Primary Knock-on Atom Research Articles

PKA distributions in InAlAs and InGaAs materials irradiated by protons with different energies

In this paper, the Primary Knock-on Atoms (PKAs) density and energy distributions in InAlAs and InGaAs materials have been analyzed by an energy stopping power improved Monte Carlo (MC) method under proton-radiation with energies of 25 keV, 50 keV, 100 keV, and 150 keV. The results show that in the initial incident stage of protons, the electronic energy loss density is 2–3 orders of magnitude higher than the nuclear energy loss density, afterwards, the injected protons accelerate to deposit more energy and finally stop in the target, producing a large number of PKAs. The injected proton density, PKA density and PKA energy density almost follow a Bragg-shape distribution. With the increase of irradiation energy, their peak-positions shift toward deeper direction with peak values decrease gradually, and moreover, the PKA peaks are always shallower than the irradiated protons. In addition, Frenkel Pairs generation rate has been calculated based on Kinchin-Pease (K-P) model modified by Ziegler, which decreases as proton energy increases because of the reduction of scattering cross section. The verification of this method combines both SRIM 2013 and Northcliffe experimental data and the results have shown compatible trends.

Radiation effect on BCC Fe nanoparticle with varying radiation energy by molecular dynamics simulation

Molecular dynamics simulations were conducted to explore primary radiation damages on body-centered cubic (BCC) Fe nanoparticle. A series of 6 cascades for each primary knock-on atom (PKA) energy (5 keV, 10 keV, 20 keV, 30 keV and 40 keV) was simulated to assure statistical precision. It has been observed that defects created due to the interactions have stayed as a single to several size clusters. Among them, most of the clusters are either single interstitials (SIAs) or vacancies (Vs). In each of the energy cases, it produces one block of a big cluster. The block cluster of SIAs stays at the near surface of the nanoparticle, however, Vs stay inside the nanoparticle. The study has shown that the total number of vacancy defects is larger than the total number of interstitial defects because more PKA energy gives more mobility that some SIAs can get enough energy to leave the Fe nanoparticle.

Theoretical and computational investigation on the radiation-induced point defects in cementite: Picosecond timescale

In this paper, we propose a novel time-dependent model for the displacement cascade in cementite. It consists of two terms, one of which depends on spherical-like inflation of the thermal spike stage and the other one on the recombination stage. The first term is obtained from spherical inflation of the cascade and the second term is resulted from solving the equation of heat conduction in spherical geometry in a uniform medium. The proposed model had a satisfactory agreement with those of resulted by molecular dynamics simulations based on employing Fe-C MEAM potential developed by Liyanage et al. (2014) for cementite. In the second goal of the current work, we determine the residual number of all types of radiation-induced point defects, including iron/carbon antisites, vacancies, and interstitials produced by primary knock-on atoms with energies of 0.5–9 keV in cementite by using molecular dynamics based on employing the potential developed by Liyanage et al. (2014). Then, the results are compared with those reported in the literature, the results of which were based on using the potential developed by Henriksson and Nordlund (2012). Surprisingly, the comparison showed fundamental differences. Thus, the molecular statics simulations were carried out for calculating the formation energies of all types of defects by using these two interatomic potentials and also the potential developed by Ruda et al. (2009). The results were used to analyze these discrepancies and to compare with those reported in the literature by using density functional theory calculations. It was concluded that the potential developed by Liyanage et al. (2014) has the best performance among two other ones for the study of radiation damage. Finally, the nudged elastic band calculations showed that the vacancies most probably migrate to the interstitial sites due to their much lower migration energies.

Free-surface effect on displacement cascades in BCC W: molecular dynamics study

We investigated the free-surface effect on displacement cascades in bcc tungsten using molecular dynamics simulations. Primary knock-on atom (PKA) is projected at different initial depths with two different projectile directions, inward and outward, to the surface. Compared to the bulk system, a simulation system with free surface contains increased number of remaining point defects and clustered defects at equilibrium. This pronounced defect production near the free surface is caused by the suppression of defect recombination events. The interstitials energetically favor the formation of adatoms at the free surface, and the nonsymmetric feature of interstitial mobility is responsible for active vacancy clustering at the sub-surface. The free surface effect extends to 8 and 4 nm in depth when the PKA projectile direction is outward and inward, respectively, with PKA energy of 30 keV at 400 K. Beyond this characteristic depth, the defect population and clustered fraction become similar to those in bulk system. Clustered vacancy develops into extended defects such as and vacancy loops. For the first time, immobile dislocation is observed in PKA simulation, which is consistent with the experimental reports of both stable and dislocations of Mason et al (2014 J. Phys.: Condens. Matter. 26 375701).

Atomistic strain and structural analysis of 120 MeV Ni ions irradiated CdSe nanocrystals through molecular dynamics simulation method

Swift heavy ion (SHI) irradiation modifies the physical and chemical properties of semiconductor sample like CdSe nanocrystals by inducing vacancies and structural change in the lattice system. Here, the atomistic strain analysis has been performed using molecular dynamics (MD) simulation on the SHI irradiated CdSe nanocrystals by approximating interatomic interaction as (ZBL) potential. MD simulation based on LAMMPS package has been employed for better understanding the time response of the sample with swift heavy ion irradiation. The primary knock-on atom (PKA) method has been used for the simulation that starts the cascade of energy transfer, which triggers the displacement of atoms. Initial parameters of PKA have been obtained from the SRIM simulation of the irradiation effect of 120 MeV Ni ions. Finally, the time evolution of the system has been studied.

Displacement cascade evolution in tungsten with pre-existing helium and hydrogen clusters: a molecular dynamics study

Abstract The effects of radiation damage on bcc tungsten with preexisting helium and hydrogen clusters have been investigated in a high-energy environment via a comprehensive molecular dynamics simulation study. This research determines the interactions of displacement cascades with helium and hydrogen clusters integrated into a tungsten crystal generating point defect statistics. Helium or hydrogen clusters of atoms~0.1% of the total number of atoms have been randomly distributed within the simulation model and primary knock-on-atom (PKA) energies of 2.5, 5, 7.5 and 10 keV have been used to generate displacement cascades. The simulations quantify the extent of radiation damage during a simulated irradiation cycle using the Wigner-Seitz point defect identification technique. The generated point defects in crystals with and without pre-existing helium/hydrogen defects exhibit a power relationship with applied PKA energy. The point defects are classified by their atom type, defect type, and distribution within the irradiated model. The presence of pre-existing helium and hydrogen clusters significantly increases the defects (5 - 15 times versus pure tungsten models). The vacancy composition is primarily tungsten (e. g., ~70% at 2.5 keV) in models with pre-existing helium, but the interstitials are primarily He (e. g., ~89% at 10 keV). On the other hand, models with pre-existing hydrogen have a vacancy composition that is primarily tungsten (more than 90% irrespective of PKA energy), and the interstitial composition is more balanced between tungsten (average 46%) and hydrogen (average 54%) interstitials across the PKA range. The distribution of the atoms reveals that the tungsten point defects prefer to reside close to the position of cascade initiation, but helium or hydrogen defects reside close to the positions where clusters are built.

Effect of confinement of SIA cluster diffusion by impurities on radiation defect accumulation due to 14 MeV neutrons in tungsten

Impurities acting as traps reduce the self-interstitial atom (SIA) cluster mobility, thereby increasing recombination and, in turn, enhancing radiation-resistance of polycrystalline materials. However, at elevated temperatures, depending on SIA-trap (impurity) binding energy, SIA clusters may trap and detrap (detach) numerous times. In tungsten, SIA clusters of all sizes glide one-dimensionally (1D) along their Burgers vector direction. This can result in detrapped SIA clusters to retrace their original 1D path, confining their 1D-glide between traps. However, SIA clusters can change the direction of their 1D-glide by overcoming a rotation barrier and impurities or solutes are known to reduce this barrier. A lower rotation barrier can result in detrapped SIA clusters to diffuse in a random 1D direction, effectively leading to 3D (net-3D) diffusion. Here we investigate the effect of two cases of SIA diffusion, namely the confined-1D diffusion and the net-3D diffusion, on the damage accumulation in polycrystalline tungsten under 14 MeV neutron irradiation using the object kinetic Monte Carlo method. Simulations were performed using cascade debris obtained from molecular dynamics simulations with primary knock-on atom (PKA) energies corresponding to 14 MeV neutrons. In the simulations with net-3D diffusion, SIA clusters of all sizes diffuse in a random 1D direction after the clusters detrap. While for the confined 1D diffusion case, clusters larger than size 5 retain their original direction of 1D glide. In both types of simulations, trapped vacancies are assumed to be permanently immobilized. Unexpectedly, the damage accumulation was lower with confined 1D diffusion than that with net-3D. We present a systematic comparison of the influence of the two cases of SIA diffusion on the radiation damage accumulation as a function of dose rate, detrapping barrier, and impurity concentration at 1025 K.

Displacement cascade evolution in tungsten with pre-existing helium and hydrogen clusters: a molecular dynamics study

Abstract The effects of radiation damage on bcc tungsten with preexisting helium and hydrogen clusters have been investigated in a high-energy environment via a comprehensive molecular dynamics simulation study. This research determines the interactions of displacement cascades with helium and hydrogen clusters integrated into a tungsten crystal generating point defect statistics. Helium or hydrogen clusters of atoms~0.1% of the total number of atoms have been randomly distributed within the simulation model and primary knock-on-atom (PKA) energies of 2.5, 5, 7.5 and 10 keV have been used to generate displacement cascades. The simulations quantify the extent of radiation damage during a simulated irradiation cycle using the Wigner-Seitz point defect identification technique. The generated point defects in crystals with and without pre-existing helium/hydrogen defects exhibit a power relationship with applied PKA energy. The point defects are classified by their atom type, defect type, and distribution within the irradiated model. The presence of pre-existing helium and hydrogen clusters significantly increases the defects (5 - 15 times versus pure tungsten models). The vacancy composition is primarily tungsten (e. g., ~70% at 2.5 keV) in models with pre-existing helium, but the interstitials are primarily He (e. g., ~89% at 10 keV). On the other hand, models with pre-existing hydrogen have a vacancy composition that is primarily tungsten (more than 90% irrespective of PKA energy), and the interstitial composition is more balanced between tungsten (average 46%) and hydrogen (average 54%) interstitials across the PKA range. The distribution of the atoms reveals that the tungsten point defects prefer to reside close to the position of cascade initiation, but helium or hydrogen defects reside close to the positions where clusters are built.

Radiation Effect on BCC Fe Nanoparticle with Varying Radiation Energy by Molecular Dynamics Simulation

Molecular dynamics simulations were conducted to explore primary radiation damages on body-centered cubic (BCC) Fe nanoparticle. A series of 6 cascades for each primary knock-on atom (PKA) energy (5 keV, 10 keV, 20 keV, 30 keV and 40 keV) was simulated to assure statistical precision. It has been observed that defects created due to the interactions have stayed as a single to several size clusters. Among them, most of the clusters are either single interstitials (SIAs) or vacancies (Vs). In each of the energy cases, it produces one block of a big cluster. The block cluster of SIAs stays at the near surface of the nanoparticle, however, Vs stay inside the nanoparticle. The study has shown that the total number of vacancy defects is larger than the total number of interstitial defects because more PKA energy gives more mobility that some SIAs can get enough energy to leave the Fe nanoparticle.

Statistics of primary radiation defects in pure nickel

Molecular dynamics simulations were applied to study radiation damage formation in collision cascades initiated by primary knock-on atoms (PKA) with energy EPKA = 5, 10, 15 and 20 keV in pure nickel at temperature T = 100, 300, 600, 900 and 1200 K. A series of 24 collision cascades per EPKA,T set was simulated to assure statistical reliability of the results. The number of Frenkel pairs, NFP, the fraction of vacancies, σvac, and self-interstitials (SIA), σSIA, in point defect clusters, the average size of vacancy and SIA clusters, Nvac and NSIA, respectively, and the average vacancy and SIA cluster per cascade yield, Yvac and YSIA, respectively, were evaluated as functions of EPKA,T. It is found that NFP∝EPKA under all simulated conditions. Both σvac and σSIA demonstrate similar dependence on EPKA. σvac matches Yvac, while σSIA correlates with NSIA and is affected by SIA diffusivity. Nvac is determined by the irradiation temperature and thermal stability of vacancy clusters. They are stable at T⩽ 300 K and Nvac∝EPKA, whereas at 600 K ⩽T⩽ 900 K, Nvac≈6 and 10, which corresponds to the sizes of regular stacking fault tetrahedra. SIA cluster per cascade yield YSIA∝NFP and therefore ∝EPKA under all simulated irradiation conditions.

Models and regressions to describe primary damage in silicon carbide

Silicon carbide (SiC) and SiC/SiC composites are important candidate materials for use in the nuclear industry. Coarse grain models are the only tools capable of modelling defect accumulation under different irradiation conditions at a realistic time and length scale. The core of any such model is the so-called “source term”, which is described by the primary damage. In the present work, classical molecular dynamics (MD), binary collision approximation (BCA) and NRT model are applied to describe collision cascades in 3C-SiC with primary knock-on atom (PKA) energy in the range 1–100 keV. As such, BCA and NRT are benchmarked against MD. Particular care was taken to account for electronic stopping and the use of a threshold displacement energy consistent with density functional theory and experiment. Models and regressions are developed to characterize the primary damage in terms of number of stable Frenkel pairs and their cluster size distribution, anti-sites, and defect type. As such, an accurate cascade database is developed with simple descriptors. One of the main results shows that the defect cluster size distribution follows the geometric distribution rather than a power law.

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.

Ab initio molecular dynamics simulation of threshold displacement energies and defect formation energies in Y4Zr3O12

Ab initio molecular dynamics simulations using Vienna ab initio simulation package were employed to calculate the threshold displacement energies and defect formation energies of Y4Zr3O12 in the δ-phase, which is the most commonly found phase in newly developed Zr- and Al-containing oxide dispersion strengthened (ODS) steels. The threshold displacement energy (Ed) values are determined to be 28 eV for the Zr3a primary knock-on atoms along the [111] direction, 40 eV for the Zr18f atoms along the [111] direction, and 50 eV for the Y recoils along the [110] direction. The minimum Ed values for O and O′ atoms are 13 eV and 16 eV, respectively. The displacement energies of anions are much smaller compared to those of cations, thus suggesting that an anion disorder is more probable than a cation disorder. All directions except the direction in which the inherent structural vacancies are aligned, the cations tend to occupy another cation site. The threshold displacement energies are larger than that of Y2Ti2O7, the conventional precipitates in Ti-containing ODS steels. Due to the partial occupancy of Y and Zr in the 18f position, the antisite formation energy is negligibly small and it may help the structure to withstand more disorder upon irradiation. These results convey that Zr/Al ODS alloys, which have better corrosion resistance properties compared to the conventional Ti-ODS alloys, may also possess superior radiation resistance.

Irradiation studies on nano-scale single crystal copper by molecular dynamics simulation

We report molecular dynamics (MD) simulation studies on the structure and tensile properties (temperature = 300 K and strain rate = 1010 s−1) of irradiated copper single crystals (101.8 Å× 50.54Å × 50.54Å) oriented along the [100] and [110] crystallographic orientations. Primary knock-on atom (PKA) method is used for radiation (0.5 keV to 5 keV). Structural studies indicate liquid like regions near the PKA region and are more in [110] orientation. The self-diffusivity (D) of copper in the PKA regions is found to increase from 4.05 × 10−5 m2/s at 1 keV irradiation energy to 27.36 × 10−5 at 5 keV irradiation energy in [110] orientation. However, no such relationship is observed in the [100] orientation. Vacancies, self-interstitials, and dislocations are more prominent in [100] orientation (dislocation density = 1 × 1016 m−2). Young’s modulus and yield strength decrease due to the formation of defects as anticipated.

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.

On the Connection of Cascade-Probability Function on the Formation of Primary-Knocked on Atoms for Ions Taking into Account Energy Losses with a Boltzman Equation

The integral-differential equation of the cascade process for ions was solved using the Laplace transform and the method of successive approximations, taking into account the energy loss during the formation of primary-knocked-on atoms (PKA) in a one-dimensional model of an elementary atom. It is shown that the solution includes a cascade-probability function (CPF) for these particles. The main properties of CPF are considered and its graphical dependencies on the depth of registration are presented. It is shown that with the specific ionization loss coefficient k = 0, the FQM turns into the simplest cascade-probability function. When λ0→ 0, λ0→∞ and n→∞, the KV-function is equal to 0. The sum of the probabilities for all possible collisions from 0 to ∞ is 1. As the detection depth h increases, for all values of n, the CRF increases, reaches a maximum and then decreases . With increasing n, the curves shift to the right.