Computer Modeling of Displacement Cascades in Beryllium Irradiated with Intensive Neutron Flux

Computer simulations of the radiation defects created in beryllium irradiated by fast neutrons (E > 0.1 MeV) using the Geant4 and SRIM packages were carried out. The atom cascade displacements in Be at a neutron fluence of 1.6× 10 n/cm2 were determined to be 0.06 dpa and the helium concentration was calculated to be 168 appm. The concentration of 6Li has been estimated to be 5% in comparison to the He concentration. Nanoscale calculations were done in 30×30×30 nm cube of fast neutron-irradiated Be. A correlation between the Be primary knock-on atom (PKA) energies and the damage cascades has been established. The final defect distributions of single vacancies, divacancies, and small vacancy clusters were examined. Our results indicate that the damages caused by He atoms are about 3 times less than damages caused by Be primary knock-on atoms (PKAs).


INTRODUCTION
The purpose of our study is the computer modeling of the damage of a Be sample caused by intensive fusion neutron irradiation.In order to achieve our goal, we have adopted similar approach used by Becquart [1].First, we have simulated the interaction of neutrons with a macroscopic Be target at high energy (E > 0.1 MeV).For this purpose, the fusion neutron spectrum data was taken from the experiment as an input for the simulation.We have recorded the initial energy and position of Be primary knock-on atoms (PKAs) and of all isotopes created in the nuclear reactions at the output of the calculation.The results obtained allowed us to calculate the concentration of He and Li isotopes and use it as an input for the next step in our simulation.Using the Monte Carlo (MC) SRIM [2] code, we have calculated the atom displacements caused by the Be and He PKAs.At the end of the simulation, the final positions of the atoms involved in damage cascades have been recorded.Finally, the atom displacements and the number of produced vacancies and interstitials as a function of the PKA energy for the isotopes created were calculated.

THE METHODOLOGY OF THE SIMULATIONS
We created a computer Monte Carlo (MC) code based on the Geant4 CERN package [3] to simulate ion and neutron in-teractions at high energies (E > 0.1 MeV) in a Be homogeneous target.We took the initial neutron energy distribution for the simulation from [4].Neutron elastic and inelastic scattering and neutron capture with and without emission of charged particles were taken into consideration.Gamma ray and secondary electron (SE) emission as well as all types of electromagnetic interaction of charged particles and photons with matter were included in the present model.The high-precision database for low-energy neutron crosssection G4NDL [3] based on the ENDF/B-VI [5] database has been used with the purpose to achieve high accuracy of the neutron interaction in Be at energies between 0.1 MeV and 14 MeV.In our numerical calculations, we have considered the production of 3 He, 3 He, and 6 Li.The 7 Li production has a threshold of 12 MeV, and therefore it takes place in a fusion reactor.Our computer simulations were carried out for a macroscopic cylindrical Be target with diameter and length of 5 cm.We should point out that the Be PKAs for the damage cascades due to neutron scattering and capture were considered for a neutron fluence of about 1.6 × 10 20 n/cm 2 (E > 0.1 MeV) and for small cubic volume with dimensions 30×30×30 nm inside the target.We have adopted the procedure, described in [4], for estimation of the damage in beryllium due to intensive neutron irradiation.The results obtained for dpa (displacement per atom) cross-section versus various neutron energy are shown in Figure 1 where it is seen that the elastic neutron scattering (n, n) cross-section is more than an order of magnitude higher than the cross-section of the neutron inelastic scattering (n, n ).The magnitude of the neutron capture cross-section in Be with gamma ray emission is relatively small but it is important for the tritium production.Our calculations show that the threshold for the (n, n )-induced dpa is about 2 MeV and for the (n, γ) is about 1 MeV.The dpa due to elastic scattering was present at over whole energy range (0.1-14 MeV) in the present simulation.The dpa cross-sections for (n, n ) and (n, γ) grow rapidly up to about 4 MeV, after that they reach saturation.The next step in our model was to carry out calculations of damages in Be using the results from the described high-energy neutron interactions.We used the binary collision approximation (BCA) and the SRIM-MC code [2] which relies on the universal pair potential of Ziegler et al. [6] and Robinson [7].The SRIM code allows [1] the calculation of the stopping of the PKA at energies higher than 10 keV/u with an accuracy of 10%.In this approach, the crystal structure of Be has been neglected.Every PKA created by the high-energy neutron interaction with Be atoms was tracked in SRIM to its stopping in the Be target.According to the model, the target atom which is hit by PKA and starts a recoil cascade is identified by its recoiling energy.The number of displacement collisions records how many target atoms were set in motion in the cascade with energies above their displacement energy which is specified at the input.The Be target vacancies are the next items which were recorded.The replacement collisions on the other hand may reduce the total vacancies up to 30%.In the model, the average displacement energy E d has been chosen to be 40 eV.The lattice binding energy was taken to be 3.32 eV equal to the cohesive energy of the Be crystal.At the end of every cascade, the ion type, the PKA energy, the recoil energy, and the atom positions have been recorded for further processing.

RESULTS AND DISCUSSION
In the present simulations, the He content was estimated to be 168 appm.The 6 Li atom concentration was estimated to be 5% of the He content for the neutron fluence of 1.6 × 10 20 n/cm 2 (E > 0.1 MeV) used in the simulations.If we scale the result for the neutron flux of 1.3 × 10 15 n/cm 2 /s expected for the fusion reactor first wall (FW), our data is in agreement with the available one in the literature [8] although our results are obtained by a different procedure.It was established in our calculations that the total damage of 0.06 dpa for a neutron fluence of 1.6 × 10 20 n/cm 2 scales well with the already reported results for 2.5 × 10 22 n/cm 2 [4].We have established that the calculated number of the replacement collisions which lead to the recombination of vacancies and self-interstitials was only 1.8% compared to the total number of displacements.This result for the first time indicates that high-energy recoils generate atomic collision cascades in Be in which a fraction of the defects recombines.The calculated results of the Be subcascades as a function of the PKA energy are shown in Figure 4.They indicate a correlation between PKA energies and the number of subcascades.It is seen in Figure 4 that PKAs with higher energies produce Energy (MeV) a large number of subcascades.It is seen that Be PKA energies in the range 20-120 keV have a higher probability to induce subcascades.Obviously, the most probable number of subcascades is around 50.Similar results but for α-Fe are discussed in [9,10].The authors pointed out that for PKA with an energy higher than some critical value in the range of 10-40 keV, the formation of subcascades is more probable.On the other hand, PKA with higher energies does not initiate as a large number of subcascades as one could expect.This is probably due to the fact that the most efficient energy transfer in Be occurs at lower energies and thus produces the greatest amount of damages.From our simulation results shown in Figure 2, it is evident that low-energy cascades (E < 100 keV) are responsible for about 70% of the defects production.The accumulation of He atoms in the Be sample is due to the stopped He atoms losing their energy in the cascade collisions.The distribution of vacancies created by beryllium atom displacements and helium atoms created by neutron capture in Be is shown in Figure 3.We considered the He atoms as interstitials which contribute to the interstitial clusters concentration.

CONCLUSIONS
Computer simulations of the creation of point defects in beryllium, irradiated by intensive fast (E > 0.1 MeV) neutron fluence up to 1.6 × 10 20 n/cm 2 , have been performed.Our numerical model includes two steps.In the first step, precise calculations of the PKA energies and positions for Be, He, and 6 Li recoils have been made.The damage in Be due to the intensive neutron irradiation was calculated to be 0.06 dpa.The He content was determined to be 168 appm which is in agreement with the available results.The 6 Li content which is important for the tritium production was calculated to be  5% of the He content.The simulation results show that 70% of the damages occur at Be PKA energies below 100 keV.The number of subcascades increases with the PKA energy and reaches saturation at about 110 keV.The most probable subcascade number is 50 for PKA energies close to 50 keV.The final Be and He atom distributions confirm that the most likely defects are single vacancies, divacancies, and small-vacancy nanovoids containing more than 5 atoms.

Figure 1 :
Figure 1: dpa cross-section for a typical deuterium-tritium reactor for different types of neutron interactions as a function of the neutron energy.

Figure 4 :
Figure 4: Correlation between the number of Be PKA subcascades and the energy.