVL) and the mean free path (MFP) quantities for studied Inconel alloys. In addition, these values are given in Table 3 for some standard materials for better comparison of obtained results. As shown in Fig. 2, HVL and MFP values of studied materials increase with the increase in photon energy. The thickest HVL and MFP values were achieved for the alloy encoded as Inconel-601 among Inconel superalloys. Except for 1173 and 1332 keV photon energies, the values of Inconel superalloys are nearly close to lead values, at other studied photon energies (toward photoelectric effect dominance area), the HVL and MFP values of Inconel alloys are noticeably greater than lead (see Table 3). In addition, the results show that HVL and MFP values of Inconel superalloys are much lower than famous barite and, ordinary concretes and sandstone rock. This means that these Inconel alloys can be used as gamma-ray radiation shielding materials. Shielding characteristics of them are approximately the size of commercially available lead silicate shielding glasses.
Fig. 2.
Half value layers (a) and mean free path (b) of the studied Inconel alloys using MCNPX code.
Table 3.
Differences (%) between MCNPX-WinXCom (A) and MCNPX-XMuDat (B) results.
| Sample | Density (g cm− 3) |
Energy (keV) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | |||||||
| A | B | A | B | A | B | A | B | A | B | ||
| Inconel-600 | 8.47 | −0.07 | 0.04 | −0.43 | −0.18 | −0.48 | −0.06 | −0.54 | −0.09 | −0.68 | −0.11 |
| Inconel-601 | 8.11 | −0.45 | −0.32 | −0.41 | −0.16 | −0.50 | −0.09 | −0.55 | −0.11 | −0.66 | −0.10 |
| Inconel-625 | 8.44 | −0.36 | −0.28 | −0.36 | −0.11 | −0.40 | 0.01 | −0.56 | −0.13 | −0.65 | −0.10 |
| Inconel-718 | 8.19 | −0.45 | −0.39 | −0.45 | −0.21 | −0.51 | −0.09 | −0.57 | −0.14 | −0.70 | −0.15 |
| Stainless steel-304 | 8.00 | −0.33 | −0.30 | −0.39 | −0.16 | −0.46 | −0.09 | −0.51 | −0.10 | −0.63 | −0.12 |
| Lead | 11.35 | −1.11 | −1.76 | −1.49 | −1.23 | −1.60 | −1.42 | −1.85 | −1.35 | −1.62 | −1.07 |
Using Eqs. (3) and 4, the MCNPX, WinXCom, and XMuDat values of effective atomic and electronic cross sections (σa and σe) are given in Tables 4 and 5.
Table 4.
HVL and MFP values of studied materials using MCNPX code.
| Sample | Density (g cm− 3) |
Energy (keV) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | |||||||
| HVL | MFP | HVL | MFP | HVL | MFP | HVL | MFP | HVL | MFP | ||
| Inconel-600 | 8.47 | 0.75 | 1.08 | 0.97 | 1.39 | 1.10 | 1.58 | 1.46 | 2.11 | 1.56 | 2.25 |
| Inconel-601 | 8.11 | 0.79 | 1.14 | 1.01 | 1.46 | 1.15 | 1.66 | 1.53 | 2.21 | 1.64 | 2.36 |
| Inconel-625 | 8.44 | 0.74 | 1.06 | 0.97 | 1.40 | 1.10 | 1.59 | 1.48 | 2.14 | 1.58 | 2.28 |
| Inconel-718 | 8.19 | 0.77 | 1.11 | 1.00 | 1.45 | 1.14 | 1.65 | 1.53 | 2.20 | 1.63 | 2.35 |
| Stainless steel-304 | 8.00 | 0.82 | 1.18 | 1.04 | 1.51 | 1.18 | 1.71 | 1.58 | 2.27 | 1.68 | 2.43 |
| Lead | 11.35 | 0.17 | 0.25 | 0.40 | 0.57 | 0.56 | 0.81 | 1.01 | 1.45 | 1.10 | 1.59 |
| Water30 | 1.00 | 5.97 | 8.61 | 7.22 | 10.42 | 8.08 | 11.66 | 10.61 | 15.31 | 11.33 | 16.34 |
| Ordinary concrete30,42−47 | 2.3 | 2.83 | 4.08 | 3.45 | 4.98 | 3.85 | 5.55 | 5.09 | 7.34 | 5.36 | 7.73 |
| Barite concrete30,42−47 | 3.35 | 1.50 | 2.16 | 2.25 | 3.24 | 2.65 | 3.83 | 3.69 | 5.33 | 3.98 | 5.74 |
| 50PbO:50SiO2 glass (mol%)4,48 | 6.00 | 0.40 | 0.57 | 0.84 | 1.21 | 1.11 | 1.60 | 1.87 | 2.70 | 2.13 | 3.07 |
| Window glass30,49 | 2.58 | 2.56 | 3.70 | 3.12 | 4.50 | 3.49 | 5.04 | 4.59 | 6.62 | 4.90 | 7.07 |
| Sandstone7,30,50 | 2.3–2.96 | 2.87 | 4.14 | 3.50 | 5.06 | 3.91 | 5.65 | 5.38 | 7.76 | 5.69 | 8.20 |
Table 5.
Effective atomic cross sections (barn) of samples.
| Sample | Density (g cm− 3) | Energy (keV) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | ||||||||||||
| A | B | C | A | B | C | A | B | C | A | B | C | A | B | C | ||
| Inconel-600 | 8.47 | 10.36 | 10.37 | 10.36 | 8.01 | 8.04 | 8.02 | 7.05 | 7.08 | 7.05 | 5.29 | 5.32 | 5.29 | 4.95 | 4.99 | 4.96 |
| Inconel-601 | 8.11 | 9.99 | 10.03 | 10.02 | 7.77 | 7.81 | 7.79 | 6.84 | 6.88 | 6.85 | 5.14 | 5.17 | 5.14 | 4.81 | 4.84 | 4.82 |
| Inconel-625 | 8.44 | 11.04 | 11.08 | 11.07 | 8.41 | 8.44 | 8.42 | 7.37 | 7.40 | 7.37 | 5.50 | 5.53 | 5.51 | 5.15 | 5.18 | 5.16 |
| Inconel-718 | 8.19 | 10.52 | 10.57 | 10.56 | 8.09 | 8.12 | 8.10 | 7.10 | 7.14 | 7.11 | 5.32 | 5.35 | 5.32 | 4.98 | 5.01 | 4.98 |
| Stainless steel-304 | 8.00 | 9.67 | 9.70 | 9.69 | 7.57 | 7.60 | 7.58 | 6.67 | 6.70 | 6.68 | 5.02 | 5.04 | 5.02 | 4.70 | 4.73 | 4.71 |
| Lead | 11.35 | 122.59 | 123.96 | 124.75 | 52.95 | 53.74 | 53.60 | 37.28 | 37.88 | 37.81 | 20.86 | 21.24 | 21.14 | 19.01 | 19.32 | 19.22 |
A: MCNPX, B: WinXCom, and C: XMuDat.
A good agreement was observed between the simulated and the theoretical values of σa and σe. Tables 4 and 5 depict that σa and σe values of the materials decrease as photon energy increases. Table 5 shows that the discrepancies between the σe values of the two computer programs are negligible. Inconel-625 has the maximum values of σa and σe compared to other Inconel alloys and stainless steel-304.
The MCNPX, WinXCom, and XMuDat values of the effective atomic number (Zeff) and effective electron density (Neff) of the materials are given in Tables 6 and 7. Also, the calculated effective atomic numbers of the samples based on Auto-Zeff software are given in Table 6.
Table 6.
Effective electronic cross sections (× 10− 2 barn) of studied materials.
| Sample | Density (g cm− 3) | Energy (keV) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | |||||||
| A | B | A | B | A | B | A | B | A | B | ||
| Inconel-600 | 8.47 | 38.43 | 38.39 | 29.83 | 29.76 | 26.28 | 26.16 | 19.73 | 19.64 | 18.50 | 18.40 |
| Inconel-601 | 8.11 | 38.19 | 38.15 | 29.76 | 29.69 | 26.24 | 26.13 | 19.72 | 19.63 | 18.49 | 18.39 |
| Inconel-625 | 8.44 | 39.18 | 39.16 | 30.06 | 29.98 | 26.40 | 26.29 | 19.77 | 19.68 | 18.53 | 18.43 |
| Inconel-718 | 8.19 | 38.72 | 38.69 | 29.92 | 29.85 | 26.32 | 26.21 | 19.74 | 19.66 | 18.51 | 18.41 |
| Stainless steel-304 | 8.00 | 37.85 | 37.84 | 29.66 | 29.60 | 26.18 | 26.08 | 19.70 | 19.62 | 18.47 | 18.38 |
| Lead | 11.35 | 151.17 | 152.13 | 65.54 | 65.37 | 46.19 | 46.11 | 25.91 | 25.78 | 23.56 | 23.44 |
A: WinXCom and B: XMuDat.
Table 7.
Effective atomic numbers (Zeff) of samples.
| Sample | Density (g cm− 3) | Energy (keV) | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | |||||||||||||||||
| A | B | C | D | A | B | C | D | A | B | C | D | A | B | C | D | A | B | C | D | ||
| Inconel-600 | 8.47 | 26.97 | 26.99 | 26.99 | 27.03 | 26.84 | 26.96 | 26.96 | 26.98 | 26.82 | 26.95 | 26.95 | 26.97 | 26.80 | 26.95 | 26.95 | 26.96 | 26.77 | 26.95 | 26.95 | 26.96 |
| Inconel-601 | 8.11 | 26.16 | 26.27 | 26.27 | 26.33 | 26.12 | 26.23 | 26.23 | 26.26 | 26.08 | 26.22 | 26.21 | 26.24 | 26.06 | 26.21 | 26.20 | 26.22 | 26.04 | 26.21 | 26.20 | 26.22 |
| Inconel-625 | 8.44 | 28.18 | 28.28 | 28.28 | 28.41 | 27.98 | 28.08 | 28.08 | 28.16 | 27.92 | 28.03 | 28.03 | 28.09 | 27.83 | 27.98 | 27.98 | 28.01 | 27.80 | 27.98 | 27.98 | 28.00 |
| Inconel-718 | 8.19 | 27.18 | 27.30 | 27.30 | 27.42 | 27.03 | 27.15 | 27.15 | 27.22 | 26.98 | 27.11 | 27.11 | 27.16 | 26.92 | 27.08 | 27.08 | 27.10 | 26.89 | 27.08 | 27.08 | 27.10 |
| Stainless steel-304 | 8.00 | 25.54 | 25.62 | 25.62 | 25.64 | 25.51 | 25.61 | 25.61 | 25.62 | 25.49 | 25.61 | 25.61 | 25.61 | 25.47 | 25.60 | 25.60 | 25.61 | 25.44 | 25.60 | 25.60 | 25.61 |
| Lead | 11.35 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 | 82.00 |
A: MCNPX, B: WinXCom, C: XMuDat, and, D: Auto-Zeff.
As evident in Table 6, the Zeff values of any method agree with one another within < ± 2% for all studied materials. The Zeff values are approximately constant with photon energy increase. Of all the Inconel alloys, the effective atomic number of the Inconel-601 is the lowest while that of Inconel-625 is the highest (about 26 in versus 28).
In the studied gamma-ray energies, the effective electron density of the Inconel alloys varies from 28.05 × 1022 to 28.57 × 1022 electron g− 1 (Table 7). It decreases slowly as the photon energy increases. It is evident that for studied Inconel alloys, Neff values are somehow identical and constant in the studied photon energy range.
Fast neutron total macroscopic cross-section
The fast neutron total macroscopic cross-sections of studied materials, ΣT, calculated through relation 7 are given in Table 8.
Table 8.
Effective electron density (Neff × 1022 electron g− 1) of samples.
| Sample | Density (g cm− 3) | Energy (keV) | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 317 | 511 | 662 | 1173 | 1332 | ||||||||||||
| A | B | C | A | B | C | A | B | C | A | B | C | A | B | C | ||
| Inconel-600 | 8.47 | 28.55 | 28.57 | 28.57 | 28.42 | 28.54 | 28.54 | 28.40 | 28.53 | 28.53 | 28.38 | 28.53 | 28.53 | 28.34 | 28.53 | 28.53 |
| Inconel-601 | 8.11 | 28.39 | 28.52 | 28.51 | 28.34 | 28.46 | 28.46 | 28.30 | 28.45 | 28.44 | 28.28 | 28.44 | 28.44 | 28.25 | 28.44 | 28.44 |
| Inconel-625 | 8.44 | 28.43 | 28.53 | 28.53 | 28.22 | 28.32 | 28.33 | 28.16 | 28.28 | 28.28 | 28.07 | 28.23 | 28.23 | 28.05 | 28.23 | 28.23 |
| Inconel-718 | 8.19 | 28.36 | 28.49 | 28.49 | 28.20 | 28.33 | 28.33 | 28.15 | 28.30 | 28.29 | 28.10 | 28.26 | 28.26 | 28.06 | 28.26 | 28.26 |
| Stainless steel-304 | 8.00 | 27.99 | 28.09 | 28.09 | 27.96 | 28.07 | 28.07 | 27.94 | 28.07 | 28.07 | 27.92 | 28.06 | 28.06 | 27.89 | 28.06 | 28.06 |
| Lead | 11.35 | 23.57 | 23.83 | 23.83 | 23.48 | 23.83 | 23.83 | 23.46 | 23.83 | 23.83 | 23.40 | 23.83 | 23.83 | 23.46 | 23.83 | 23.83 |
A: MCNPX, B: WinXCom, C: XMuDat.
The stainless steel-304 material was found to have the highest fast neutron total macroscopic cross-section values due to its low density. Inconel-625 comprises the least value of fast neutron total macroscopic cross-section between Inconel superalloy materials. The Inconel-600 superalloy material with 0.325 cm− 1 fast neutron total macroscopic cross-section was found to have the highest fast neutron total macroscopic cross-sections among Inconel superalloys. As shown in Table 9, Inconel-625 and 718 comprise cobalt-59 (natural abundance = 100%) in their elemental compositions which prevents these alloys’ use in neutron shielding applications. Despite the gamma-ray shielding capabilities of Inconel alloys, these superalloys are not appropriate for neutron shielding applications due to the nickel and cobalt contentment. It should be noted that nickel isotopes have low thermal neutron cross sections compared to cobalt element and have longer half-lives (half-lives of 65Ni and 63Ni are 7.6 × 104 and 100.1 years respectively)51.
Table 9.
The fast neutron total macroscopic cross-sections (ΣT) of inconel alloys using MCNPX.
| Sample | Inconel-600 | Inconel-601 | Inconel-625 | Inconel-718 | Stainless steel-304 | Lead |
|---|---|---|---|---|---|---|
| ΣT (cm− 1) | 0.325 | 0.312 | 0.309 | 0.321 | 0.398 | 0.142 |
| Density (g cm− 3) | 8.47 | 8.11 | 8.44 | 8.19 | 8.00 | 11.35 |
It is noteworthy that some observed differences between the simulated and other theoretical values could be because of the MCNPX code and the model itself, such as physical and mathematical models, uncertainties in the nuclear/atomic data, improper modeling of source energy and geometry, and also, differences in the techniques and databases used in each method, etc. The results of the Monte Carlo simulations depend mainly on the nuclear data libraries linked to the numerical tool, so the authors believe that the most important reason for differences between the simulated and other theoretical values is related to the nuclear data libraries used in each method. These considerations are limitations of the modeling; however, the suggested model tries to estimate the photon interaction parameters of the samples to a high extent.
Conclusion
Materials with high-temperature operating properties are needed in nuclear reactors, rocket motors, spacecraft, gas turbines, etc. Nickel-based alloys such as Inconel superalloys are the main candidates for high-temperature applications. In the present work, the µm, HVL, MFP, σa, σe, Zeff, Neff, and ΣT values of the four types of Inconel superalloys, stainless steel-304 and lead were simulated and calculated theoretically using MCNPX Code, WinXCom, XMuDat and Auto-Zeff programs for 192Ir, 18F, 137Cs and 60Co, gamma-ray scourses and 1 MeV fast neutrons. The results indicate that the MCNPX code simulation provides reliable values of the photon interaction parameters of various Inconel superalloys within ± 2% compared to WinXCom, XMuDat, and Auto-Zeff programs. The data calculated using the XMuDat program showed better agreement with WinXCom data compared to MCNPX simulated results. Observed good agreement between theoretical methods reveals that the chosen Monte Carlo code (MCNPX) and aforementioned computer programs could be useful to calculate the photon and fast neutron interaction characteristics of different types of Inconel superalloy and stainless steel.
Author contributions
R.Bagheri carried out the Monte Carlo simulations, calculations, analyzed the data and wrote the original draft of the manuscript. H.Ranjbar supervised the study, conceptualized the research framework, reviewed and edited the manuscript.Both authors discussed the results, implications and reviewed the final manuscript.
Data availability
All data generated or analyzed during this study are included in this published article.
Declarations
Competing interests
The authors declare no competing interests.
Footnotes
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
- 1.Donya, M., Radford, M., ElGuindy, A., Firmin, D. & Yacoub, M. H. Radiation in medicine: origins, risks and aspirations. Glob Cardiol. Sci. Pract.2014, 437–448 (2014). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2.Huang, C. F. & McConathy, J. Fluorine-18 labeled amino acids for oncologic imaging with positron emission tomography. Curr. Top. Med. Chem.13, 871–891 (2013). [DOI] [PubMed] [Google Scholar]
- 3.Kurudirek, M., Aygun, M. & Erzeneoglu, S. Z. Chemical composition, effective atomic number and electron density study of Trammel sieve waste (TSW), Portland cement, lime, pointing and their admixtures with TSW in different proportions. Appl. Radiat. Isot.68, 1006–1011 (2010). [DOI] [PubMed] [Google Scholar]
- 4.Manohara, S. R., Hanagodimath, S. M. & Gerward, L. Photon interaction and energy absorption in glass: a transparent gamma ray shield. J. Nucl. Mater.393, 465–472 (2009). [Google Scholar]
- 5.Kurudirek, M., Turkmen, I. & Ozdemir, Y. A study of photon interaction in some Building materials: high-volume admixture of blast furnace slag into Portland cement. Radiat. Phys. Chem.78, 751–759 (2009). [Google Scholar]
- 6.Akkurt, I. et al. The properties of various igneous rocks for γ-ray shielding. Constr. Build. Mater.21, 2078–2082 (2007). [Google Scholar]
- 7.Obaid, S. S., Gaikwad, D. K. & Pawar, P. P. Determination of gamma ray shielding parameters of rocks and concrete. Radiat. Phys. Chem.144, 356–360 (2018). [Google Scholar]
- 8.Gaikwad, D. K. et al. Comparative study of gamma ray shielding competence of WO3-TeO2-PbO glass system to different glasses and concretes. Mater. Chem. Phys.213, 508–517 (2018). [Google Scholar]
- 9.Toto, E., Lambertini, L., Laurenzi, S. & Santonicola, M. G. Recent advances and challenges in polymer-based materials for space radiation shielding. Polymers16, 382 (2024). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 10.More, C. V., Alsayed, Z., Badawi, M. S. & Thabet, A. A. Pawar P. P. Polymeric composite materials for radiation shielding: a review. Environ. Chem. Lett.19, 2057–2090 (2021). [DOI] [PMC free article] [PubMed] [Google Scholar]
- 11.Aygun, Z. & Aygun, M. Evaluation of radiation shielding potentials of Ni-based alloys, Inconel-617 and Incoloy-800HT, candidates for high temperature applications especially for nuclear reactors, by EpiXS and Phy-X/PSD codes. J. Polytech.26, 795–801 (2023). [Google Scholar]
- 12.Chen, X., Liu, L., Liu, J. & Pan, F. Microstructure, electromagnetic shielding effectiveness and mechanical properties of Mg-Zn-Y-Zr alloys. Mater. Des.65, 360–369 (2015). [Google Scholar]
- 13.Singh, V. P. & Badiger, N. M. An investigation on gamma and neutron shielding efficiency of lead-free compounds and alloys. Indian J. Pure Appl. Phys.54, 443–448 (2016). [Google Scholar]
- 14.Mankins, W. L. & Lamb, S. Nickel and Nickel Alloys, In ASM Metals Handbook Properties and Selection: Nonferrous Alloys and Special-Purpose Materials. ASM International: Novelty, OH, USA, ; ISBN 978-1-62708-162-7. (1990).
- 15.Archana, M., Rao, C. J., Ningshen, S. & Philip, J. High-temperature air and steam oxidation and oxide layer characteristics of alloy 617. J. Mater. Eng. Perform.30, 931–943 (2021). [Google Scholar]
- 16.Thakur, A. & Gangopadhyay, S. State-of-the-art in surface integrity in machining of nickel-based super alloys. Int. J. Mach. Tools Manuf.100, 25–54 (2016). [Google Scholar]
- 17.Thellaputta, G. R., Chandra, P. S. & Rao, C. S. P. Machinability of nickel based super alloys: A review. Mater. Today. 4, 3712–3721 (2017). [Google Scholar]
- 18.Sayyed, M. I. et al. Evaluation of radiation shielding features of Co and Ni-based superalloys using MCNP-5 code: potential use in nuclear safety. Appl. Sci.10, 7680, 1–14 (2020). [Google Scholar]
- 19.Sriwongsa, K. et al. Radiation and fast neutron shielding properties of nickel-based superalloys: inconel 600, 718 and 725 superalloys. Integr. Ferroelectr.224, 120–133 (2022). [Google Scholar]
- 20.Ravangvong, S. et al. Estimation and comprehensive for radiation and neutron shielding of Ni-base superalloys: inconel 600, 601, 617, 625, 625LCF, 686, 690 and 693. NUJST31, 30–41 (2023). [Google Scholar]
- 21.Pelowitz, D. B. MCNPXTM User’s Manual, Version 2.6.0, Report LA-CP-07-1473 (Los Alamos National Laboratory, 2008).
- 22.McConn, R. J., Gesh, C. J., Pagh, R. T., Rucker, R. A. & Williams, R. G. Radiation portal monitor project, compendium of material composition data for radiation transport modeling. Revision 1, Pacific Northwest National Laboratory Richland, Washington 99352 10.2172/1023125 (2011).
- 23.Bagheri, R., Yousefi, A. & Shirmardi, S. P. Study on gamma-ray Attenuation characteristics of some amino acids for 133Ba, 137Cs, and 60Co sources. Nucl. Sci. Tech.31, 1–15 (2020). [Google Scholar]
- 24.Bagheri, R. & Khorrami Moghaddam, A. Gamma-ray Attenuation characteristics of some essential amino acids for 57Co, 192Ir, 18F, and 116mIn sources. Front. Biomed. Technol.9, 29–37 (2021). [Google Scholar]
- 25.Sayyed, M. I., Tekin, H. O., Kılıcoglu, O., Agar, O. & Zaid, M. H. M. Shielding features of concrete types containing sepiolite mineral: comprehensive study on experimental, XCOM and MCNPX results. Results Phys.11, 40–45 (2018). [Google Scholar]
- 26.Bagheri, R., Khorrami Moghaddam, A., Shirmardi, S. P., Azadbakht, B. & Salehi, M. Determination of gamma-ray shielding properties for silicate glasses containing Bi2O3, PbO, and BaO. J. Non-Cryst Solids. 479, 62–71 (2018). [Google Scholar]
- 27.Kurudirek, M., Özdemir, Y., Şimşek, Ö. & Durak, R. Comparison of some lead and non-lead based glass systems, standard shielding concretes and commercial window glasses in terms of shielding parameters in the energy region of 1 keV–100 GeV: a comparative study. J. Nucl. Mater.407, 110–115 (2010). [Google Scholar]
- 28.Hubbell, J. H. & Seltzer, S. M. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 KeV–20 MeV for elements 1 < Z < 92 and 48 additional substances of dosimetric interest. NISTIR 5632 (Gaithersburg, MD: National Institute of Standards and Physics Laboratory), 13–111 (1995).
- 29.Boone, J. M. & Chavez, A. E. Comparison of X-ray cross sections for diagnostic and therapeutic medical physics. Med. Phys.23, 1997–2005 (1996). [DOI] [PubMed] [Google Scholar]
- 30.Gerward, L., Guilbert, N., Jensen, K. B. & Levring, H. WinXCom: a program for calculating X ray Attenuation coefficients. Radiat. Phys. Chem.71, 653–654 (2004). [Google Scholar]
- 31.Nowotny, R. & XMuDat Photon Attenuation Data on PC. Tech. Rep. IAEA-NDS-195 (International Atomic Energy Agency), 1998).
- 32.Taylor, M. L., Smith, R. L., Dossing, F. & Franich, R. D. Robust calculation of effective atomic numbers: the Auto-Zeff software. Med. Phys.39, 1769–1778 (2012). [DOI] [PubMed] [Google Scholar]
- 33.Taylor, M. L., Franich, R. D., Trapp, J. V. & Johnston, P. N. The effective atomic number of dosimetric gels. Australas. Phys. Eng. Sci. Med.31, 131–138 (2008). [DOI] [PubMed] [Google Scholar]
- 34.Taylor, M. L., Franich, R. D., Johnston, P. N., Millar, R. M. & Trapp, J. V. Systematic variations in polymer gel dosimeter calibration due to container influence and deviations from water equivalence. Phys. Med. Biol.52, 3991–4005 (2007). [DOI] [PubMed] [Google Scholar]
- 35.Taylor, M. L. Robust determination of effective atomic numbers for electron interactions with TLD-100 and TLD-100H thermoluminescent dosimeters. Nucl. Instr Meth Phys. Res. B. 269, 770–773 (2011). [Google Scholar]
- 36.Kumar, T. K. & Reddy, K. V. Effective atomic numbers for materials of dosimetric interest. Radiat. Phys. Chem.50, 545–553 (1997). [Google Scholar]
- 37.Murty, V., Winkoun, D. & Devan, K. Effective atomic numbers for W/Cu alloy using transmission experiments. Appl. Radiat. Isot.53, 945–948 (2000). [DOI] [PubMed] [Google Scholar]
- 38.Murty, V. Effective atomic numbers for W/Cu alloy for total photon Attenuation. Radiat. Phys. Chem.71, 667–669 (2004). [Google Scholar]
- 39.El-Kateb, A., Rizk, R. & Abdul-Kader, A. Determination of atomic cross-sections and effective atomic numbers for some alloys. Ann. Nucl. Energy. 27, 1333–1343 (2000). [Google Scholar]
- 40.Knoll, G. F. Radiation Detection and Measurement. 4th Edition, Wiley, Hoboken, 217 (2010).
- 41.Byrne, J. Neutrons, Nuclei and Matter: An Exploration of the Physics of Slow Neutrons. CRC PressJanuary 1, ISBN-10:0750303662. (1996).
- 42.Demir, F. et al. Determination of radiation Attenuation coefficients of heavyweight- and normal-weight concretes containing colemanite and barite for 0.663 mev γ-rays. Ann. Nucl. Energy. 38, 1274–1278 (2011). [Google Scholar]
- 43.Akkurt, I., Akyıldırım, H., Mavi, B., Kilincarslan, S. & Basyigit, C. Photon Attenuation coefficients of concrete includes barite in different rate. Ann. Nucl. Energy. 37, 910–914 (2010). [Google Scholar]
- 44.Bouzarjomehri, F., Bayat, T., Dashti, M. H., Ghisari, R. J. & Abdoli N. 60Co γ-ray Attenuation coefficient of barite concrete. Iran. J. Radiat. Res.4, 71–75 (2006). [Google Scholar]
- 45.Stankovic, S. J., Ilic, R. D., Jankovic, K., Bojovic, D. & Longar, B. Gamma radiation absorption characteristics of concrete with components of different type materials. Acta Phys. Pol. A. 117, 812–816 (2010). [Google Scholar]
- 46.Bashter, I. I. Calculation of radiation Attenuation coefficients for shielding concretes. Ann. Nucl. Energy. 24, 1389–1401 (1997). [Google Scholar]
- 47.Akkurt, I., Akyıldırım, H., Karipcin, F. & Mavi, B. Chemical corrosion on gamma ray Attenuation properties of barite concrete. J. Saud Chem. Soc.16, 199–202 (2012). [Google Scholar]
- 48.Singh, K. J., Singh, N., Kaundal, R. S. & Singh, K. Gamma-ray shielding and structural properties of PbO-SiO2 glasses. Nucl. Instrum. Meth B. 207, 944–948 (2008). [Google Scholar]
- 49.Vascott, T. & Seward, T. P. III High temperature glass melt property database for process modeling, 1st Edition. Wiley-American Ceramic Society Publication, Westerville, Ohio (2005).
- 50.Khanlari, G., Rafiei, B. & Abdilor, Y. Evaluation of strength anisotropy and failure modes of laminated sandstones. Arab. J. Geosci.8, 3089–3102 (2015). [Google Scholar]
- 51.Pfennig, G., Klewe-Nebenius, H. & Seelmann-Eggebert, W. Karlsruher Nklidkarte 6th Edition. Harlow: Longman Press (1995).
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Data Availability Statement
All data generated or analyzed during this study are included in this published article.