# Assessment of Five Concrete Types as Candidate Shielding Materials for a Compact Radiation Source Based on the IECF

^{1}

^{2}

^{*}

## Abstract

**:**

_{Rt}) for the fast neutrons and the total mass attenuation coefficients (µ

_{m}), the half-value layer (HVL), the mean free path (MFP), the effective atomic number (Z

_{eff}), and effective electron density (N

_{eff}) for photons inside the materials. The model considered the radiation source energy and the material properties of the concrete types. The results revealed that the serpentine-containing concrete exhibited the highest ∑

_{Rt}with 12 cm of concrete thickness needed to attenuate an incident neutron flux to 1/100 of its initial value. In addition, the BC shows the highest µ

_{m}with a 38 cm concrete thickness needed to attenuate the 3 MeV energy X-ray flux to 1/100 of its initial value. This study suggests that a 40 cm thickness of SC or BC adequately shields the radiation generated from an IECF system with a maximum particle production rate of up to 1 × 10

^{7}n/s.

## 1. Introduction

^{3}lab in the Physics Department at Assiut University. The central technology is integrated with other facilities for multidisciplinary applications, including material science, medicine, and radiography. The planned IECF system will generate 2.45-MeV neutrons and hard X-rays from the deuterium-deuterium fusion occurring inside the system, with concurrent particle scattering interactions within the system components. Determining the shielding requirement and the necessary concrete thickness to attenuate the radiation to 1/100 of its initial value is the central core of the present study. An essential parameter for radiation shielding in a material is the attenuation efficiency (% reduction in flux) compared to incident radiation. The attenuation of the neutrons in the shielding materials changes based on the neutron energy and the microstructure of the shielding material [22,23], which for thermal neutrons is referred to as the macroscopic thermal neutron cross-section attenuation. In contrast, for fast neutrons, this is referred to as the macroscopic effective removal cross-section [24,25,26]. Meanwhile, the mass attenuation coefficient is considered the primary parameter to describe the relationship between the incident photons and the shielding material [27,28,29].

## 2. Materials and Methods

#### 2.1. Radiation Source and the Facility Layout

^{7}n/s DD neutrons. The IECF operation requires several tens of mA current and tens of kV voltage to be applied on the cathode to establish a potential well between the cathode and anode. Thermionic electrons are generated from the cathode; these electrons ionize the D

_{2}gas, start a glow discharge between the electrodes, and subsequently ‘spike’ a D plasma inside the system. The D ions in the plasma are then accelerated by the steep potential field gradient towards the centre of the cathode. Thus, fusion occurs in this central collision zone between ions and/or electrode surfaces, generating neutrons and protons, as shown in Equation (1).

^{+}+ D

^{+}→

^{3}He + n (2.45 MeV) or T + p (3.03 MeV)

^{3}, 60 cm from the floor, and 130 cm from each side with 200 cm from the top. A schematic drawing for the vacuum vessel, including the electrode dimensions, observation windows, and the fusion traces in the vessel are given in Figure 1b.

#### 2.2. Shielding Materials

#### 2.3. Calculation Model

#### 2.3.1. Neutron Attenuation

_{0}and I are the incident and attenuated neutron intensities before and after passing through the distance x (cm) of shielding material. The value ∑

_{t}(cm

^{−1}) is the physical quantity that describes the neutron attenuation in the matter, while it is called the total macroscopic cross-section, which can be given as [39,40,41]:

^{−3}) is the material density, N

_{a}(Mol

^{−1}) is Avogadro’s number, σ

_{t}(cm

^{2}) is the microscopic cross-section that includes the scattering- and absorption-microscopic cross-section (ρ

_{t}= ρ

_{s}+ ρ

_{a}), and A (g mol

^{−1}) is the atomic mass number. One can see that the value of the total macroscopic cross-section in Equation (3) depends on the material’s properties and the incident neutrons through the macroscopic cross-section, which changes based on the neutron energy. Therefore, another parameter to describe the neutron attenuation called the removal cross-section ∑

_{R}(cm

^{−1}), is widely used [4,42,43,44,45,46]. The ∑

_{R}is the probability that a fast or fission energy neutron takes a first collision, which removes it from the group of penetrating uncollided neutrons [47,48]. The relation between the macroscopic cross-section and the removal cross-section depends on the hydrogen percentage in the medium material and the neutron energy. When neutrons with energies between 2 and 12 MeV penetrate a medium containing a high concentration of light atoms, such as hydrogen, the value of ∑

_{R}= ∑

_{t}, while for a small fraction of hydrogen, the value of ∑

_{R}= 2/3 ∑

_{t}for energies between 6 and 8 MeV [24]. When the shielding material consists of one or more chemical compounds, it is not as simple as a pure element; the total effective removal cross-section (∑

_{Rt}) is given in the form [24]:

_{i}and ρ

_{i}(g cm

^{−3}) are the fraction by weight (indicated by the partial density of the elements) and the density of the medium material, respectively, and (∑

_{Ri}/ρ)

_{i}(cm

^{2}g

^{−1}) is the mass removal cross-section of the ith constituent. The partial density of the ith constituent is given by w

_{i}= (t

_{i})/(ρ), and (t

_{i}) is the fractional weight of the ith constituent. The effective removal cross-section of the proposed concrete shielding materials can be calculated from Equation (4).

#### 2.3.2. Photons Attenuation

_{l}(cm

^{−1}), defined as how easily a beam of photons can penetrate 1 cm of the shielding material. From a radiation protection standpoint, the greater the attenuation exhibited for a small thickness x (cm) is, the better the material is at shielding the photons. So, the selection of shielding material for photons depends mainly on the attenuation properties it exhibits. The relation which describes a photon beam penetrating matter is given in a form similar to the neutron attenuation:

_{0}and I are the incident and attenuated photon intensities, respectively, the latter of which decreases exponentially with the distance inside the material x (cm). Another parameter linked to the material properties is introduced, called the mass attenuation coefficient µ

_{m}(cm

^{2}g

^{−1}), which takes the density of the medium into account for photon attenuation and is given in the form:

_{i}is the fractional weight given in Section 2.3.1, and the assumption assumes that the different elements are homogenously distributed throughout the material. In addition to the mass attenuation coefficient of photons, two essential parameters for the radiation protection field are introduced here, the half-value layer (HVL) and the mean free path (MFP). The HVL is defined as the thickness of the concrete specimens that will reduce the photon beam to half, while the MFP is the average distance travelled by photons between two events (collisions, scattering, etc.). Equations (8) and (9) give the values of the HVL and MFP based on the mass attenuation coefficient [12,16,51,52]:

_{eff}) is equivalent to the atomic number but is used for compounds and mixtures of different materials, and this along with the effective electron density (N

_{eff}) are critical parameters for selecting the shielding materials. The effective electron density is derived from the effective atomic number and is defined as the number of electrons per unit mass. The following expressions introduce Z

_{eff}and N

_{eff}for the composite materials:

_{i}, A

_{i}, and w

_{i}are the atomic number, atomic weight, and the weight fraction of element i in the material, respectively. The mass attenuation coefficient, linear attenuation coefficient, half-value layer, mean free path, effective atomic number, and electron density for the photons passing inside the proposed shielding materials are estimated using Equations (6)–(11) at different energies expected from the IECF: 3, 2, 1.5, 1, 0.5, 0.2, and 0.05 MeV.

#### 2.3.3. Methodology

## 3. Results

#### 3.1. Neutrons Attenuation

_{i}of the concrete elements were collected at 2.45 MeV and then inserted into Equation (3) with the properties of the materials listed in Table 1 [54,55,56,57,58,59]. The fast neutron removal cross-section (∑

_{Ri}) values for each element of the materials were calculated, and the results are shown in Table 2. Then, the effective fast neutron removal cross-section was estimated from Equation (4) and displayed in the bottom row of Table 2. It can be seen from the table that the ∑

_{Rt}ranges between 0.09989 and 0.36635 cm

^{−}

^{1}.

_{4}), with the Ba (Z = 56) adding to the overall density of the concrete. In this context, barite can be considered an additive for increasing concrete density. Serpentine-containing concrete contains serpentine minerals as a particulate additive to the aggregate. Serpentine has the generalized formula: (Mg, Fe, Ni, Mn, Zn)

_{2–3}(Si, Al, Fe)

_{2}O

_{5}(OH)

_{4}, and therefore constitutes an additive source of H in the concrete in addition to the CSH mineral content.

_{Rt}, while OC-2 showed the smallest value among the five types of concrete. The high value of the ∑

_{Rt}for the SC could be attributed to the high relative ∑

_{Ri}of H (76% of ∑

_{Rt}) and the high total microscopic cross-section of the element, with high scattering and absorption cross-sections for fast neutrons in comparison to the other elements such as O (56% of the material density) in the same concrete type. On the other hand, even though OC-2 also includes H in the constituent mineral compounds, its contribution to the ∑

_{Rt}was only 17% due to the relatively small element fractional weight, 0.56% of the total density, compared to the O (50% of the material density). The effective fast neutron removal cross-section values for IMC and BC were almost the same, which could be attributed to the relatively small fractional weight of H, of less than 1% of the total density, in comparison to the high fractional weight of other elements such as O with 38 and 31% of the total density, which reduces the total microscopic cross-section (σ)

_{i}and hence the total effective fast neutron removal cross-section values. It is essential to mention that none of the concrete types under investigation included boron, which has a high affinity for neutron absorption. The value of ∑

_{Rt}calculated from the present methods was in good agreement with other methods presented in the literature [2,15]. As seen in Table 2, the concrete material with the highest effective fast neutron removal cross-section is the SC with ∑

_{Rt}= 0.36635 cm

^{−}

^{1}. This concrete type was expected to attenuate neutrons better than other concrete types.

#### 3.2. X-ray Attenuation

_{m}given in Equation (5). The mass attenuation coefficients for the constituent elements of the concretes listed in Table 1 are collected to determine the total mass attenuation coefficients of the five concrete materials at different X-ray energies (3, 2, 1, 0.5, 0.2, and 0.05 MeV) generated from the IECF system [54,55,56,57,58,59].

_{mi}for the elemental compositions of the concrete materials for an X-ray at 1 MeV and 200 keV energies are shown in Table 3, while the µ

_{mt}values for the concrete materials for an X-ray at 1 MeV and 200 keV energies are shown in Table 4. It can be seen from the table that the values varied from 0.06113 to 0.06804 cm

^{2}g

^{−}

^{1}, for which SC and BC exhibited the most significant and smallest total mass attenuation coefficients, respectively, among the concrete types at a 1 MeV X-ray energy. At different X-ray energies, from 0.2 MeV, the total mass attenuation coefficients for the shielding materials were calculated using the same technique, and the results are also given in Table 4. One can see that the µ

_{mt}values depend on the photon energy and the chemical composition of the concrete material. In addition, it was found that the variations in µ

_{mt}with the incident photon energy for all five concrete materials followed a similar trend. The values of µ

_{mt}decreased with the increased photon energy. Moreover, the relation between the photon energy and the µ

_{mt}values was not linear. The values of HVL, MFP, Z

_{eff}, and N

_{eff}of the photons in the shielding materials were calculated, and examples at 0.2 and 1 MeV energies are listed in Table 4. One can see that BC had the smallest HVL and MFP values; in contrast, OC-2 had the highest values. The value of µ

_{mt}calculated from the present methods is in good agreement with other techniques in the literature [49,53,54,55,56,57,58,59].

_{mt}from Table 4. This can be explained based on the effect of the concrete density, as seen in Table 1; BC has the most significant density, 3.35 g cm

^{−3}, compared to the other types.

_{mt}, µL, HVL, MFP, and Z

_{eff}in general, and especially at low photon energy, which can be attributed to the barite atoms inside the concrete, while OC-1 and OC-2 had the smallest values. In addition to the effective attenuation of the concrete types, the price may influence the selection of the shielding material.

## 4. Conclusions

_{Rt}) for fast neutrons and the total mass attenuation coefficients (µ

_{mt}), half-value layer (HVL), the mean free path (MFP), the effective atomic number (Z

_{eff}), and the effective electron density (N

_{eff}) for X-rays were determined for each material type and compared. The results obtained from this study show that the material density, chemical content, and total mass attenuation coefficient strongly affected the values of ∑

_{Rt}and µ

_{mt}. Serpentine concrete (SC) was found to have the highest ∑

_{Rt}value, while ordinary concrete-2 (OC-2) had the lowest value. At the same time, barite concrete (BC) and ilmenite-magnetite concrete (IMC) had almost the same values of ∑

_{Rt}for neutron attenuation. The obtained attenuation curves show that SC and BC would need the smallest material thickness to attenuate an incident neutron and photon flux to 1/100 of their initial intensities, respectively, compared to the other concrete types. The neutron attenuation curves for BC, OC-1, OC-2, and IMC were similar to that of SC. Moreover, the X-ray attenuation curves are very similar for SC, OC-1, OC-2, and IMC, with the BC being the most effective photon shield at lower incident energies.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The 3 × 3 × 3 m

^{3}lab layout, including the radiation source at the centre (

**a**), the IECF chamber configuration system layout, and the ion traces (

**b**).

**Figure 2.**The model used to investigate the thickness of shielding material needed for the IECF system is illustrated. n–E

_{i}and x–E

_{i}refer to the neutron and X-ray energies generated from the IECF and attenuated through the shielding material.

**Figure 3.**The variation in the neutron attenuation as a function of the concrete thickness for five concrete types, IMC, OC-1, BC, OC-2, and SC.

**Figure 4.**The attenuation of X-rays in the investigated concrete materials using Equation (5) at X-ray energies of (

**a**) 0.2 MeV and (

**b**) 1 MeV.

**Figure 5.**The total mass attenuation coefficients (

**a**), linear attenuation coefficients (

**b**), half-value layers (

**c**), mean free paths (

**d**), the effective atomic numbers (

**e**), and effect electron densities (

**f**) for X-rays with different energies from 0.05 up to 3 MeV for the investigated concrete materials.

**Table 1.**The elemental composition, atomic and mass numbers, fraction by weight, partial density, and density of the concrete materials used in the present study.

Element Properties | IMC | OC-1 | BC | OC-2 | SC | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

S | A | Z | w_{i} | ρ_{i} | w_{i} | ρ_{i} | w_{i} | ρ_{i} | w_{i} | ρ_{i} | w_{i} | ρ_{i} |

H | 1 | 1.008 | 0.57 | 0.0157 | 2.21 | 0.0508 | 0.36 | 0.0121 | 0.56 | 0.0132 | 7.20 | 0.1872 |

C | 6 | 12.011 | 0.08 | 0.0022 | 0.25 | 0.0058 | 0.15 | 0.0039 | ||||

O | 8 | 15.999 | 37.85 | 1.0523 | 57.75 | 1.3283 | 31.18 | 1.0445 | 49.56 | 1.1647 | 55.6 | 1.4456 |

Na | 11 | 22.989 | 1.52 | 0.0349 | 1.71 | 0.0402 | ||||||

Mg | 12 | 24.305 | 3.65 | 0.1014 | 0.13 | 0.0029 | 0.11 | 0.0037 | 0.24 | 0.0056 | 10.20 | 0.2652 |

Al | 13 | 26.982 | 1.79 | 0.0497 | 2.10 | 0.0483 | 0.42 | 0.0141 | 4.56 | 0.1072 | 2.50 | 0.065 |

Si | 14 | 28.086 | 4.85 | 0.1349 | 30.56 | 0.7029 | 1.04 | 0.0348 | 31.35 | 0.7367 | 17.55 | 0.4563 |

P | 15 | 30.974 | 0.01 | 0.0002 | ||||||||

S | 16 | 32.060 | 0.06 | 0.0016 | 10.78 | 0.3611 | 0.12 | 0.0028 | ||||

K | 19 | 39.098 | 1.08 | 0.0248 | 1.92 | 0.0451 | 0.08 | 0.0021 | ||||

Ca | 20 | 40.080 | 8.88 | 0.2469 | 4.39 | 0.1009 | 5.02 | 0.1682 | 8.26 | 0.1941 | 5.64 | 0.1466 |

Ti | 22 | 47.880 | 12.82 | 0.3563 | ||||||||

V | 23 | 50.942 | 0.08 | 0.0021 | ||||||||

Cr | 24 | 51.996 | 0.04 | 0.0010 | ||||||||

Mn | 25 | 54.938 | 0.30 | 0.0084 | ||||||||

Fe | 26 | 55.847 | 28.28 | 0.7863 | 0.70 | 0.0161 | 4.75 | 0.1595 | 1.22 | 0.0287 | 1.08 | 0.0281 |

Ni | 28 | 58.690 | 0.04 | 0.0012 | ||||||||

Ba | 56 | 137.330 | 46.34 | 1.5524 | ||||||||

Density (g cm^{−3}) | 2.78 | 2.30 | 3.35 | 2.35 | 2.60 |

**Table 2.**The ∑

_{Ri}and the ∑

_{Rt}values for each element of the concrete materials whole material were calculated using Equations (3) and (4).

Elements | IMC | OC-1 | BC | OC-2 | SC |
---|---|---|---|---|---|

∑_{Ri}(cm^{−1}) | |||||

H | 0.02450 | 0.07932 | 0.01882 | 0.02054 | 0.29213 |

C | 0.00017 | 0.00046 | 0.00031 | ||

O | 0.01904 | 0.02404 | 0.01890 | 0.02108 | 0.02616 |

Na | 0.00302 | 0.00347 | |||

Mg | 0.00521 | 0.00015 | 0.00019 | 0.00029 | 0.01364 |

Al | 0.00298 | 0.00290 | 0.00084 | 0.00642 | 0.00390 |

Si | 0.00620 | 0.03228 | 0.00160 | 0.03384 | 0.02096 |

P | 0.00001 | ||||

S | 0.00009 | 0.02091 | 0.00016 | ||

K | 0.00130 | 0.00237 | 0.00011 | ||

Ca | 0.01324 | 0.00542 | 0.00902 | 0.01041 | 0.00787 |

Ti | 0.01288 | ||||

V | 0.00010 | ||||

Cr | 0.00005 | ||||

Mn | 0.00032 | ||||

Fe | 0.03601 | 0.00074 | 0.00729 | 0.00131 | 0.00129 |

Ni | 0.00015 | ||||

Ba | 0.04454 | ||||

∑_{Rt} (cm^{−1}) | 0.12095 | 0.14962 | 0.12211 | 0.09989 | 0.36635 |

**Table 3.**The mass attenuation coefficients (µ

_{ml}) of the elements of the concrete types for 1 and 0.2 MeV X-rays.

Element | µ_{mi} (1 MeV)(cm ^{2} g^{−1}) | µ_{mi} (0.2 MeV)(cm ^{2} g^{−1}) |
---|---|---|

H | 0.12630 | 0.24290 |

C | 0.06361 | 0.12290 |

O | 0.06372 | 0.12370 |

Na | 0.06100 | 0.11990 |

Mg | 0.06296 | 0.12450 |

Al | 0.06146 | 0.12230 |

Si | 0.06361 | 0.12750 |

P | 0.06182 | 0.12500 |

S | 0.06373 | 0.13020 |

K | 0.06216 | 0.13190 |

Ca | 0.06388 | 0.13760 |

Ti | 0.05891 | 0.13140 |

V | 0.05794 | 0.13180 |

Cr | 0.05930 | 0.13780 |

Mn | 0.05852 | 0.13910 |

Fe | 0.05995 | 0.14600 |

Ni | 0.06160 | 0.11990 |

Ba | 0.05803 | 0.40450 |

**Table 4.**The total mass attenuation coefficients (µ

_{mt}), the half value layer (HVL), the mean free path (MFP), the effective atomic number (Zeff), and the electron density (Neff) of the concrete types at 0.2 MeV

^{#}and 1 MeV * X-ray energies.

Concrete Type | Total µ_{mt} *(cm ^{2} g^{−1}) | HVL * (cm) | MFP * (cm) | Z_{eff} * | N_{eff} *(10 ^{23} e/g) | Total µ_{mt} ^{#}(cm ^{2} g^{−1}) | HVL ^{#}(cm) | MFP ^{#}(cm) | Z_{eff} ^{#} | N_{eff} ^{#}(10 ^{23} e/g) |
---|---|---|---|---|---|---|---|---|---|---|

IMC | 0.06185 | 4.03013 | 5.81548 | 16.54016 | 2.89570 | 0.13228 | 1.88443 | 2.71924 | 17.35705 | 3.02560 |

OC-1 | 0.06538 | 4.60831 | 6.64980 | 10.58819 | 2.98000 | 0.12639 | 2.33360 | 3.36738 | 10.70426 | 3.01267 |

BC | 0.06113 | 3.38418 | 4.88338 | 33.81705 | 2.63872 | 0.25674 | 0.80573 | 3.36738 | 45.99331 | 3.23884 |

OC-2 | 0.06350 | 4.64376 | 6.70095 | 11.58687 | 3.00708 | 0.12912 | 2.33304 | 3.36658 | 11.74539 | 3.04822 |

SC | 0.06804 | 3.91742 | 5.65284 | 9.964079 | 3.00542 | 0.13403 | 1.98871 | 2.86971 | 10.10404 | 3.04764 |

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## Share and Cite

**MDPI and ACS Style**

Ahmed, R.; Saad Hassan, G.; Scott, T.; Bakr, M.
Assessment of Five Concrete Types as Candidate Shielding Materials for a Compact Radiation Source Based on the IECF. *Materials* **2023**, *16*, 2845.
https://doi.org/10.3390/ma16072845

**AMA Style**

Ahmed R, Saad Hassan G, Scott T, Bakr M.
Assessment of Five Concrete Types as Candidate Shielding Materials for a Compact Radiation Source Based on the IECF. *Materials*. 2023; 16(7):2845.
https://doi.org/10.3390/ma16072845

**Chicago/Turabian Style**

Ahmed, Rawheya, Galal Saad Hassan, Thomas Scott, and Mahmoud Bakr.
2023. "Assessment of Five Concrete Types as Candidate Shielding Materials for a Compact Radiation Source Based on the IECF" *Materials* 16, no. 7: 2845.
https://doi.org/10.3390/ma16072845