Design and fabrication of a Nano-based neutron shield for fast neutrons from medical linear accelerators in radiation therapy

In this study, simulations were performed using MCNPX MC code version 2.6.0 [28]. A narrow-beam geometry was modeled that included a point source (emitting neutrons vertically to the entrance surface of a detector), a collimator made of cadmium surrounding the point source, the designed nano-material shield, a sphere volume with diameter of 1 cm defined as a detector, and a collimator made of cadmium surrounding the detector (Fig. 1a). A shield was simulated between the source and the detector (Fig. 1a). Tally F4 (F4:n) was utilized for detecting the number of neutrons reaching the detector in terms of neutron/cm². In MCNP MC code, the F4:n tally calculates the average neutron fluence per simulated source-neutron within the cell detector.

Initially, the fluence of neutrons in the detector cell (I₀) was calculated for the narrow beam geometry without the nanoshields between the source and detector. Next, nanoshields with different thicknesses were placed between the source and detector cell, and the fluences of neutrons were calculated in the detector cell (I_x) for each of them. Afterward, the transmission factors were determined by dividing I_x to I₀. Finally, the macroscopic cross-section of each nanoshield in different concentrations and thicknesses was calculated by Eq. 1.

Three types of neutron energies were used in our simulations. First, monoenergetic neutrons including 1–10 MeV with steps of 1 MeV were defined in our calculations. The second neutron source was the neutron spectra of an Am-Be source (Fig. 2a) obtained from previous studies [29, 30]. The third neutron source was the 18 MV photon beam of Varian 2100 C/D medical linear accelerator (Fig. 2a) obtained from other studies [3, 31, 32]. Finally, to compare our MC results with experimental measurements and to test the designed and fabricated nanoshields, the experimental measurements were performed with a neutron source of an Am-Be in the laboratory (Fig. 2b). Because of the lack of access to energy spectrum raw data from the Am-Be source in the laboratory, this spectrum was not used in the simulations.

To validate this model, photon mass attenuation coefficients were tested for lead shields for different energies. The MC simulations were tested versus published reference data (33).

To validate the simulated model for the calculation of neutrons, the macroscopic cross-section for paraffin wax (C₃₀H₆₂) with a density of 0.88 g/cm³ and a monoenergetic neutron source (E _eff = 4.5 MeV ²⁴¹Am–Be) was applied using the MC model and compared with the published reference data (34).

Nanocomposites were designed as cylinders with a diameter of 30 cm, and the inner space was divided into cubic cells in the nanometer dimension using the lattice feature of MCNPX MC code (Fig. 1b). Nanoshields made of boron carbide and iron oxide NPs 100 nm in diameter in a matrix of silicone resin were simulated (Fig. 1b). These shields were modeled with a weight percentage of 10, 20, 30, 40, and 50 nanomaterials in silicone resin. Shields were simulated with a thickness of 0.5, 1, 1.5, 2, 3, 4, and 5 cm to obtain more accurate macroscopic cross-sections in different densities. Special configurations using two shields were also simulated. This simulation geometry was designed to evaluate the double-layer shielding effect of Fe₃O₄ and B₄C nanoshields on photo-neutrons (Fig. 1c). Two overall thicknesses of 1, 2, 3, and 4 cm (half thickness for each nanoshield) were simulated. Evidently, the lattice represents the silicone resin matrix of shields, and spherical NPs of B₄C and Fe₃O₄ were located at the center of each cube. Depending on the nano-materials and their concentration, and considering the fixed diameter of 100 nm spheres of B₄C and Fe₃O₄, different cube sizes were modeled to obtain different volumes and, consequently, to achieve different concentrations of each nanomaterial in each shield. Initially, nanomaterials were separately used in each shield and tested as a single-layer shield, and subsequently, nano-iron oxide and nano-boron carbide were modeled together as a double-layer shield; the iron oxide shield was placed toward the source and the boron carbide was located toward the detector.

In the second step, nanoshields were fabricated based on the results of MC simulation. To fabricate nanoshields, nano-iron oxide and nano-boron carbide were purchased from Iranian Nanomaterials Pioneers Company and the size and homogeneity of NPs were evaluated by scanning electron micrograph (SEM). The diameter of nano-iron oxide and nano-boron carbide was equal to 20–30 nm (Fig. 3a) and 55 nm (Fig. 3b), respectively. Densities of silicone resin, iron oxide, and boron carbide were 1.24, 5.17, and 2.51 g/cm³, respectively.

Nanoshields were prepared in cylindrical samples with a diameter of 4 cm and thicknesses of 0.5, 1, 1.5, and 2 cm. They were made by adding iron oxide and boron carbide to the silicone resin. Shields were separately prepared in 10, 20, and 30 wt% (wt.%) of nanomaterial concentration for iron oxide and boron carbide. Four samples of nanoshields were produced for each percentage. Nano-materials were blended with silicone by an electric blender, and a hardener was added to each sample during blending. When NP concentration exceeded 30%, the mixture of silicone resin and nanomaterials did not properly solidify after being mixed.

Fabricated shields were tested in a laboratory with an Am-Be source (Fig. 2c). The source was placed in a water tank with the diameters of 2.5 × 1.5 × 1.5 m (L × W × H) and with 10 cm of pure water between source and shields (the experimental setup is illustrated in Fig. 1d). The BF₃ neutron detector was covered with cadmium leaves to eliminate scattered neutrons. Shields were placed in front of a neutron detector with a diameter of 2 cm.

Counts were measured in 15-min periods and repeated 3 times for each sample for averaging. The measurements were separately performed for each shield and finally done for the combined shield, including 1 cm of iron oxide close to the source and 1 cm of boron carbide toward the detector side. After the measurement, the macroscopic cross-section for iron oxide and boron carbide shields was calculated using Eq. 1.

The main sources of experimental uncertainties included limited accuracy of the BF3 detector, uncontrolled changes to the environment and conditions (e.g., receiving the scatted neutrons to the detector), limitations, and simplifications of the experimental procedure. In this regard, the uncertainties from the experimental setup and repeated measurements were negligible and are provided in the related sections. It is noteworthy that the statistical uncertainties of the results from the MC simulations were less than 1% in all cases.

The results of the simulation for the photon source and lead shield were compared with the data from the National Institute of Standards and Technology (NIST) [33]. These results demonstrated a difference of < 1.8% with data of lead attenuation from NIST (Fig. 4).

For neutrons’ source and paraffin wax, simulation results were compared with experimental data [34]. The values of the macroscopic cross-section for experimental [34] and MC methods were 0.192 ± 0.014 and 0.195 cm¹, respectively. Considering uncertainties in neutron calculations (less than 0.01), the resulting difference of 1.5% was acceptable for our MC model validation.

The macroscopic cross-sections of boron carbide and iron oxide nanocomposites were calculated for several weight percentages (wt.%) of NPs and 10 consecutive energies. For simplicity, only the results of composites with a concentration of 50 wt.% are presented in Fig. 5. In general, attenuation efficiency decreases with the increase in energy, but it shows some fluctuations. In addition, attenuation efficiency is significantly higher (approximately double) for both boron carbide and iron oxide at 1 MeV compared to higher energies (2 to 10 MeV). In all concentrations of NPs, the macroscopic cross-section was higher for boron carbide relative to iron oxide in the energy range of 2–10, but for 1 MeV, iron oxide acted superior to boron carbide. In other words, the macroscopic cross-section of iron oxide was ~ 11% higher than that of boron carbide in 50 wt.% concentration.

The applied neutron spectrum (Fig. 2a) had an energy range between 0.4 eV and ~ 15 MeV, and mainly from 1 to 3 MeV. Transmission factors for mono- and double-layer nanocomposites in front of the Am-Be source were calculated by the MC method (Tables 1 and 2). Based on Table 1, B₄C had a superior ability in eliminating neutrons compared to Fe₃O₄ for all concentrations, and this superiority increased with filler concentration. At the concentration of 10 wt.%, both nanocomposites showed similar attenuation, but with an increase in NP concentration, boron carbide exhibited more efficiency in eliminating neutrons. The macroscopic cross-sections of nanocomposites are depicted in Fig. 6a, which demonstrates the difference between attenuation yields of two nanocomposites. For instance, the macroscopic cross-section for boron carbide rose from 0.12 cm⁻¹ for 10% to 0.192 cm⁻¹ for 50%. However, for iron oxide, it was 0.109 cm⁻¹ for 10 wt.% and increased to 0.133 cm⁻¹ for 50 wt.%. Furthermore, the cross-section for the double-layer shield was equal to 0.21 cm⁻¹ for the concentration of 50% (Fig. 6d).

The transmission factors for the concentration of 50% and a thickness of 4 cm were 0.59 and 0.45 for mono-layer shields of iron oxide and boron carbide, respectively, and 0.44 for the double-layer shield (Tables 1 and 2).

The Am-Be source in the laboratory has an energy peak at 2.31 MeV (Fig. 2c). The spectrum was provided by the company after installing the Am-Be source. Table 3 shows the experimentally measured transmission factor in different thicknesses and for various percentages of NPs. With an increase in nanomaterial concentration, boron carbide shows more efficiency in eliminating neutrons. At the percentage of 30 and a thickness of 2 cm, it reduces the number of neutrons by 34%, compared to 29% for iron oxide. As expected, attenuation for the double-layer shield is more than two nanoshields separately. The transmission factor for the double-layer shield with a thickness of 2 cm is 0.62 (Table 3).

The macroscopic cross-section in Fig. 6c demonstrates the difference between attenuation yields of the mentioned nanomaterials. The macroscopic cross-section for boron carbide rises by 0.04 cm^− 1 from 10 to 30%, while this increase is 0.03 cm^− 1 for iron oxide.

The experimental results for monolayer shields of Fe3O4 and B₄C and double-layer shields (Table 3) demonstrate satisfactory agreement with the simulation results (Tables 1 and 2). The difference between MC and measurements is in the range of 10%. There was about 9% difference between experimental measurement of neutron attenuation and MC results, which can be attributed to the discrepancy between fabricated nanocomposites where the NPs were heterogeneously distributed inside the resin matrix. However, in the MC simulations, NPs were homogenously dispersed with the resin matrix. Besides, the uncertainties in providing energy spectra during the installation of the Am-Be neutron source as experimentally and subsequently measurements (about 5%), primarily due to the uncertainty in the source strength, had a non-negligible effect on the observed discrepancy between MC and measurement results.

The applied neutron spectrum of linac (Fig. 2a) has an energy range between 40 keV and ~ 10 MeV and contains a peak at 1 MeV. Tables 1 and 2 present the attenuation in different thicknesses and for various percentages of NPs for mono- and double-layer nanoshields. As can be seen, attenuation is higher for the double-layer shield than mono-layer shields. Based on the comparison of transmission factor for mono-layer and double-layer shields (concentration of 50% and thickness of 4 cm), the values for iron oxide, boron carbide, and double-layer shields were 0.53, 0.40, and 0.37, respectively. Attenuation increases for both nanocomposites by an increase in NP concentration (wt.%), and at 10 wt.%, both nanocomposites show similar attenuation. However, with an increase in the weight percentage of boron carbide, it shows more efficiency in eliminating neutrons. At the percentage of 50 and a thickness of 5 cm, it reduces the number of neutrons by 67% (Table 1). The reduction is only 55% for iron oxide (Table 1).

The macroscopic cross-section in Fig. 6b indicates the difference between attenuation yields of two nanocomposites. The macroscopic cross-section for boron carbide rose from 0.144 cm⁻¹ for 10 wt.% to 0.226 cm⁻¹ for 50 wt.%. For iron oxide, it was 0.132 cm⁻¹ for 10 wt.% and increased to 0.159 cm⁻¹ for 50 wt.%. According to Fig. 6e, for double-layer shields the macroscopic cross-section increased from 0.16 cm⁻¹ for the concentration of 10% to 0.25 cm⁻¹ for 50 wt.%. It is of note that for each spectra, a permanent increase is observed in attenuation as the concentration of the NPs increases (Fig. 6).

Figure 7 a and b demonstrate the energy spectra of neutrons reaching the detector for a total thickness of 2 cm of all studied nanocomposites (50% NPs) in front of the Am-Be and linac spectra, respectively. These nanocomposites include 2 cm of iron oxide, boron carbide, and 2 cm of double-layer shields (1 cm for iron oxide and 1 cm for boron carbide).