2.1 GEANT4

GEANT4 is a widely used Monte Carlo package for the simulation of transfer of particles through matter. It is employed in high-energy-particle plasma physics, nuclear applications, accelerator modelling, medical physics, cosmic ray physics, etc. In this code, neutrons are simulated using four different high-precision (HP) data-driven hadronic physics models (G4NeutronHPElastic, G4NeutronHPInelastic, G4NeutronHPCapture, and G4NeutronHPFission). In the GEANT4 input files, neutrons can be defined to have an energy in the range of 0.025 eV (thermal region) to 20 MeV (fast region). In this study, the geant4.10.02.p01 version of the code was used to estimate the neutron-sample interactions.

2.2 FLUKA

FLUKA is one of the Monte Carlo codes that very accurately model electromagnetic, cosmic, and nuclear interactions for all materials. It is widely used in high-energy particle physics, shielding, detector design, modelling cosmic ray interactions, medical dosimetry, radio-biology, radiation protection, etc. We used the FLUKA Monte Carlo code to determine absorbed doses, macroscopic cross-sections, neutron fluencies, and produced radioisotopes by samples after neutron irradiation. In this study, the FLUKA.2011.2b.6 version was used.

The GEANT4 and FLUKA Monte Carlo codes were previously used in our studies on gamma and neutron shielding [15–19]. GEANT4 and FLUKA differ from each other in terms of neutron transport. FLUKA uses its own cross-section libraries, while GEANT4 uses the Hadron Physics (HP) ENDF(Evaluated Nuclear Data File) library. Cross-section models and neutron energy limits libraries are used in the two codes.

2.3 Simulation Setup

The samples were modelled using the FLUKA and GEANT4 Monte Carlo simulation codes. GEANT4 and FLUKA simulations were performed to estimate neutron absorption crosssections (∑_R/ρ [cm²/g]- ∑_R: Effective removal cross section, ρ: Density of sample), total track lengths, and energy balances. The dimensions of the sample were set to 10×10×10 mm³. Boron was added in the rhenium sample at different weight percentages owing to its high neutron total macroscopic cross-section. 10-μCi ²⁴¹Am-Be neutrons were used in the simulations. A total of 260 neutron cross-section libraries are used in FLUKA; the G4NDL3.14 neutron cross-section library is selected for the GEANT4 simulations. An image of the experimental setup and illustration of the employed geometry in the theoretical simulations are shown in Fig. 1.

Fig. 1.Full-screen View

(Color online) Simulation geometry and experimental setup.

2.4 Sample Preparation

In this study, neutron shielding capacities of rhenium-boron structures were investigated. We prepared four samples with different percentages of boron in rhenium. All of them had a mass of 2.5 g and diameter of 2 cm. Rhenium and boron powders were milled for 3 h. After pelleting using the SPECAC hydraulic press equipment at 600 MPa, the disc samples were annealed at 1,200 °C for 6 h. The sample names, their densities, and B-Re percentages are listed in Table 1. The produced samples are shown in Fig. 2.

Fig. 2.Full-screen View

(Color online) Produced samples.

2.5 Experimental Methods

In the neutron equivalent dose rate experiments, a ²⁴¹Am/Be neutron source (10 mCi) and Canberra neutron detector were used. The ²⁴¹Am/Be source emits 2–11 MeV energetic neutrons. The conventional ²⁴¹Am/Be neutron source is a mixture of americium dioxide and beryllium metal powders. The NP-100B detector system (boron trifluoride-(BF₃)-filled neutron detector) can detect over a wide energy range, from slow to fast neutrons. Equivalent dose rate results were obtained using the radiological assessment display and control system (RADACS) software on the system PC. The experimental setup comprises a neutron source, neutron detector, and sample, as shown in Fig. 1. The detector is placed 30 cm in front of the source.

The mass absorption cross-section can be calculated from ∑_R /ρ, where ∑_R istheeffective removal cross-section:

${\sum }_R={\displaystyle \sum }_i{\rho }_i{\left({\sum }_R/\rho \right)}_i$

and ρ is the density of the sample [20].

3.1 Monte Carlo Simulation Results

Table 2 shows the results for the two shielding parameters, total particle track length and energy balance after the interactions. GEANT4 was used to estimate the total track length (l_t) after the particle-sample interactions; it is calculated (see GEANT4 manual) as the sum of the step lengths in the cell:

$l_{\text{t}}=s_i/w{f}_i$

where s_i is the collision score, w is the neutron weight, and f_i is the value of the response function. The results show that the total track length decreases with the decrease of the rhenium percentage in the sample, which implies that the neutron flux decreases. The lower neutron flux implies that the sample is a good neutron-shielding material. Therefore, among the considered samples, Re40-B60 is the best neutron-shielding material.

Next, energy balance is the sum of deposited energy and energy leakage; it corresponds to the Q value of a nuclear reaction:

$x+X\to y+Y+Q\left(\text{MeV}\right)+\dots$

The energy balance (Q) reveals the absorbed dose in the sample. Therefore, high-performance shielding materials exhibit a high energy balance owing to the high absorbed dose rate. Table 2 shows the energy balance results for all samples. The energy balance increases with the decrease of the rhenium percentage, which further confirms that Re40-B60 is the best neutron shielding sample. Table 3 shows the neutron mass absorption cross-sections, which support the above results. The neutron shielding capacity of the Re40-B60 sample, which has a high neutron mass absorption cross-section (∑/ρ), is higher than those of the other samples.

3.2 Equivalent Dose Rate Results

According to the simulation results, four samples were fabricated, and equivalent dose rate measurements and Monte Carlo calculations were performed. The experimental equivalent dose rate and simulation results (absorbed by the detector) [in µSv/h] are shown in Fig. 3. In addition, the experimental equivalent dose rate results with statistical evaluation are shown in Table 4. The figure shows that the equivalent dose rate is the lowest for Re40-B60. A larger absorbed dose by the detector, implies a lower absorbed dose by the sample. A low equivalent dose rate absorbed by the detector implies a high neutron shielding capability of the sample. Therefore, Re40-B60 exhibits the largest neutron shielding capability. It is worth noting that Re60-B40, Re58-B42, Re50-B50, and Re40-B60 exhibit better neutron shielding capacities than that of the 316LN steel.

Fig. 3.Full-screen View

(Color online)Neutron equivalent dose rate measurements, compared with FLUKA results.