Primary Knock-on Atom Energy Research Articles

Irradiation-initiated plastic deformation in prestrained single-crystal copper

With large-scale molecular dynamics simulations, we investigate the response of elastically prestrained single-crystal Cu to irradiation as regards the effects of prestrain magnitude and direction, as well as PKA (primary knock-on atom) energy. Under uniaxial tension, irradiation induces such defects as Frenkel pairs, stacking faults, twins, dislocations, and voids. Given the high dislocation concentration, twins and quad-stacking faults form through overlapping of different stacking faults. Voids nucleate via liquid cavitation, and dislocations around void play a lesser role in the void nucleation and growth. Dislocation density increases with increasing prestrain and PKA energy. At a given prestrain, there exists a critical PKA energy for dislocation activation, which decreases with increasing prestrain and depends on crystallographic direction of the applied prestrain.

Threshold displacement energy and damage function in graphite from molecular dynamics

The environment dependent interatomic potential (EDIP) including Ziegler–Biersack–Littermark (ZBL) interactions for close encounters is applied to cascades starting from a host atom and from an interstitial atom. We find the room temperature displacement threshold to be 25 eV, increasing to 30 eV at 900 K. The latter correlates well with the measured threshold for vacancy production. Additionally, divacancy production is found to occur, including interlayer divacancies from around 60 eV. The data suggest a new, continuous damage function applies, where the threshold region depends on the square root of the primary knock-on atom (PKA) energy in excess of the threshold, evolving to a linear dependence on PKA energy.

Molecular dynamics simulation of radiation damage cascades in diamond

Radiation damage cascades in diamond are studied by molecular dynamics simulations employing the Environment Dependent Interaction Potential for carbon. Primary knock-on atom (PKA) energies up to 2.5 keV are considered and a uniformly distributed set of 25 initial PKA directions provide robust statistics. The simulations reveal the atomistic origins of radiation-resistance in diamond and provide a comprehensive computational analysis of cascade evolution and dynamics. As for the case of graphite, the atomic trajectories are found to have a fractal-like character, thermal spikes are absent and only isolated point defects are generated. Quantitative analysis shows that the instantaneous maximum kinetic energy decays exponentially with time, and that the timescale of the ballistic phase has a power-law dependence on PKA energy. Defect recombination is efficient and independent of PKA energy, with only 50% of displacements resulting in defects, superior to graphite where the same quantity is nearly 75%.

Structural changes in elastically stressed crystallites under irradiation

The response of elastically stressed iron and vanadium crystallites to atomic displacement cascades was investigated by molecular dynamics simulation. Interatomic interaction in vanadium was described by a many-body potential calculated in the Finnis–Sinclair approximation of the embedded atom method. Interatomic interaction in iron was described by a many-body potential constructed in the approximation of valence-electron gas. The crystallite temperature in the calculations was varied from 100 to 600K. The elastically stressed state in the crystallites was formed through uniaxial tension by 4–8% such that their volume remained unchanged. The energy of a primary knock-on atom was varied from 0.5 to 50keV. It is shown that the lower the temperature and the higher the strain degree of an initial crystallite, the lower the threshold primary knock-on atom energy for plastic deformation generation in the crystallite. The structural rearrangements induced in the crystallites by an atomic displacement cascade are similar to those induced by mechanical loading. It is found that the rearrangements are realized through twinning.

Displacement cascades and defect annealing in tungsten, Part III: The sensitivity of cascade annealing in tungsten to the values of kinetic parameters

A study has been performed using object kinetic Monte Carlo (OKMC) simulations to investigate various aspects of cascade aging in bulk tungsten (W) and to determine its sensitivity to the kinetic parameters. The primary focus is on how the kinetic parameters affect the intracascade recombination of defects. Results indicate that, due to the disparate mobilities of SIA and vacancy clusters, annealing is dominated by SIA migration even at 2050K. It was found that for 100keV cascades initiated at 300K, recombination is dominated by the annihilation of large defect clusters, while for all the other primary knock-on atom (PKA) energies and temperatures, recombination is primarily due to the migration and rotation of small SIA clusters, while the large SIA clusters escape the simulation cell. The annealing efficiency exhibits an inverse U-shaped curve behavior with increasing temperature, especially at large PKA energies, caused by the asymmetry in SIA and vacancy clustering assisted by the large differences in their mobilities. This behavior is unaffected by the dimensionality of SIA migration, and it persists over a broad range of relative mobilities of SIAs and vacancies.

Displacement cascades and defects annealing in tungsten, Part I: Defect database from molecular dynamics simulations

Molecular dynamics simulations have been used to generate a comprehensive database of surviving defects due to displacement cascades in bulk tungsten. Twenty-one data points of primary knock-on atom (PKA) energies ranging from 100eV (sub-threshold energy) to 100keV (∼780×Ed, where Ed=128eV is the average displacement threshold energy) have been completed at 300K, 1025K and 2050K. Within this range of PKA energies, two regimes of power-law energy-dependence of the defect production are observed. A distinct power-law exponent characterizes the number of Frenkel pairs produced within each regime. The two regimes intersect at a transition energy which occurs at approximately 250×Ed. The transition energy also marks the onset of the formation of large self-interstitial atom (SIA) clusters (size 14 or more). The observed defect clustering behavior is asymmetric, with SIA clustering increasing with temperature, while the vacancy clustering decreases. This asymmetry increases with temperature such that at 2050K (∼0.5Tm) practically no large vacancy clusters are formed, meanwhile large SIA clusters appear in all simulations. The implication of such asymmetry on the long-term defect survival and damage accumulation is discussed. In addition, 〈100〉{110} SIA loops are observed to form directly in the highest energy cascades, while vacancy 〈100〉 loops are observed to form at the lowest temperature and highest PKA energies, although the appearance of both the vacancy and SIA loops with Burgers vector of 〈100〉 type is relatively rare.

Displacement cascades and defect annealing in tungsten, Part II: Object kinetic Monte Carlo simulation of tungsten cascade aging

The results of object kinetic Monte Carlo (OKMC) simulations of the annealing of primary cascade damage in bulk tungsten using a comprehensive database of cascades obtained from molecular dynamics (Setyawan et al.) are described as a function of primary knock-on atom (PKA) energy at temperatures of 300, 1025 and 2050K. An increase in SIA clustering coupled with a decrease in vacancy clustering with increasing temperature, in addition to the disparate mobilities of SIAs versus vacancies, causes an interesting effect of temperature on cascade annealing. The annealing efficiency (the ratio of the number of defects after and before annealing) exhibits an inverse U-shape curve as a function of temperature. The capabilities of the newly developed OKMC code KSOME (kinetic simulations of microstructure evolution) used to carry out these simulations are described.

On the lower energy limit of electronic stopping in simulated collision cascades in Ni, Pd and Pt

We have investigated the effect of the choice of kinetic energy threshold Tc for electronic stopping (Se) in molecular dynamics (MD) simulations of collision cascades. We find that while the choice of Tc has only a negligible effect in low energy cascades, it has a pronounced effect on the fraction of defects found in clusters in high energy cascades. In order to gain insight into the level of energy losses expected in cascades, we have simulated a large number of cascades in Ni, Pd and Pt, with primary knock-on atom (PKA) energies between 30eV and 200keV. Since the energy losses affect the total atomic displacements especially in high energy cascades, we use this measure to determine a reasonable value of Tc. By directly comparing the simulated mixing efficiency to ion beam mixing experiments, we conclude that a threshold of Tc=1eV is too low for simulations of high energy cascades in all materials considered. A value of Tc=10eV is more realistic, although for Pd and Pt, this results in a slight over-prediction of the mixing efficiency.

Prediction of Irradiation Spectrum Effects in Pyrochlores

The formation energy of cation antisites in pyrochlores (A2B2O7) has been correlated with the susceptibility to amorphize under irradiation, and thus, density functional theory calculations of antisite energetics can provide insights into the radiation tolerance of pyrochlores. Here, we show that the formation energy of antisite pairs in titanate pyrochlores, as opposed to other families of pyrochlores (B = Zr, Hf, or Sn), exhibits a strong dependence on the separation distance between the antisites. Classical molecular dynamics simulations of collision cascades in Er2Ti2O7 show that the average separation of antisite pairs is a function of the primary knock-on atom energy that creates the collision cascades. Together, these results suggest that the radiation tolerance of titanate pyrochlores may be sensitive to the irradiation conditions and might be controllable via the appropriate selection of ion beam parameters.

A SIMPLE METHOD TO CALCULATE THE DISPLACEMENT DAMAGE CROSS SECTION OF SILICON CARBIDE

We developed a simple method to prepare the displacement damage cross section of SiC using NJOY and SRIM/TRIM. The number of displacements per atom (DPA) dependent on primary knock-on atom (PKA) energy was computed using SRIM/TRIM and it is directly used by NJOY/HEATR to compute the neutron energy dependent DPA cross sections which are required to estimate the accumulated DPA of nuclear material. SiC DPA cross section is published as a table in DeCART 47 energy group structure. Proposed methodology can be easily extended to other materials.

Simulation of defects in fusion plasma first wall materials

Numerical calculations of radiation damages in beryllium, alpha-iron and tungsten irradiated by fusion neutrons were performed using molecular dynamics (MD) simulations. The displacement cascades efficiency has been calculated using the Norgett-Robinson-Torrens (NRT) formula, the universal pair-potential of Ziegler-Biersack-Littmark (ZBL) and the EAM inter-atomic potential. The pair potential overestimates the defects production by a factor of 2. The ZBL pair potential results and the EAM are comparable at higher primary knock-on atom (PKA) energies (E > 100 keV). We found that the most common types of defects are single vacancies, di-vacancies, interstitials and small number of interstitial clusters. On the bases of calculated results, the behavior of vacancies, empty nano-voids and nano-voids with hydrogen and helium were discussed.

Structural dependence of threshold displacement energies in rutile, anatase and brookite TiO2

Systematic molecular dynamics simulations of low energy cascades have been performed to examine how threshold displacement events are effected by changes in crystal structure. Exploiting the structural proximity of the rutile, anatase and brookite polymorphs of TiO2, a quantitative examination of defect production has been carried out including detailed defect analysis and the determination of values of the threshold displacement energy (Ed). Across all polymorphs comparable values of Ed are reported for oxygen at around 20 eV, with the value for Ti in rutile (73 ± 2 eV) significantly higher than that in brookite (34 ± 1 eV) and anatase (39 ± 1 eV). Quantifying defect formation probability as a function of Primary Knock-on Atom (PKA) energy, simulations in rutile indicate a consistent reduction in defect formation at energies higher than Ed relative to anatase and brookite. Defect cluster analysis reveals a significant proportion of di-Frenkel pairs in anatase at Ti PKA energies around Ed. These clusters, which are stabilised by the localisation of two Frenkel pairs, are associated with a recombination barrier of approximately 0.19 eV. As such, annihilation is likely under typical experimental conditions which suggests an expected increase in the measured Ti value of Ed. Identical O defect populations produced at the threshold by the O PKA in both rutile and anatase explain the comparable values of Ed. At higher O PKA energies, the commencement of defect production on both sublattices in anatase is observed in contrast to the confinement of defects to the O sublattice in rutile. The overall trends reported are consistent with in-situ irradiation experiments and thermal spike simulations, suggesting the contrasting radiation response of the polymorphs of TiO2 is apparent during the initial stages of defect production.

The effect of temperature on primary defect formation in Ni–Fe alloy

Molecular dynamics (MD) simulations have been used to study the influence of temperature on defect generation and evolution in nickel and Ni–Fe alloy (with 15%and 50% Fe content) with a 10-keV primary knock-on atom (PKA) at six different temperatures from 0 to 1500K. The recently available Ni–Fe potential is used with its repulsive part modified by Vörtler. The temporal evolution and temperature dependence of stable defect formation and in-cascade clustering processes are analysed. The number of stable defect and the interstitial clustering fraction are found to increase with temperature whereas the vacancy clustering fraction decreases with temperature. The alloy composition dependence of the stable defect number is also found for the PKA energy considered here. Additionally, a study of the temperature influence on the cluster size distribution is performed, revealing a systematic change in the cluster size distributions, with higher temperature cascades producing larger interstitial clusters.

Molecular dynamics simulation of displacement cascades in U–Mo alloys

Molecular dynamics simulations are employed to investigate the displacement cascades in U–Mo alloys. The cascade process is analyzed in detail. The effects of initial directions of primary knock-on atom (PKA), Mo content and PKA energies on the final damage state are evaluated. The results suggest that the direction of the PKA has no effect on the final primary damage state. A high content of Mo will raise the number of defects and the probability of Mo replacement. Most of the sizes of defects cluster are no larger than three and the probabilities of producing larger interstitial and vacancy clusters are increased with higher PKA energy. The fractions of Mo interstitial in clusters with size larger than three and isolated Mo interstitials is low, while more than half the total Mo interstitials are contained in dumb-bells. Finally, it is found that the number of U–U dumb-bells is the highest and the number of Mo–Mo dumb-bells is the lowest in both alloys. The number of Mo–Mo dumb-bells seems to be independent of Mo content but the numbers of U–U and U–Mo dumb-bells decline with the increase of Mo content in alloys.

A molecular dynamics-based comparison of defect production in collision cascades during the bombardment of iron with different ions

We present a computer simulation study on the influence of incident ions on the energy transferred to primary knock-on atoms (PKAs) and defects produced in the cascade collision of irons. Three types of ions (H, Fe, and Xe, which are frequently used in irradiation experiments) with an energy of 3 MeV were simulated. According to the calculation results of SRIM, the average energy transferred to PKAs by Fe ions was the highest among the three types. Then, cascade collisions induced by PKAs with different energies were simulated by the molecular dynamics method. The maximum number of defects produced during irradiation increased, and the time taken by defect number peak formation was extended with the increased energy of PKAs. The difference in radial distribution function between pre- and post-irradiation irons showed that a higher energy of PKA transferred resulted in a flatter curve. Besides, the law of defects varying in temperature was also investigated. All the researches imply that heavy ions can substitute for neutrons in irradiation experiments which is a practicable way, but the influence of conditions must be taken into account.

Large-scale molecular dynamics simulations of collision cascades caused by primary knock-on atoms in Fe

We report on large-scale molecular dynamics (MD) simulations of energetic primary knock-on atoms (PKA) in crystal BCC Fe. We carry out 1000 randomly directed PKA collision cascades simulations at PKA energies of 0.1, 0.5, 1, 2, 3, 4 and 5 keV using the large-scale atomic molecular massively parallel simulator code. We study the statistical spread of the number of displaced atoms and recombination within a collision cascade in Fe. It is shown that the PKA must be launched in around a few hundred different randomly chosen directions for the variance in the number of displaced atoms to reach a steady value. We also compare our results for the number of displaced atoms with that from the Norgett, Robinson and Torrens model and other MD simulations of collision cascades.

Defect formation in iron by MeV ion beam investigated with a positron beam and electrical resistivity measurement

This study involves the investigation of defect production in iron involving cascade damage processes produced by MeV ion irradiation. Defect configuration after cascade damage is expected to be preserved at low temperatures below Stage I where interstitial atoms begin to migrate. MeV ion beam irradiation of pure iron was carried out at 12K, and then positron beam Doppler-broadening measurements and electrical resistivity measurements were carried out at the same temperature. By these methods, defect production efficiency, which is defined as the ratio of residual defects to defect formation calculated by the Norgett–Robinson–Torrens (NRT) model, was evaluated for iron irradiated with protons and carbon ions. The defect production efficiency values from the electrical resistivity and the computational calculation coincide well to support the validity of the computational approaches to the phenomenon. The values from the positron beam qualitatively represent the difference in the primary knock-on atom (PKA) energy spectrum of H+ and C+, but the values were lower than those obtained from the electrical resistivity measurements and the computational calculation, possibly due to inhomogeneous distribution of vacancies caused by cascades and enhanced mutual annihilation of Frenkel pairs.

The discrepancies in multistep damage evolution of yttria-stabilized zirconia irradiated with different ions

This paper reports a comprehensive investigation of structural damage in yttria-stabilized zirconia irradiated with different ions over a wide fluence range. A similar multistep damage accumulation exists for the irradiations of different ions, but the critical doses for occurrence of second damage step, characterized by a faster increase in damage fraction, and the maximum elastic strain at the first damage step are varied and depend on ion mass. For irradiations of heavier ions, the second damage step occurs at a higher dose with a lower critical elastic strain. Furthermore, larger extended defects were observed in the irradiations of heavy ions at the second damage step. Associated with other experiment results and multistep damage accumulation model, the distinct discrepancies in the damage buildup under irradiations of different ions were interpreted by the effects of electronic excitation, energy of primary knock-on atom and chemistry contributions of deposited ions.

Displacement damage calculations in PHITS for copper irradiated with charged particles and neutrons

The radiation damage model in the Particle and Heavy Ion Transport code System (PHITS) uses screened Coulomb scattering to evaluate the energy of the target primary knock-on atom (PKA) created by the projectile and the “secondary particles,” which include all particles created from the sequential nuclear reactions. We investigated the effect of nuclear reactions on displacement per atom (DPA) values for the following cases using a copper target: (1) 14 and 200MeV proton incidences, (2) 14 and 200MeV/nucleon 48Ca incidences, and (3) 14 and 200MeV and reactor neutrons incidences. For the proton incidences, the ratio of partial DPA created by protons to total decreased with incident proton energy and that by the secondary particles increased with proton energy. For 48Ca beams, DPA created by 48Ca is dominant over the 48Ca range. For the 14 and 200MeV neutron incidences, the ratio of partial DPA created by the secondary particles increases with incident neutron energy. For the reactor neutrons, copper created by neutron–copper nuclear elastic scattering contributes to the total DPA. These results indicate that inclusion of nuclear reactions and Coulomb scattering are necessary for DPA estimation over a wide energy range from eV to GeV.

Computer simulation of radiation damage caused by low energy neutron in zirconium

Based on the Geant4 program-the package for simulating particle transportation in materials, simulations of the irradiation by neutrons with 1 MeV energy in zirconium were conducted The two adjacent elastic collisions between injected neutron and target atoms produce numerous primary knock-on atoms (PKA). It is found that the average distance of adjacent collisions is 29.47 mm, and the kinetic energy of most PKAs ranges from 1 keV to 15 keV. The damaged area induced by the PKAs is in nanometer scale, which is far less than the distance between the two PKAs. According to the fact that, the subsequent cascade collisions caused by the two PKAs can be considered as a set of independent processes, it is reasonable to study the cascade collisions of the PKAs by means of molecular dynamics method. The cascade collision progress of PKAs with different energies was performed, and the number of interstitial atoms and the size of the damaged regions in the material were extracted. Through the combination of Monte Carlo method and molecular dynamics simulation, a complete physical picture of the primary damage caused by the 1 MeV neutrons in the zirconium was obtained.