Displacement Cascade Simulations Research Articles

Modification of a ReaxFF potential at short range for energetic materials

The ReaxFF can describe the properties of energetic materials (EMs) at equilibrium state, but does not work properly in simulating high-energy particle irradiation process because of its weak short-range interaction. In this paper, a modification was made for such a potential by connecting Ziegler-Biersack-Littmark (ZBL) potential to ReaxFF-lg through comparing to Density Functional Theory (DFT) results to accurately describe short-range interactions. After modification, the newly fitted ReaxFF-lg/ZBL potential predicts better the equation of state for EMs In displacement cascade simulations, comparing to results from ab initio molecular dynamics (AIMD), ReaxFF-lg/ZBL presented the similar transferred energy from a primary knock-on atom to surrounding atoms, better than the original ReaxFF-lg potential. Further large-scale displacement cascade simulations indicated ReaxFF-lg/ZBL could be applied for cascade simulations with PKA energy from less than 1 keV to high energy (e.g. 35 keV) cases, which is suitable for effectively simulating high-energy displacement cascades in EMs using molecular dynamics method.

Molecular Dynamics Simulations of Displacement Cascades in BCC-Fe: Effects of Dislocation, Dislocation Loop and Grain Boundary

The interactions between displacement cascades and three types of structures, dislocations, dislocation loops and grain boundaries, in BCC-Fe are investigated through molecular dynamics simulations. Wigner–Seitz analysis is used to calculate the number of point defects induced in order to illustrate the effects of three special structures on the displacement cascade. The displacement cascades in systems interacting with all three types of structure tend to generate more total defects compared to bulk Fe. The surviving number of point defects in the grain boundary case is the largest of the three types of structures. The changes in the atomic structures of dislocations, dislocation loops and grain boundaries after displacement cascades are analyzed to understand how irradiation damage affects them. These results could reveal irradiation damage at the microscale. Varied defect production numbers and efficiencies are investigated, which could be used as the input parameters for higher scale simulation.

Molecular dynamics study of primary radiation damage in TiVTa concentrated solid-solution alloy

The primary radiation damage in pure V and TiVTa concentrated solid-solution alloy (CSA) was studied using a molecular dynamics method. We have performed displacement cascade simulations to explore the generation and evolution behavior of irradiation defects. The results demonstrate that the defect accumulation and agglomeration in TiVTa CSA are significantly suppressed compared to pure V. The peak value of Frenkel pairs during cascade collisions in TiVTa CSA is much higher than that in pure V due to the lower formation energy of point defects. Meanwhile, the longer lifetime of the thermal spike relaxation and slow energy dissipation capability of TiVTa CSA can facilitate the recombination of point defects. The defect agglomeration rate in TiVTa CSA is much lower due to the lower binding energy of interstitial clusters and reduced interstitial diffusivity. Furthermore, the occurrence probability of dislocation loops in TiVTa CSA is lower than that in pure V. The reduction in primary radiation damage may enhance the radiation resistance of TiVTa CSA, and the improved radiation tolerance is primarily attributed to the relaxation stage and long-term defect evolution rather than the ballistic stage. These results can provide fundamental insights into irradiation-induced defects evolution in refractory CSAs.

Insights into radiation resistance of titanium alloys from displacement cascade simulations

Radiation damage in beam window materials limits the use of high power proton beams in high energy physics research. The alloy Ti-6Al-4V is presently used as a beam window material but a prospective alternative, Ti-15V-3Cr-3Sn-3Al has been proposed. Since both these alloys contain dual phases at room temperature, we compare the radiation damage in the α and β-phases of these two materials via primary knock-on atom (PKA) cascade simulations in the 10–40 keV energy range. At PKA energies 30 and 40 keV, the number of Frenkel pairs in the ballistic stage is higher in the β-phase of Ti-6Al-4V than that in the β-phase of Ti-15V-3Cr-3Sn-3Al almost by a factor of 2. The α-phase, of both these alloys, by far outperforms the β-phases of the two alloys, both in terms of damage during the ballistic stage and in terms of the surviving defects. The average displacement threshold energy (Ed) in the α-phase of both alloys was found to be 66 eV while that in the β-phase of Ti-15-3-3 was 55 eV and in the β-phase of Ti-6-4 was 46. While the number of surviving defects is almost equal in both alloys, the vacancy and interstitial clustering mechanisms differ notably, which can impact the degree of radiation hardening and loss of ductility. Our simulations show larger vacancy and interstitial clusters form in Ti-6Al-4V as compared to that in Ti-15-3-3-3 alloy. These results indicate that Ti-15-3-3-3 alloys may be a promising candidate for next generation beam window material with a higher radiation tolerance than the existing Ti-6-4 alloy.

Displacement cascades database from molecular dynamics simulations in tungsten

In this work, we have carried out a series of displacement cascade simulations in tungsten (W), including seven different primary-knock-on atom (PKA) directions, and PKA energy covers 1 to 300 keV at 363 K; 10, 50, 100, and 200 keV cascades are considered at 600 K, and 10 and 50 keV cascades are simulated at 300 K. Then, a systematic database of W cascade simulations has been established, containing more than 2000 cascades. The number of Frenkel pairs, the type of defect, and its spatial distribution were all determined. The effects of PKA direction, PKA energy and temperature have been discussed in terms of defect generation, defect clustering, and dislocation loops. It is found that, the PKA direction may have an effect on the configuration of defects, such as the formation probability of 〈100〉 interstitial loops, C15 clusters and the sub-cascades, and also has an effect on the number of Frankel pairs when PKA energy larger than 50 keV. Furthermore, from 363 K to 600 K, the number of Frankel pairs is reduced by ∼10%, and high temperature can promote the clustering of interstitial. We further found that temperature may affect the distribution of dislocation loops, and the number of 〈100〉 interstitial dislocation loops is more at 363 K than at 600 K. These results can provide a database of key input parameters for the subsequent larger-scale simulations, and give an important reference for the prediction of defect behaviour, mechanical and thermal properties of W-based materials under fusion neutron irradiation.

Study on displacement cascade and tensile simulation by molecular dynamics: Formation and properties of point defects

The molecular dynamics method is used to investigate the formation and properties of irradiation-induced damage (point defects). Displacement cascade simulations are performed to study the effects of primary knock-on atom (PKA) energy, temperature, vacancy concentration and tensile pre-strain on irradiation-induced damage in [Formula: see text]-Fe. An increase in PKA energy, vacancy concentration and tensile pre-strain can lead to an increase in defect numbers. In contrast, an increase in temperature decreases the defect numbers. After cascade collisions, tensile tests are performed to investigate the effect of point defects on mechanical properties. The yield stress and corresponding strain of irradiated Fe decrease with an increase in the number density of Frenkel pairs. Results show that irradiation accelerates damage of the internal structure, decreases the number of slip bands and increases the instability of the structure during plastic deformation.

Atomistic simulation of energetic displacement cascades near an Ni–graphene interface

Ni–graphene nanocomposites have greatly promising applications in supercritical water-cooled reactors due to their outstanding performances. However, many fundamental mechanisms of irradiation behaviors in the composites are still unclear. Here we investigate the displacement cascades near an Ni–graphene interface using atomistic simulations. Different cascade energies and ambient temperatures were introduced to bring out the effect of irradiation. The increasing cascade energy in the interval 0.5–10 keV could significantly promote the formation of defects, while there is slight effect on the number of surviving defects in Ni matrix when adjusting the ambient temperature from 100 K to 900 K. The damaged graphene could be self-healing by the synergistic effects of irradiation annealing and ambient temperature annealing. The interface exhibits high sink efficiency for irradiation defects in all cases. This study provides an important insight into the understanding of the microscopic evolution of defects in cascades for the composites.

Quantifying the impact of an electronic drag force on defect production from high-energy displacement cascades in α-zirconium

Molecular dynamics displacement cascade simulations with PKA energies up to 40 keV at 600 K have been performed to investigate the impact of electronic energy losses in α-zirconium. The following data sets are compared: 1) displacement cascades performed with nuclear stopping only and 2) displacement cascades with simultaneous nuclear and electronic stopping. Electronic energy losses are modeled by a drag force with strength proportional to the energy-dependent electronic stopping power using the intrinsic “fix electron/stopping” command in LAMMPS. Consistent with typical characteristics of cascade defect generation, the production efficiency of Frenkel pairs falls below 20% of the NRT-predicted value for high PKA energies, defect clustering increases with PKA energy, and two distinct power-law regimes of the form NF=A(Ep)mcorrelate the surviving number of Frenkel pairs; the separate power-law fits describe defect production prior to and following sub-cascade formation. When implemented, electronic energy losses account for a 10–20% reduction in surviving Frenkel pairs for high-energy PKAs. The energy loss method implemented in LAMMPS results in nuclear damage energies comparable with the values predicted by SRIM using the full-cascade option, and represents a user-friendly method to incorporate ionization losses in molecular dynamics simulations.

Interatomic potentials of W–V and W–Mo binary systems for point defects studies

Interatomic potentials for tungsten–vanadium (W–V) and tungsten–molybdenum (W–Mo) binary systems have been developed based on Finnis–Sinclair formalism. The potentials are based on an accurate previously developed potential of pure W. Potential parameters of V–V, Mo–Mo, W–V and W–Mo were determined by fitting to a large database of experimental data as well as first principle calculations. These potentials were able to describe various fundamental physical properties of pure V and Mo, such as a lattice constant, cohesive energy, elastic constants, bulk modulus, vacancy and self-interstitial atom formation energies, stacking fault energies and a relative stability of <100> and ½<111> interstitial dislocation loops. Other fundamental properties of the potentials described included alloy behaviours, such as the formation energies of substitutional solute atoms, binding energies between solute atoms and point defects, formation energies and lattice constants of artificial ordered alloys. These results are in reasonable agreement with experimental or first principle results. Based on these results, the developed potentials are suitable for studying point defect properties and can be further used to explore displacement cascade simulations.

Kinetics of radiation defect formation in iron under high displacement rate irradiation

In this study, the kinetics of vacancy and interstitial formation has been simulated in iron at a temperature of 600 K under irradiation at high radiation defect production rate 6.5·10-3,3.25·10-3,1.63·10-3dpa/s and displacement energies of 10 keV, 15 keV, 20 keV. The reaction-diffusion equations and molecular dynamics simulation of displacement cascades have been combined to calculate the kinetics of radiation defect formation. We have introduced the criterion to estimate homogeneity of distribution of radiation defects in the system. The kinetics of radiation defect formation has been calculated up to doses of ~5·10−5 dpa, whereas stationary values of their concentration are achieved at ~10−5 dpa. It has been shown, that high defect production rate of irradiation causes inhomogeneous distribution of the radiation defects with a finite life-time. Also, we consider the effect of high defect production rate and displacement energy on kinetics of radiation defect formation and the self-diffusion mechanism in iron at the considered temperature.

Atomistic simulations for the effects of stacking fault energy on defect formations by displacement cascades in FCC metals under Poisson’s deformation

We performed molecular dynamics simulations of displacement cascades in FCC metals under Poisson’s deformation using interatomic potentials differing in stacking fault energy (SFE), in order to investigate the effect of tensile strain on the SFE dependence of defect formation processes. There was no clear SFE dependence of the number of residual defects and the size distribution of defect clusters under both no strain and the applied strain, while the strain enhanced the defect formation to a certain extent. We also observed that the strain affected the formations of self-interstitial atom (SIA) clusters depending on their size and the Burgers vector. These results were consistent with the analysis based on the defect formation energies. Meanwhile, the number of SIA perfect loops was higher at lower SFE under both no strain and the applied strain, leading to an increase in the ratio of glissile SIA clusters with a decrease in SFE. Further, the absolute number of SIA perfect loops was increased by the applied strain, while the SFE dependence of the number of SIA perfect loops was not affected. These findings were associated with the difference in formation energy between an SIA perfect loop and an SIA Frank loop. The insights extracted from this study significantly contribute to the modeling of microstructural evolution in nuclear materials under irradiation, especially for low SFE metals such as austenitic stainless steels.

Simulation of atomic displacement cascades in the binary alloy Zr-1%Nb near symmetrical tilt grain boundaries by molecular dynamics method

ABSTRACTThe atomic displacement cascades simulation near symmetrical tilt grain boundaries (GBs) in binary alloy Zr-1%Nb was considered in this paper. Three symmetrical tilt GBs: , with the axis of rotation and with the axis of rotation were considered. Further defect structure analysis in modeling crystallite was conducted. For atomic displacement cascades simulation, we used molecular dynamics method and two different interatomic potentials. A tendency of the point defects produced in the cascade to accumulate near the GB plane, which was an obstacle to the spread of the cascade, was discovered. The results of the point defects’ clustering produced in the cascade were obtained. Clusters of vacancies and self-interstitial atoms were represented mainly by single point defects for both potentials. Vacancies formed clusters of a large size (more than 20 vacancies per cluster) for both potentials. The maximal size of the interstitial cluster was less than 20 point defects and was formed only in one potential. Interstitial atom clusters were mainly small-sized. Significant Nb atoms’ proportion in interstitial configuration (single defects, interstitial dimmers and interstitial clusters) was established. It means than Nb atoms actively went out from crystallite matrix in interstitial configurations.

A comparative study of primary damage state in Ni and NiCr/NiFe with a model grain boundary structure

The interaction of displacement cascades with atomic interfaces, specifically grain boundaries (GBs) is of great importance in design and development of radical advanced Ni-based super alloys with self-healing capabilities for future fission reactors. In this work, pure Ni and NiCr (with 5, 10, 15 and 20 at.% Cr content) and NiFe (with 5, 10 and 15 at.% Fe content) alloys with symmetric tilt Σ5[1 0 0](0 1¯ 3)θ = 37° GBs are used as model structures to study the influence of Cr and Fe on the primary and long-term radiation response of Ni-based alloys with microstructures. Molecular dynamics is used in simulating the primary damage event and the continuous ion bombardments in NiCr/NiFe structures to qualitatively represent the severe irradiation condition expected in next-generation fission reactors. In general, we observe that the GBs in “pristine” and “damaged” (∼after being continuously bombarded) forms preferentially absorb radiation-produced interstitials both Ni and Cr/Fe, over vacancies which results in accumulation and clustering of immobile vacancies in the grain interiors. The presence of Cr and Fe does not significantly affect the sink properties of our model GB and therefore, does not change the clustering behavior of excess vacancies in the bulk grains on picosecond (ps) timescale. The only evident phenomenon is a notable variation in the energetics and probably kinetics of point defects that slightly changes the evolution pattern of displacement cascades in the damage regions on ps timescale. The GB roughening incident is also observed in both Ni and NiFe/NiCr alloys during irradiation. In alloys with GBs, we also analyzed changes in the short range order parameter of irradiated structures. Our results indicate that in the primary event of radiation damage, a single bombardment is not enough to induce any trend in ordering or disordering of Cr and Fe solutes; in a prolonged irradiation, on the other hand, MD results reveal a very weak tendency of solutes to diffuse toward each other, although we did not observe any obvious Cr or Fe clustering in any of the performed displacement cascade simulations. Eventually, on ps timescale, we conclude that the Cr and Fe solutes contribute in enhancement of radiation tolerance of binary alloys in similar ways as Ni atoms do; but further details about the diffusion mechanisms of solutes on a longer timescale is essentially required to have more accurate predictions from a radiation damage perspective.

Role of pre-existing point defects on primary damage production and amorphization in silicon carbide (β-SiC)

Abstract Molecular dynamics simulations of displacement cascades were conducted to study the effect of point defects on the primary damage production in β-SiC. Although all types of point defects and Frenkel pairs were considered, Si interstitials and Si Frenkel pairs were unstable and hence excluded from the cascade studies. Si (C) vacancies had the maximum influence, enhancing C (Si) antisites and suppressing C interstitial production, when compared to the sample without any defects. The intracascade recombination mechanisms, in the presence of pre-existing defects, is explored by examining the evolution of point defects during the cascade. To ascertain the role of the unstable Si defects on amorphization, simulations involving explicit displacements of Si atoms were conducted. The dose to amorphization with only Si displacements was much lower than what was observed with only C displacements. The release of elastic energy accumulated due to Si defects, is found to be the amorphizing mechanism.

Extreme ion irradiation of oxide nanoceramics: Influence of the irradiation spectrum

Oxide nanoceramics combine the enhanced radiation tolerance of nanocrystalline materials with the chemical inertness of oxides, and are promising materials for highly corrosive and intense radiation environments. In this work, nanocrystalline Al2O3 thin films are irradiated at 600 °C with either 12 MeV Au5++18 MeV W8+ or 4 MeV Ni2+ ions. The radiation damage exposure exceeds 450 displacements per atom. A comprehensive analysis of the irradiated samples is accomplished by X-Ray Diffractometry (XRD), Transmission Electron Microscopy (TEM) and Scanning-TEM (STEM). Results are compared in an effort to establish correlations between the irradiation spectrum and the response of this class of materials to radiation environments. The results show that grain growth is the main microstructural change induced by ion irradiation in the material, regardless of the ion utilized in this work. The phase evolution may be depth-dependent, and depends strongly on the ion utilized and on the irradiation spectrum. 12 MeV Au5++18 MeV W8+ irradiations favor the formation of γ-Al2O3 and α-Al2O3, while 4 MeV Ni2+ irradiations yield mainly δ-Al2O3, accompanied by small α-Al2O3 centers. Molecular dynamics simulations of displacement cascades are used to support discussions on the mass effect brought about by the different ions.

Primary radiation damage of Zr-0.5%Nb binary alloy: atomistic simulation by molecular dynamics method

Ab initio calculations predict high positive binding energy (∼1 eV) between niobium atoms and self-interstitial configurations in hcp zirconium. It allows the expectation of increased niobium fraction in self-interstitials formed under neutron irradiation in atomic displacement cascades. In this paper, we report the results of molecular dynamics simulation of atomic displacement cascades in Zr-0.5%Nb binary alloy and pure Zr at the temperature of 300 K. Two sets of n-body interatomic potentials have been used for the Zr-Nb system. We consider a cascade energy range of 2–20 keV. Calculations show close estimations of the average number of produced Frenkel pairs in the alloy and pure Zr. A high fraction of Nb is observed in the self-interstitial configurations. Nb is mainly detected in single self-interstitial configurations, where its fraction reaches tens of percent, i.e. more than its tenfold concentration in the matrix. The basic mechanism of this phenomenon is the trapping of mobile self-interstitial configurations by niobium. The diffusion of pure zirconium and mixed zirconium-niobium self-interstitial configurations in the zirconium matrix at 300 K has been simulated. We observe a strong dependence of the estimated diffusion coefficients and fractions of Nb in self-interstitials produced in displacement cascades on the potential.

The interaction between atomic displacement cascades and tilt symmetrical grain boundaries in α-zirconium

ABSTRACTThe atomic displacement cascade simulations near symmetric tilt grain boundaries (GBs) in hexagonal close packed-Zirconium were considered in this paper. Further defect structure analysis was conducted. Four symmetrical tilt GBs –∑14, ∑14 with the axis of rotation [0 0 0 1] and ∑32, ∑32 with the axis of rotation – were considered. The molecular dynamics method was used for atomic displacement cascades’ simulation. A tendency of the point defects produced in the cascade to accumulate near the GB plane, which was an obstacle to the spread of the cascade, was discovered. The results of the point defects’ clustering produced in the cascade were obtained. The clusters of both types were represented mainly by single point defects. At the same time, vacancies formed clusters of a large size (more than 20 vacancies per cluster), while self-interstitial atom clusters were small-sized.

Comparative study of displacement cascades simulated with ‘magnetic’ potentials and Mendelev-type potential in α-Fe

Different interatomic potentials produce displacement cascades with different features, and hence they significantly influence the results obtained from the displacement cascade simulations. The displacement cascade simulations in α-Fe have been carried out by molecular dynamics with three ‘magnetic’ potentials (MP) and Mendelev-type potential in this paper. Prior to the cascade simulations, the ‘magnetic’ potentials are hardened to suit for cascade simulations. We find that the peak time, maximum of defects, cascade volume and cascade density with ‘magnetic’ potentials are smaller than those with Mendelev-type potential. There is no significant difference within statistical uncertainty in the defect production efficiency with Mendelev-type potential and the second ‘magnetic’ potential at the same cascade energy, but remarkably smaller than those with the first and third ‘magnetic’ potential. Self interstitial atom (SIA) clustered fractions with ‘magnetic’ potentials are smaller than that with Mendelev-type potential, especially at the higher energy, due to the larger interstitial formation energies which result from the ‘magnetic’ potentials. The defect clustered fractions, which are input data for radiation damage accumulation models, may influence the prediction of microstructural evolution under radiation.

Atomistic material behavior at extreme pressures

AbstractComputer simulations are routinely performed to model the response of materials to extreme environments, such as neutron (or ion) irradiation. The latter involves high-energy collisions from which a recoiling atom creates a so-called atomic displacement cascade. These cascades involve coordinated motion of atoms in the form of supersonic shockwaves. These shockwaves are characterized by local atomic pressures &gt;15 GPa and interatomic distances &lt;2 Å. Similar pressures and interatomic distances are observed in other extreme environment, including short-pulse laser ablation, high-impact ballistic collisions and diamond anvil cells. Displacement cascade simulations using four different force fields, with initial kinetic energies ranging from 1 to 40 keV, show that there is a direct relationship between these high-pressure states and stable defect production. An important shortcoming in the modeling of interatomic interactions at these short distances, which in turn determines final defect production, is brought to light.

Molecular dynamics simulation and first principles calculations of radiation-induced Cu clusters in Fe-3 at.% Cu alloy

Molecular dynamics (MD) simulations of displacement cascades in Fe-3 at.% Cu alloy were carried out with various primary knocked-on atom (PKA) energies at different temperature. The results showed that if PKA energy was lower than 20 keV, no stable clusters of Cu was found. However, when energy equaled to 20 keV, Cu cluster containing seven Cu atoms was found and Cu cluster could be stabilized after 5 ps. MD simulations and first principles calculations showed that irradiation-induced vacancies played a key role in the formation of the Cu cluster, and Cu atoms congregation decreased the energy of systems.