1. Introduction
High efficiency materials in radiation environments and safety remarks in the nuclear industry has been the concern of Nuclear Material Scientists and necessitates them to introduce new materials. Each nuclear facility, even each part of it, requires particular materials to operate properly. One of those materials that was recently introduced is a kind of Ultra Advance Ceramic (UAC) called HfB2. HfB2 elements, Hafnium (Hf) and Boron (B), have a high capacity to absorb neutrons [1-3]. Neutrons thermal cross sections of stable Hf and B are 14 and 3980 Barns, respectively. Some HfB2 properties are listed in table (1).
| Properties | Value |
|---|---|
| Molar mass (gr) | 200.112 |
| Melting temperature (℃) | 3380 |
| Density at 25℃ (g/cm3) | 11.2 |
| Water solubility | Insoluble |
| Crystal structure | Hexagonal |
| Young's modulus (GPa) | 480 |
| Hardness (GPa) | 28 |
| Coefficient of thermal expansion(℃-1) | 6.3 × 10-6 |
| Heat capacity at 25℃(J mol-1 ℃-1) | 49.5 |
| Thermal conductivity (W m-1 ℃-1) | 104 |
These excellent thermal, mechanical, and nuclear properties are the reasons for using HfB2 as a control rod in fission power plant reactors (e.g. Pressurized Water Reactors (PWR)) [4]. Neutron calculation and measurement in fusion facilities like tokomak are very important [5, 6] and HfB2 also may play an important role as the first wall of tokomaks.
Therefore, HfB2 ceramic with all these properties would be a good candidate for such purposes. Despite of these interesting properties, there are some difficulties in using HfB2 under irradiation of neutrons. This issue originates from the nuclear interactions especially 10B (n, α) 7Li.
For example through 10B (n, α) 7Li interaction, the 10B isotope transforms into an 7Li isotope plus an alpha particle. There are two modes of interaction as follow:
n + 10B➛7Li*+ α, Q= 2.31 MeV + γ (0.48 MeV)(93%)
n + 10B ➛7Li+ α, Q=2.78 MeV (7%)
Although these interactions are dominant, other interactions like:
11B (n, α) 8Li (β-) → 8Be*(2α) or
178Hf (n, α) 175Yb or
180Hf (n, α) 177Yb,
may also happen. The emitted particle which is basically 4He will be absorbed by the material and will cause defects and dislocation in HfB2 which collapses its structure.
According to the literature, thermal neutrons produce alpha particles with an average energy of 1.48MeV and aLithium ion with an average energy of 0.83MeV [7]. The interaction of neutron with HfB2 also, produces prompt γ rays which need more precautions when shielding is intended with this compound.
Several experiments have been carried out to determine the cross section of the 10B (n, α) 7Li interaction [8, 9]. Some investigators have compared the practical results with databases such as; the Evaluated Nuclear Data Format (ENDF) or the Japanese Evaluated Nuclear Data Library (JENDL), in a limited energy range [10, 11].
In this study the well known Geant4 has been used to simulate the behavior of HfB2 interaction with neutrons in a wide range of neutron energy. The high Precision of Geant4 (HP) model covers the spectrum of 0-20MeV neutron energy. In this range, the Geant4 Nuclear Data Library (G4NDL) matches the ENDF and JENDL. The model considers neutron interaction with matter, including Capture, Elastic, Inelastic { (n,γ), (n,α), (n,2n), (n,nα), (n,np }, and also different models for the ion interactions [12]. Geant4 has been used for several simulation purposes and shows its validity [13, 14, 15, 16, and 17].
2. Virtual Experiment
A rectangular bulk sample with surface area of 10cm×10cm and thicknesses of 2mm, 10mm, 20mm, 50mm and 100mm has been selected for the simulation. The bulk sample was bombarded by a square neutron beam with the same surface area in a fixed distance of 10cm from the surface of the bulk sample, as shown in figure (1). The sample surface was then hit by 10^6 neutrons during each virtual experiment.
Various simulations have been carried out with mono energy neutrons of 0.025 eV, 1 eV, 1 keV, 100 keV, 1 MeV, 10 MeV and14 MeV to determine the production alpha particles resulting from10B(n, α)7Li or other (n, α) interactions. Figure (2) depicts all interactions from a 100 mm thickness of HfB2 slab, except 14 MeV neutrons. It was observed that, in the range of 0.025eV –100keV of neutron energies, the amount of alpha particle spectrums had a drastic fluctuation reaching 1.8 MeV. The compound did not produce any more alpha particles. In figure (2), the fluctuation is due to the alpha particle collisions. On the other hand, the fluctuation is due to counting all alpha particles either produced or collided ones. As we know when alpha particles collide with matter it loses its energy in specific amounts which means we have particles in discrete energy. So if we count all these particles then we have such fluctuations in the spectrum. This spectrum shows the alpha particles that exist in the material at any moment of time. 10 MeV energy has been divided into 256 channels; therefore with the discrete energy of alpha particles we must have more or less amounts in each channel. This fluctuation would be seen for high counting especially in the logarithmic scale. If we notice the spectrum for 1MeV or 10MeV neutron energy, we can see that all the alpha particles are not enough so we do not have such fluctuation in those spectrums.
It was also recognized that, at 1MeV neutrons, the alpha particles have an energy range of 0- 4.5MeV. 4.5MeV alpha particle energy is not because of B (n, α) Li. These alphas could be created via other inelastic interactions of neutron with matter. At 10 MeVof neutron energy, the amount of produced alpha particles changes to around 4%, which indicates that only 4% of the 10 MeV neutron flux has been involved in the (n, α) interaction to produce alpha particles. This amount then gradually decreases and ends before 8MeV.
The general shape of the alpha particles spectrum is the same for different thicknesses of the HfB2 slab. Figure (3) is plotted for 14MeV neutrons interactions with different thicknesses of HfB2 slab. It indicates that thicker slabs produce more alpha particles. Figure (3) also reveals that, the amount of lower energy alpha particles is higher with descending trends towards a 1.8 MeV alpha particle energy. At 1.8 MeV, a flat peak appears, then followed by a gradually continuing slope and it suddenly drops at 7.4 MeV. After that, the alpha particles’ energy ended at 8 MeV.
The interaction of neutrons with HfB2 produces some amounts of energy which would be absorbed by the compound. The deposited energy, as part of a single neutron, was analyzed by different thicknesses of HfB2 slab and the results are plotted in figure (4). As reported by some researchers [7], in 10B (n, α)7Li interaction, the sum of the 4He and 7Li kinetic energies (0.83MeV+1.48MeV) is 2.31MeV. The starting point in figure (4) shows that the 0.025eV thermal neutrons produce 2.48 MeV or average, which closely agrees with reported value.
Departing from the starting point, the deposited energy within the compound reduces and reaches to its minimum value of around 0.2-0.5MeV, followed by a rapid increase thereafter. The increase of deposited energy could be due to the multiplication of elastic interactions that may produce low energy neutrons in conjunction with the repeating interaction of 10B (n, α) 7Li.
This phenomenon has been analyzed and depicted separately in figure (5). The figure shows that neutrons’ elastic interactions starts from 10KeV onward and boosts swiftly as the energy of the neutrons becomes higher.
3. Conclusion
The behavior of HfB2 interaction with a wide energy range of neutrons was studied. Boron has a major influence on HfB2 performance and its large thermal neutron cross section plays the main role. Although, Boron can absorb more neutrons, the 10B (n, α) 7Li interaction may introduce some defects in HfB2 structure. Based on this concept, the amount of produced alpha particles and deposited energy within the HfB2 compound interacting with neutrons has been simulated. This virtual experiment approach is very helpful in inserting alpha detectors as well as neutron detectors in between the HfB2 composite, which is very challenging and even impossible. Neutron irradiation to the HfB2 composite affects the amount of Boron during this time. So, all computation of defective effects is time dependent for future studies.
