Thermal Spike Phase Research Articles

Helium bubble evolution under cascade in bcc iron relevant to fusion conditions investigated by a novel coupling MD-OKMC method

The direct interaction between cascade and helium bubbles during the thermal spike phase plays an important role in the helium bubbles evolution in metals, which was not fully considered by the present long-time simulation methods. To address this issue, in this work we developed a coupling MD-OKMC method to investigate the helium bubble evolution under irradiation cascade in bcc iron. The short-time collision cascade was simulated by the molecular dynamics (MD), and the long-time helium bubble evolution was modeled by the object kinetic Monte Carlo (OKMC). The MD and OKMC simulations were alternated to imitate the gradual increase of both irradiation dose and helium concentration under experiment conditions. The impact of temperature on the helium bubble evolution under irradiation cascade in bcc iron was investigated and the results were compared with the data from neutron irradiation experiment. It's found that the results of the coupling MD-OKMC were consistent with the experiment results, and were better in agreement with the experiment than the traditional OKMC.

Electronic effects on radiation damage in α-iron: A molecular dynamics study

Iron (Fe)-based alloys, which have been widely used as structural materials in nuclear reactors, can significantly change their microstructure properties and macroscopic properties under high flux neutron irradiation during operation, thus, the problems associated with the safe operation of nuclear reactors have been put forward naturally. In this work, a molecular dynamics simulation approach combined with electronic effects is developed for investigating the primary radiation damage process in α-Fe. Specifically, the influence of electronic effects on the collision cascade in Fe is systematically evaluated based on two commonly used interatomic potentials for Fe. The simulation results reveal that both electronic stopping (ES) and electron–phonon coupling (EPC) can contribute to the decrease of the number of defects in the thermal spike phase. The application of ES reduces the number of residual defects after the cascade evolution, whereas EPC has a reverse effect. The introduction of electronic effects promotes the formation of the dispersive subcascade: ES significantly changes the geometry of the damaged region in the thermal spike phase, whereas EPC mainly reduces the extent of the damaged region. Furthermore, the incorporation of electronic effects effectively mitigates discrepancies in simulation outcomes when using different interatomic potentials.

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.

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.

High thermal coarsening resistance of irradiation-induced nanoprecipitates in Cu-Mo-Si alloys

Irradiation by 1.8 MeV Kr ions at room temperature (RT) was employed to induce nanoprecipitation in two Cu-Mo-Si ternary alloys, Cu96Mo1Si3 and Cu90Mo3.5Si6.5. The nature and the stability of these precipitates during high temperature annealing and irradiation were studied using X-ray diffraction and transmission electron microscopy. In Cu90Mo3.5Si6.5, Kr irradiation at RT resulted in the formation of a high number density (>1023 m−3) of Mo-Si rich nanoprecipitates, ∼3 nm in size, the formation of which was attributed to Mo-Si interactions during the thermal spike phase of displacement cascades. The size of these irradiation-induced Mo-Si precipitates remained unchanged after annealing at 750 °C for 1hr. This near absence of thermal coarsening contrasted with a significant thermal coarsening of the more Mo-rich precipitates formed by direct annealing in that same ternary alloy, and with the even larger coarsening of pure Mo precipitates formed by RT irradiation in binary Cu-Mo alloys. During high temperature irradiation, precipitation is also observed, and some precipitates were significantly enriched in Mo. As for thermal annealing, those precipitates displayed increased coarsening. The remarkable thermal coarsening resistance of RT irradiation-induced Mo-Si precipitates is attributed to the suppression of Mo solubility in a Cu matrix containing Si-rich precipitates, and to the narrow precipitates size distribution generated by RT irradiation. This former point was quantified using thermodynamic calculations with the CALPHAD method.

Simulating radiation damage accumulation in α-Fe: A spatially resolved stochastic cluster dynamics approach

Abstract Neutron irradiation of high purity α -Fe to 10 - 1 DPA is simulated using spatially resolved stochastic cluster dynamics (SRSCD). In doing so, a novel scheme is developed that addresses the following challenges to simulations of defect accumulation in bulk materials: how to introduce displacement cascades in a numerically efficient manner while maintaining the spatial resolution necessary for accurate defect evolution within cascades; how to account for interactions between defects already present in the material and cascades during the thermal spike phase; and how to choose appropriate cascade energies that reflect damage accumulation due to high-energy neutrons. The spatial resolution necessary for displacement cascade implantation is maintained via an accelerated adaptive meshing scheme. Direct cascade mixing with point defects present in the material is studied and shown to be necessary for defect saturation above 10 - 3 DPA. Defect population evolution is shown to only weakly depend on the cascade energy used in this study, allowing the use of a single cascade energy for simulating high energy neutron irradiation. Using this scheme, traps for mobile one-dimensional diffusing SIA loops are shown to strongly affect the final defect microstructure, and simulated defect accumulation results are compared to experimental results over the range of DPA studied here. The computational efficiency and accuracy of this technique make it a good candidate for inclusion in multi-scale models of radiation-induced material behavior changes.

Evolution of Defects and Defect Clusters in β-SiC Irradiated at High Temperature

A molecular dynamics study has been performed to investigate the generation and evolution of damage states in irradiated β-SiC at high temperature. It is found that most of the C antisites (SiC) are created during the early collisional phase, while the Si antisites (CSi) are significantly produced during the thermal spike phase. A modified near-neighbor point defect density (NPDD) is introduced to study the spatial aggregation of different defects during the displacement cascades, and feature of defect clusters evolution is analyzed in details. The dominated types of vacancy clusters after the displacement cascades are two- and three-size chainlike ones. And the vacancy NPDD (V-NPDD) decreases as the recoil energy increases. Furthermore, after the thermal spike phase, there is an additional annealing process during which the interstitials and antisites turn into defect clusters, respectively.

Ejection of Au and Si nanocrystals from Au implanted Si(1 0 0) by MeV heavy ion irradiation

Si(100) substrates implanted with 32keV Au− ions, were irradiated with 3MeV Au3+ ions at an angle of 60°. Transmission electron microscopy (TEM) studies on sputtered particles collected on catcher grids revealed the presence of Au and Si nanocrystals. The size distribution of collected Au nanocrystals exhibited inverse power law dependence with a decay exponent of 2. Atomic force microscopy (AFM) analysis of irradiated sample showed the presence of surface craters along with hillocks. The formation of Au and Si nanocrystals in MeV ion irradiated Au doped amorphous Si layer can be attributed to the localized melting due to thermal spike phase of atomic displacement cascades produced by MeV Au ion impacts.

Interplay of energy dissipation, ion-induced mixing, and crystal structure recovery, and surface effects in ion-irradiated magnetic Fe/Cr/Fe trilayers

The influence of the ion irradiation by 30 keV Ga${}^{+}$ ions on the crystal structure, chemical ordering, magnetic properties, and topography of epitaxial Fe/Cr/Fe trilayers was investigated by different analytical techniques. We present direct experimental evidence, supported by theoretical estimates, that two processes take place concurrently due to the Ga-ion implantation. (i) A complete atom mixing of the Cr atoms within the Fe multilayers is occurring due to the collision cascades during the ballistic regime, and (ii) an essentially complete recovery of the initial single-crystal quality of the Fe multilayers by healing the melted and damaged area through the thermal spike phase occurs. Based on the experimental range distributions and theoretical modeling, channeling of Ga${}^{+}$ ions in the experiments is found to contribute weakly to ion penetration and stopping, and the relative fraction of the well-channeled ions is marginally small. On the other hand, this weak channeling is sufficient to reduce the sputter yield by a factor of more than 5 in comparison with the sputtering of polycrystalline samples, evidence for the fact that the magnitude of channeling is not of primary importance for the sputtering. We offer an explanation for the observation of dramatic and abrupt changes in the surface roughness with increasing fluences in terms of a transformation from a single-phase single-crystal implanted region (bcc-Fe) to a mixture of the polycrystalline \ensuremath{\alpha}-Fe-like bcc and \ensuremath{\alpha}-Fe${}_{3}$Ga structures within the outer half of the original Fe/Cr/Fe trilayer at fluences above 6.25 \ifmmode\times\else\texttimes\fi{} 10${}^{16}$ ion/cm${}^{2}$. The wall-like elevations appearing at the boundary of the irradiated areas were analyzed experimentally by varying the irradiation conditions. We showed that the wall size is governed by the ion-current density applied. A physical explanation for the appearance of such topographic features is presented, which would be valid for any material irradiated by a focused ion beam.

On the origin of large interstitial clusters in displacement cascades

Displacement cascades with wide ranges of primary knock-on atom (PKA) energy and mass in iron were simulated using molecular dynamics. New visualisation techniques are introduced to show how the shock-front dynamics and internal structure of a cascade develop over time. These reveal that the nature of the final damage is determined early on in the cascade process. We define a zone (termed ‘spaghetti’) in which atoms are moved to new lattice sites and show how it is created by a supersonic shock-front expanding from the primary recoil event. A large cluster of self-interstitial atoms can form on the periphery of the spaghetti if a hypersonic recoil creates damage with a supersonic shock ahead of the main supersonic front. When the two fronts meet, the main one injects atoms into the low-density core of the other: these become interstitial atoms during the rapid recovery of the surrounding crystal. The hypersonic recoil occurs in less than 0.1 ps after the primary recoil and the interstitial cluster is formed before the onset of the thermal spike phase of the cascade process. The corresponding number of vacancies is then formed in the spaghetti core as the crystal cools, i.e. at times one to two orders of magnitude longer. By using the spaghetti zone to define cascade volume, the energy density of a cascade is shown to be almost independent of the PKA mass. This throws into doubt the conventional energy-density interpretation of an increased defect yield with increasing PKA mass in ion irradiation.

Stability of helium clusters during displacement cascades

The interactions of displacement cascades with helium-vacancy clusters in α-Fe are investigated using molecular dynamics simulations. Initial He-vacancy clusters consist of 20 vacancies with a helium-to-vacancy ratio ranged from 0.2 to 3 and primary knock-on atom (PKA) energy, E p, varies from 2 keV to 10 keV. The results show that the effect of displacement cascades on a helium-vacancy cluster strongly depends on the helium-to-vacancy ratio and PKA energy. For the same PKA energy, the size of helium-vacancy clusters increases with the He/V ratio, but for the same ratio, the cluster size changes more significantly with increasing PKA energy. It has been observed that the He-vacancy clusters (He-V) can be dissolved for the He/V ratio less than 1, but they are able to renucleate during the thermal spike phase, forming small He-V nuclei. For the He/V ratio larger than 1, the He-V clusters are very stable for the energies considered and they can absorb a number of vacancies produced by displacement cascades, forming larger He-V clusters.

Classical molecular dynamics study of primary damage created by collision cascade in a ZrC matrix

Classical molecular dynamics simulation of a high energy collision cascade initiated at 50 keV is used to study the primary damage state in a stoichiometric mono crystalline ZrC matrix. Analysis of the dynamics and the morphology of the displacement cascade reveals three distinct, well-defined time frames: collision phase, thermal spike and relaxation phase. On average, most of the atoms migrate over short distances, typically less than 11 Å, leading to numerous collision sequences in each sublattice. No amorphisation is observed, only a few point defects are created at the end of the collision cascades. All the Zr interstitials form a dumbbell structure oriented in the 〈1 1 1〉 direction and C interstitials are either isolated or form a 〈1 1 1〉 dumbbell structure. However, unlike metals, few antisites are created. Clusters of two interstitials of different species have a tendency to form small interstitial dislocation loops in the (1 1 1) plane.

Thermal spikes in Ag/Fe and Cu/Fe ion beam mixing

Ion beam mixing has been studied since 1980, and since then a lot of experimental and theoretical work has been done and knowledge has been gathered. Nevertheless, there are still many fundamental aspects that need to be clarified and with that aim many experiments need to be performed. Copper and iron are miscible in the liquid state, while silver and iron are not. However, both systems are thermally immiscible in the solid state. In order to have an insight into the importance of mixing within thermal spikes during ion beam irradiation, we deposited Cu/Fe and Ag/Fe bilayers onto Si substrates and irradiated them at room temperature with 2 MeV Cu and 2.5 MeV Au ions. A combination of Rutherford backscattering spectrometry (RBS) and atomic force microscopy (AFM) was used to analyze the atomic transport at the interface and the morphology changes of the samples. From the element profiles at the interface we conclude a mixing efficiency, which is indeed larger than the prediction of the ballistic model in the Cu/Fe system and smaller in the Ag/Fe system. Since ballistic mixing is expected in any case, we argue that demixing and phase separation in the Ag/Fe system occur in the thermal spike phase of the cascade as a consequence of the positive heat of mixing. Further mixing does occur in the thermal spike in the Cu/Fe system and they remain mixed even at the solid state because of the high cooling rate. In addition, ion irradiation induces a large surface roughening of the Ag and Cu top layers as proven by AFM. This effect is important for the correct interpretation of the results. Furthermore, this recrystallization affects also the interface, producing a rough interface, that appears in the RBS spectra as an atomic ‘diffusion’ at the interface.

Computer simulation of displacement cascades in nanocrystalline ni.

Large-scale molecular dynamics of cascade production of the primary damage state are performed in fcc nanocrystalline Ni of average grain diameters of 5 and 12 nm. Primary knock-on atom kinetic energies of 5-30 keV are simulated. During the thermal spike phase, significant atomic motion towards the surrounding grain boundary structure is observed, characterized by many replacement-collision sequences. Upon resolidification, the excess volume condenses to form vacancy dominated defects with a complex partial dislocation network forming at higher energies.

Vacancy loop formation by 'cascade collapse' in a-Fe: A molecular dynamics study of 50keV cascades

Direct formation of a large vacancy loop by displacement cascade in α-Fe has been observed for the first time in a molecular dynamics (MD) computer simulation study. This phenomenon occurred in one anomalous run out of 100 simulations of 50 keV primary knock-on atom energy cascades, in which one large displacement cascade was produced instead of the formation of smaller subcascades. Two large self-interstitial atom clusters were produced at the periphery of the cascade core, followed by the formation of a very high concentration region of vacancies at the centre of the cascade during the quenching of the thermal spike phase. Finally, one large vacancy loop with Burgers vector b = a 0 was formed by cascade collapse. A very-low-probability, one hundredth or probably less, for vacancy loop formation in the present MD simulation is consistent with the experimental observation of a low defect yield in irradiated α-Fe.

Nanoparticle ejection from Au induced by single Xe ion impacts

In situ transmission electron microscopy has been used to observe sputtered Au during Xe ion irradiation in transmission geometry. The sputtered Au was collected on an electron transparent carbon foil. Nanoparticles were observed on the collector foil after they were ejected by single ion impacts. The ejection is from the melt zone formed during the thermal spike phase of a displacement cascade produced near the surface by a single ion impact. Such single ion impacts are also capable of producing craters. Ejected nanoparticles can make a significant contribution to sputtering.

Simulation of cluster ejection following high-energy Au n→Au(111) bombardment

Following the recent report by Andersen et al. of extremely large nonlinear sputtering yields caused by the bombardment of gold targets with small, high energy gold clusters [Phys. Rev. Lett. 80 (1998) 5433], we carried out simulations showing: (1) that the thermal spike phase of the collision cascade contributes significantly to these nonlinear yields; and (2) that individual ‘mega-events’ with yields up to ∼2500 contribute significantly to the total sputtering yields [Shapiro and Tombrello, Nucl. Instrum. Meth. B 152 (1999) 221]. Here we extend our simulations to examine the cluster component of the sputtering yield. We find that clusters with n≥2 constitute a large fraction of the yield. In the early stages of sputtering (≤3 ps) clusters with as many as ∼800 atoms are ejected. These very large clusters are not stable; however, after allowing the simulations to evolve for an additional 100 ps, clusters with as many as ∼300 atoms remain. The yields of clusters with n≤∼10 follow typical power law distributions, while the yield of clusters with n>∼10 significantly exceed the predictions of the power-law distribution. Our simulations also show that clusters with more than a few tens of atoms are emitted exclusively during the thermal spike phase.

Mechanism of surface influence on dislocation loop yield in copper andCu3Au

A recently developed hybrid binary-collision/continuum model [V. G. Kapinos and D. J. Bacon, Phys. Rev. B 52, 4029 (1995)] of temperature and defect evolution in displacement cascades has been used to investigate the influence of a nearby surface on vacancy defect formation in cascade events. The shape, vacancy, and thermal conditions in cascade zones that melt and intersect the surface during the thermal spike phase have been analyzed. Simplified geometries of such zones have been simulated by molecular dynamics on the basis of these data and the mechanisms of vacancy generation in the melt zone analyzed. It has been demonstrated that additional vacancies are formed in the resolidified zone under the surface through a combination of thermal sputtering and viscous flow of atoms from the cascade core. Quantitative relationships between the geometry and size of the melt zone and number of additional vacancies have been considered, and used in the hybrid model to calculate the depth, yield, and size distribution of vacancy dislocation loops in Cu and ${\mathrm{Cu}}_{3}\mathrm{Au}$ irradiated with 50-keV ${\mathrm{Ni}}^{+}$ ions. The results are in good agreement with experimental data obtained by transmission electron microscopy of ion-irradiated thin foils.

A molecular dynamics study of temperature effects on defect production by displacement cascades in α-iron

Assessment of the hardening and embrittlement of pressure vessel steels and welds as a function of neutron dose uses trend curves derived from surveillance specimens. For some materials in the UK typical of those used in older plant, these curves incorporate an empirical factor to describe the temperature-dependence of matrix hardening. In the present work, molecular dynamics (MD) simulations have been used to obtain detailed information on defect number and arrangement produced in the primary cascade state of radiation damage as functions of irradiation temperature, T irr, in α-iron. To allow for heat dissipation during the thermal spike phase, the continuum treatment of heat conduction was used to adjust the temperature of the boundary atoms in MD throughout the cascade process. The continuum parameters were calibrated to match those of the atomic structure. This new hybrid model allows for the variability in form between one cascade and another and has been applied to defect generation by cascades of either 2 or 5 keV at 100 K, 400 K, 600 K and 900 K. The effect of T irr on the production of Frenkel pairs is small but statistically significant: the total number decreases by about 20–30% as T irr increases from 100 K to 900 K. The decrease is smaller than would be consistent with the factor in the trend curves, implying that most of the observed temperature dependence arises from postcascade processes.

Point defect movement and annealing in collision cascades

The effect of collision cascades on preexisting point defects in crystalline materials was studied by simulating 5 keV collision cascades in gold, copper, aluminum, platinum, and silicon. The results indicate that collision cascades do not significantly affect interstitials or vacancies outside the liquid core of the cascade, although in the fcc metals the heating of the crystal due to the cascade causes some thermal migration of the interstitials. Within the liquid cascade core, both interstitials and vacancies move towards the center of the molten region when it resolidifies and recombine or cluster there. At elevated temperatures, random jumps of interstitials during the thermal-spike phase can cause significant additional trapping of interstitials in the liquid. In contrast to the annealing effects of preexisting damage in the fcc metals, in silicon the amount of new damage created by a cascade is roughly independent of the number of initial point defects. The difference is attributed to the nature of the bonding in the materials.