Primary Knock-on Atom Energy Research Articles

Enhanced radiation tolerance of the Ni-Co-Cr-Fe high-entropy alloy as revealed from primary damage

High-entropy alloys (HEAs) have received much attention for the development of nuclear materials because of their excellent irradiation tolerance. In the present study, the generation and evolution of irradiation-induced defects in the NiCoCrFe HEA were investigated by molecular dynamics (MD) simulations to understand the mechanisms of its irradiation tolerance compared with bulk Ni. The displacement cascades were simulated for the energies of primary knock-on atoms (PKA) ranging from 10 to 50 keV to understand the irradiation resistance in HEAs. In general, there are more displaced atoms produced in the thermal spike phase, but fewer defects survived at the end of the cascades in the NiCoCrFe alloy than in Ni. Both interstitial and vacancy clusters increase in size or number with increasing PKA energy in both materials, but they do so more slowly in the NiCoCrFe HEA. The delayed damage accumulations in the NiCoCrFe HEA are attributed to the high defect recombination caused by the following two mechanisms. First, the enhanced thermal spike and the low thermal conductivity of HEAs for heat dissipation result in the higher efficiency of defect recombination. Furthermore, the substantially small binding energies of interstitial loops in the NiCoCrFe HEA, as compared with those in Ni, are responsible for the delayed interstitial clustering in the NiCoCrFe HEA.

Optimal sampling of MD simulations of primary damage formation in collision cascades

For a few decades now, molecular dynamics (MD) simulations have been extensively used for studying primary damage formation in collision cascades in materials exposed to fast particle irradiation. Because of the stochastic nature of defect production phenomena, it is vital to model collision cascades in batches with the same set of essential simulation parameters that includes primary knock-on atom (PKA) energy and target temperature in the first instance. No generally accepted practice has been established so far to determine the optimal size of the sampling set of MD simulations of collision cascades. The suggested simple a posteriori sampling set size validation method is based on reviewing the dependence of the average and median number of Frenkel pairs generated in collision cascades on the amount n of simulated cascades in a series with identical simulation parameters. As the average and median number of Frenkel pairs converges with raising n, the optimal sampling set size is determined as a function of the simulation conditions. It is shown how it depends on the PKA energy, irradiation temperature, alloy composition and the interaction of collision cascades with the free surfaces.

Radiation damage calculations for charged particle emission nuclear reactions

Taking the quantum tunneling and Coulomb barrier into account, the present work proposes the calculation of Primary Knock-on Atom (PKA) energy for charged particle emission reactions. The method proposed in this paper and that used in NJOY have a large difference of PKA energy for charged particle emissions. For a D+T fusion neutron-induced 6Li(n,t)4He PKA, the maximum PKA energy calculated with NJOY is 2.9 MeV, whereas 14.2 MeV is obtained with the formula proposed in the present work. The subsequent total neutron-induced Displacement per Atom (DPA) calculated with the two methods has a small difference for most isotopes of which the DPA is predominated by neutron scattering reactions, such as 56Fe and 58Ni. However, the difference can be important for nuclei with charged particle emission channels open at thermal energy, such as 6Li, 10B, and 59Ni. Using the damage cross sections (calculated by NJOY with and without modifications) and SRIM/TRIM-2008 calculations, the relative differences on total DPA rates of the compound material 90%56Fe-9%58Ni-1%59Ni are within 1% for two fast spectra, 1.5% for fusion first wall, about 5% for the heavy reflector, and 25% for a pressurized water reactor vessel.

Nanoscale lattice strains in self-ion implanted tungsten

Developing a comprehensive understanding of the modification of material properties by neutron irradiation is important for the design of future fission and fusion power reactors. Self-ion implantation is commonly used to mimic neutron irradiation damage, however an interesting question concerns the effect of ion energy on the resulting damage structures. The reduction in the thickness of the implanted layer as the implantation energy is reduced results in the significant quandary: Does one attempt to match the primary knock-on atom energy produced during neutron irradiation or implant at a much higher energy, such that a thicker damage layer is produced? Here we address this question by measuring the full strain tensor for two ion implantation energies, 2 MeV and 20 MeV in self-ion implanted tungsten, a critical material for the first wall and divertor of fusion reactors. A comparison of 2 MeV and 20 MeV implanted samples is shown to result in similar lattice swelling. Multi-reflection Bragg coherent diffractive imaging (MBCDI) shows that implantation induced strain is in fact heterogeneous at the nanoscale, suggesting that there is a non-uniform distribution of defects, an observation that is not fully captured by micro-beam Laue diffraction. At the surface, MBCDI and high-resolution electron back-scattered diffraction (HR-EBSD) strain measurements agree quite well in terms of this clustering/non-uniformity of the strain distribution. However, MBCDI reveals that the heterogeneity at greater depths in the sample is much larger than at the surface. This combination of techniques provides a powerful method for detailed investigation of the microstructural damage caused by ion bombardment, and more generally of strain related phenomena in micro-volumes that are inaccessible via any other technique.

Investigation of the temperature effect on the primary radiation damage near the grain boundary in tungsten using Molecular dynamics simulations

Molecular dynamics (MD) simulations were conducted to investigate the influence of temperature on primary radiation damage in tungsten (W). By investigating on the number of surviving defects, it was suggested that the increment of temperature improved the radiation resistance of the W, which was further improved with the existence of grain boundaries (GBs). Second, the maximum average kinetic energy of all of the atoms in the GB comprehensively reflected the influences of the temperature, the primary knock-on atom (PKA) energy, and the distance between the PKA and GB on the overlap of the cascade center and the GB. Thus, it could be regarded as a quantitative factor that explained the GB influence on the evolution of the interstitials. Finally, the size distribution of the interstitial clusters exhibited negative correlation with the temperature. In contrast, when the temperature rose above 900 K, the size of the vacancy cluster increased with temperature.

Cascades Damage in γ-Iron from Molecular Dynamics Simulations

The degradation of austenitic stainless steels under irradiation environment is a known problem for nuclear reactors, which starts from atoms displacement cascade. Here, molecular dynamics (MD) simulations have been used to investigate the formation of atomic displacement cascade in γ-iron for energies of the primary knock-on atom (PKA) up to 40 keV at 300 K. The number of Frenkel pairs increased sharply until a peak value was reached, which occurred at a time in the range of 0.1-2 ps. After that, a number of defects gradually decreased and became stabilized. Compared with α-iron, there was less defects in the stable stage, and more clustered defects were produced in γ-iron. Within the range of PKA energies, two regimes of power-law energy-dependence of the defect production were observed, which converge on 16.8 keV. The transition energy also marks the onset of the formation of large self-interstitial atom (SIA) clusters and vacancy clusters. Interstitial and vacancy clusters were in the form of Shockley, Frank dislocation loops and Stir-Rod dislocation loops.

Enhanced Radiation Tolerance of the Ni-Co-Cr-Fe High-Entropy Alloy as Revealed from Primary Damage

High-entropy alloys (HEAs) have received much attention for the development of nuclear materials because of their excellent irradiation tolerance. In the present study, the creation and evolution of irradiation-induced defects in the NiCoCrFe HEA were investigated by molecular dynamics (MD) simulations to understand the mechanisms of their irradiation tolerance compared with bulk Ni. The displacement cascades were simulated for the energies of primary knock-on atoms (PKA) ranging from 10 to 50 keV to understand the irradiation resistance in HEAs. In general, there are more displacements produced in the thermal spike phase, but fewer defects survived at the end of the cascades in the NiCoCrFe alloy than in Ni. Both interstitial and vacancy clusters increase in size or number with increasing PKA energy in both materials, but they do so more slowly in the NiCoCrFe HEA. The delayed damage accumulations in the NiCoCrFe HEA are attributed to the high defect recombination caused by the following two mechanisms: the enhanced thermal spike and the low thermal conductivity of HEAs for heat dissipation result in the higher efficiency of defect recombination, and the substantially small binding energies of interstitial loops in the NiCoCrFe HEA, when compared with those in Ni, are responsible for the delayed interstitial clustering in the NiCoCrFe HEA.

Relativistic effect on atomic displacement damage for two-body inducing discrete reactions

The relativistic effect on two-body discrete reaction inducing atomic recoil energy and the sequent damage energy is studied for 6Li, 56Fe, 184W, and 238U. The relativistic correction is within 1% if incident neutron energy is below 20 MeV. For incident neutron energy up to 200 MeV or even 800 MeV, the relativistic effect should be taken into account for treating two-body kinematics. The relativistic correction is about 0.05Ein/MeV% for neutron elastic scattering for nuclei from 56Fe to 238U and smaller for (n,α) and (n,t) reactions. Analyses on damage energy show that the relativistic corrections are generally within 2% for incident neutron below 200 MeV for nuclei lighter than 56Fe because of the “saturation” of damage energy. However, the current damage theory cannot be applied for Primary Knock-on Atom (PKA) energy higher than 24.9ARZR4/3 keV, which is 10 times lower than the maximum PKA energy for D+T fusion neutron elastic scattering of 6Li.

Simulation of Primary Radiation Damage in Nickel

The process of radiation damage formation in collision cascades initiated by primary knock-on atoms (PKAs) with energy EPKA = 5, 10, 15, and 20 keV in nickel at temperatures T = 100, 300, 600, 900, and 1200 K was studied using the molecular dynamics method. To ensure the statistical validity of the results, a series of 24 cascades was modeled for each pair of (EPKA, T) parameters. The simulation results were analyzed to determine the number NFP of Frenkel pairs, fractions of vacancies σvac and interstitial atoms σSIA in clusters of point defects, average sizes of vacancy 〈Nvac〉 and interstitial 〈NSIA〉 clusters, and average numbers of vacancy 〈Yvac〉 and interstitial 〈YSIA〉 clusters produced in collision cascades as functions of the PKA energy and simulation temperature. It was found that the relation 〈NFP〉 = 2 ± 0.9 × $$E_{\text{PKA}}^{{1.1 \pm 0.1}}$$ holds true at all the examined values of (EPKA, T). The functional dependences of 〈σvac〉 and 〈σSIA〉 on EPKA were identical. The dependence of 〈σvac〉 follows that of 〈Yvac〉, while 〈σSIA〉 is governed by 〈NSIA〉 and the mobility of interstitials. The value of 〈Nvac〉 depends on the irradiation temperature and the thermal stability of vacancy clusters. These clusters are stable at T ≤ 300 K, and 〈Nvac〉 ∝ EPKA; at 600 ≤ T ≤ 900 K, 〈Nvac〉 ≈ 6 and 10, which corresponds to the sizes of regular stacking fault tetrahedra. The value of 〈YSIA〉 is proportional to 〈NFP〉 and, consequently, to EPKA in the entire range of PKA energies.

Simulated research on displacement damage of gallium nitride radiated by different neutron sources

Gallium nitride (GaN), one of the third-generation wide-bandgap semiconductors, offers significant application for advanced electronic devices utilized in neutron irradiation environments, like the defense, space, and aerospace, etc. In these applications, neutron irradiation-induced defects affect the properties of GaN and eventually degrade the performance of devices. In this work, neutron transport process in GaN is simulated by using the Monte Carlo-based code, Geant4 toolkit under four different irradiation conditions, e.g. high flux isotope reactor, high temperature gas-cooled reactor, pressurized water reactor, and atmospheric neutron irradiation. The energy spectra of primary knock-on atoms (PKA) in GaN and the corresponding weighted spectra under those irradiation conditions are analyzed. It is found that there is one unusual “peak” at around 0.58 MeV in the Primary recoil spectrum, regardless of the irradiation conditions. This peak is attributed to the neutron reaction of hydrogen nucleus, i.e., (n, p). Because of the remarkable (n,p) reaction cross-section of low-energy neutron, the intensity of this peak is related to the ratio of low-energy neutron to the total neutron spectrum. By comparing these PKA energy spectra in GaN, we can see that the PKA energy spectrum created under atmospheric neutron irradiation is similar to that in the high flux isotopic reactor. Specifically, the energy distribution of PKA is wide, and the magnitude of energy is lower than those under fission neutron irradiation conditions. In combination with the effects of nuclear reaction products on electrical properties, the high flux isotopic reactor is more suitable for simulating the irradiation of GaN in an atmospheric neutron energy spectrum environment. These above results can provide not only some insights into the evaluation of the degradation of GaN-based electronic devices under neutron irradiation, but also dataset for the study of radiation damage effect of GaN in simulated neutron environment.

On the classification and quantification of crystal defects after energetic bombardment by machine learned molecular dynamics simulations

The analysis of the damage on plasma facing materials (PFM), due to its direct interaction with the plasma environment, is needed to build the next generation of nuclear machines, where tungsten has been proposed as a candidate. In this work, we perform molecular dynamics (MD) simulations using a machine learned inter-atomic potential, based on the Gaussian Approximation Potential framework, to model better neutron bombardment mechanisms in pristine W lattices. The MD potential is trained to reproduce realistic short-range dynamics, the liquid phase, and the material recrystallization, which are important for collision cascades. The formation of point defects is quantified and classified by a descriptor vector (DV) based method, which is independent of the sample temperature and its constituents, requiring only modest computational resources. The locations of vacancies are calculated by the k-d-tree algorithm. The analysis of the damage in the W samples is compared to results obtained by EAM Finnis-Sinclair and Tersoff-ZBL potentials, at a sample temperature of 300 K and a primary knock-on atom (PKA) energy range of 0.5-10 keV, where a good agreement with the reported number of Frenkel pair is observed. Our results provide information about the advantages and limits of the machine learned MD simulations with respect to the standard ones. The formation of dumbbell and crowdion defects as a function of PKA is discussed.

Reduction of defect generation and development of sinks at nanocluster boundary in oxide dispersion-strengthened steel

The radiation resistance mechanisms of nanoclusters (NCs) in oxide dispersion-strengthened (ODS) steels have been investigated. Molecular dynamics simulation has been used to investigate defect generation during the primary damage state of a displacement cascade in ODS steels for NCs of various radii and a range of primary knock-on atom (PKA) energies. Y2O3 NCs considerably enhance the radiation resistance of ODS steels by reducing the peak defect generation during the cascade within the Fe matrix. The NC also affects the morphology of the collision cascades, depending on PKA energy. At lower energies, the NC’s outer circumference act as a cessation point forming a dampened shockwave compared to a pure Fe system. At higher energies, the PKA energy is able to transfer through the NC, thus causing two smaller shockwaves in the Fe matrix. Along with the alteration of the cascade morphology, the NC boundary acts as a strong defect sink to absorb defects and defect clusters, leading to significant recombination of interstitials and vacancies away from the NC. The interfacial energy of the NCs with the Fe matrix increases with increasing diameter of the oxide NCs. The evolution of the NC is tracked through the primary damage state of a cascade, and the effects of ballistic dissolution play a key role in this evolution, most evident in the 2 nm NC.

Relaxation volumes of microscopic and mesoscopic irradiation-induced defects in tungsten

The low-energy structures of irradiation-induced defects in materials have been studied extensively over several decades, as these determine the available modes by which a defect can diffuse or relax, and how the microstructure of an irradiated material evolves as a function of temperature and time. Consequently, many studies concern the relative energies of possible defect structures, and empirical potentials are commonly fitted to or evaluated with respect to these. But recently [S. L. Dudarev et al., Nucl. Fusion 58, 126002 (2018)], we have shown that other parameters of defects not directly related to defect energies, namely, their elastic dipole tensors and relaxation volumes, determine the stresses, strains, and swelling of reactor components under irradiation. These elastic properties of defects have received comparatively little attention. In this study, we compute relaxation volumes of irradiation-induced defects in tungsten using empirical potentials and compare to density functional theory results. Different empirical potentials give different results, but some clear potential-independent trends can be identified. We show that the relaxation volume of a small defect cluster can be predicted to within 10% from its point-defect count. For larger defect clusters, we provide empirical fits as a function of defect cluster size. We demonstrate that the relaxation volume associated with a single primary-damage cascade can be estimated from the primary knock-on atom energy. We conclude that while annihilation of defects invariably reduces the total relaxation volume of the cascade debris, there is still no conclusive verdict about whether coalescence of defects reduces or increases the total relaxation volume.

Molecular dynamics simulations of high-energy radiation damage in W and W–Re alloys

High-energy collision cascades with an energy of up to 300 keV for the primary knock-on atom (PKA) have been initially simulated in W and W–Re alloys containing 5 or 10 at.% Re atoms using the molecular dynamics method with recently fitted W–Re interatomic potentials. The effects of PKA energy and Re concentration on defect production, defect clustering and states of dislocation loops have been quantitatively analysed. The results show that the presence of Re atoms does not significantly affect either the number of surviving defects or their clustered fractions. In addition, the interstitial dislocation loops are dominated by the 1/2<111> loops. Mixed interstitial loops with 1/2<111> and <100> Burgers vectors and interstitial loops that have the same Burgers vectors but are located on different habit planes have also been observed. Further analysis indicates that the pinning effect induced by the Re atom segregation leads to the lower mobility of the interstitial clusters and interstitial 1/2<111> loops in W–Re alloys than in pure W, which is expected to influence the subsequent evolution of radiation-induced defects in W–Re alloy.

Evaluation of tungsten as divertor plasma-facing material: results from ion irradiation experiments and computer simulations

The effect of the primary knock-on atom (PKA) spectrum in radiation damage and the subsequent defect structure formation and their impact in deuterium (D) trapping has been investigated using computer simulations and surrogate ion irradiation experiments. The neutron spectrum for an ‘ITER-like’ divertor shape and parameters has been generated using ATTILA and SPECTER codes to identify the relevant PKA energies. It has been observed that 10 MeV boron (B) produces a PKA spectrum similar to that obtained from a reactor-like neutron spectrum. Experiments have been carried out with ions of gold (Au), B, helium (He) and D with energies ranging from 0.1 MeV–80 MeV for a fluence range of ions m−2– ions m−2, and distinctly different PKA spectra have been produced. While 80 MeV Au ions produced dense and small clusters of interstitial defects (<10 nm), B produced large dislocation loops up to 60 nm in size. At room temperature, the imprint of the cascade is well captured by the vacancies due to their low mobility, and the vacancy defects observed in Au and B irradiation showed significant differences. Molecular dynamics simulations show that at PKA energies exceeding 150 keV, the fragmentation of the cascades takes place, which tends to limit the size of individual defects in the case of 80 MeV Au irradiation. A mechanism based on the competitive capture of mobile interstitials has been proposed to explain the observed large dislocation loops as well as dislocation lines in different irradiation experiments.

Displacement Cascades in Monocrystalline Silicon: Effects of Temperature, Strain, and PKA Energy

With large-scale molecular dynamics, we investigate displacement cascades in monocrystalline silicon with regard to the effects of temperature, strain, and primary knock-on atom energy on defect generation and evolution. With temperature increasing, both the thermal spike region and the peak defect count increase, while the effect of temperature on the surviving defect number is negligible. Nevertheless, higher temperature shows negative effect on clustering of vacancy. The effects of uniaxial strain on defect production and clustering is negligible, while its hydrostatic counterpart is evident. With the increment of hydrostatic strain, both the peak and surviving defect count increase (decrease) under tensile (compressive) hydrostatic loading. Meantime, tensile hydrostatic strain will promote defect clustering. More defects and larger defect clusters are produced at higher energy. Otherwise, interstitials are hard to form clusters under different conditions.

MD simulations of primary damage formation in L12 Ni3Al intermetallics

Computer modelling by molecular dynamics (MD) was employed to study radiation damage created in collision cascades in L12 Ni3Al intermetallic compound. Either Al or Ni primary knock-on atoms (PKA) with PKA energy 5 keV ≤EPKA≤ 20 keV were initiated in the intermetallic crystals at ambient temperatures 100 K ≤T≤ 1200 K. At least 24 different cascades for each (EPKA, T, PKA type) set were simulated in order to mimic an isotropic spatial and random temporal distribution of PKAs. The total yield of nearly 1000 simulated cascades provides the largest yet reported sampling to get statistically reliable quantitative results. The obtained MD simulation data were analysed to get the number of Frenkel pairs, the fraction of point defects in point defect clusters, the fraction of Al and Ni vacancies, self-interstitial atoms (SIA) and anti-sites created in collision cascades as a function of (EPKA, T, PKA type). It was found that under identical simulation conditions, collision cascades in L12 Ni3Al initiated by Al PKAs generate more radiation damage, whereas collision cascades initiated by Ni PKAs produce more chemical disorder. Preferred formation of Ni SIAs in collision cascades in Ni3Al was observed under all ambient temperatures and PKA energies.

A new type angular-dependent interatomic potential and its application to model displacement cascades in uranium

A new type angular-dependent potential has been proposed to describe atomistic interaction of uranium. It consists of three part contributions, namely pair, embedded and angular-dependent parts, to the system energy, in which the former two parts are based on embedded-atom method (EAM), and the last one is inspired by modified embedded-atom method (MEAM). It turns out that the new potential can reproduce well the cohesive energy, lattice constants and elastic constants of α-U and γ-U. Moreover, compared to previous EAM and MEAM potentials for uranium in literature, the new proposed potential can describe the formation energies of the relaxed vacancy and interstitial more precisely. In addition, the calculation efficiency of the potential is higher than that of MEAM. Applying this potential, the displacement cascades in α-U have been studied via molecular dynamics simulation. Calculation suggests a wide displacement threshold energy for α-U ranging from 12 to 57 eV. However, the number of defects is almost independent to the primary knock-on atom (PKA) direction when the PKA energy is same and greater than 1 KeV, suggesting a low anisotropy of α-U in the process of displacement cascades.

A contribution of L10 ordered crystal structure to the high radiation tolerance of γ-TiAl intermetallics

Molecular dynamics simulations were employed to study radiation damage created in collision cascades in L10 TiAl intermetallic compound and fcc Ti-50at.%Al disordered solid solution. Either Al or Ti primary knock-on atoms (PKA) with PKA energy 5 keV⩽EPKA⩽20 keV were initiated in the two materials at temperature T ranging from 100 K to 1200 K. From 36 to 48 different cascades for each (EPKA,T) set were simulated in order to emulate an isotropic spatial and random temporal distribution of PKAs, generate representative sampling and obtain statistically reliable quantitative results. The number of Frenkel pairs, 〈NFPγ-TiAl〉 and 〈NFPTi-50Al〉, formed in L10 TiAl intermetallics and Ti-50at.%Al disordered solid solution, respectively, and averaged over collision cascades with the same (EPKA,T) was used as a quantitative measure of radiation resistance against primary damage formation. It is shown that the relationship 〈NFPγ-TiAl〉⩽〈NFPTi-50Al〉 is fulfilled under all simulation conditions, i.e. L10 ordered crystal structure of TiAl intermetallics is essential for its high radiation tolerance. However, a relatively high resistance to the formation of primary radiation defects is retained even after complete disordering of L10 TiAl that points out to the existence of additional mechanisms contributing to its radiation tolerance.

Molecular dynamics simulations of displacement cascade and threshold energy in ordered alloy Al3U

The displacement threshold energy and collision cascades in ordered alloy Al3U with L12 structure are studied by molecular dynamics simulations. It turns out that as compared with Al recoils, U primary recoils generally have a lower average displacement threshold energy Ed (i.e. 41 eV vs 20 eV) and show less crystallographic anisotropy. The [1 1 0] direction which can produced a …-U-Al-U-Al… replacement collision sequence is found to have a high Ed, but does not create a long antisite defect chain. We have simulated 100 cascades with different energies of primary knock-on atom (PKA) ranging from 1 to 5 keV to make clear which role the energy, direction and PKA’s species has played on defect production. The number of surviving stable defects has a power-law dependence on energy. Displacement cascades tend to form large size clusters involving many point defects with increasing PKA’s energy, and the U PKA generally forms clusters with size larger than the Al recoil.