Knock-on Atom Research Articles

Deep learning potential model of displacement damage in hafnium oxide ferroelectric films

A model for studying displacement damage in irradiated HfO2 ferroelectric thin films was developed using deep learning and a repulsive table, combining the accuracy of density functional theory with the efficiency of molecular dynamics. This model accurately predicts the properties of various HfO2 phases, such as PO (Pca21), T (P42/nmc), AO (Pbca), and M (P21/c), and describes the atom collision-separation process during irradiation. The displacement threshold energies for the Hf atoms, three-coordinated O atoms, and four-coordinated O atoms are 57.72, 41.93, and 32.89 eV, respectively. The defect formation probabilities (DFPs) for the O primary knock-on atoms (PKAs) and Hf PKAs increase with energy, reaching 1. Below 80.27 eV, the O PKAs are more likely to form point defects than the Hf PKAs. Above this energy, the Hf PKAs have a higher DFP because the O PKAs form replacement loops more easily, inhibiting the generation of point defects. This study provides a comprehensive understanding of defect formation, which is crucial for increasing the reliability of HfO2 ferroelectric devices under irradiation.

Simulation of displacement damage in Si & SiO2 caused by protons

Nowadays Si & SiO2 have been the most widely used materials in semiconductor devices as CPU and other various integrated circuit chips, utilized in aerospace electronic systems, and at the same time protons are important components of cosmic rays that can cause displacement damage in Si & SiO2. Therefore, it is essential to study the displacement damage of Si & SiO2 caused by protons. The software of Geant4 is adopted in this paper, to simulate transportation process of incident protons with different energy in Si & SiO2. The simulation results indicates that primary knock-on atom (PKA) generated by incident proton in Si & SiO2 is predominant in lower energy range, its spatial distribution increases gradually along the direction of incident proton, and the scattering angle of the PKA is about 90°, following a Gaussian distribution approximately. And in lower energy range, 28Si and 16O generated by elastic scattering are a primary source of radiation damage in Si & SiO2. But as the proton energy increases, the contribution of nuclear inelastic scattering becomes more and more important, but the overall level of induced damage diminishes gradually. Meanwhile, the simulation results indicate that with increasing depth of the material, the non-ionizing energy loss (NIEL) increases gradually, and NIEL caused by elastic scattering is higher near the surface layer of the materials, and as for NIEL caused by nuclear inelastic scattering is also higher near the surface layer of the materials. The simulation results in this paper can provide useful data and theoretical guidance for study on Si & SiO2 displacement damage caused by proton irradiation.

Molecular dynamics assessment of primary damage efficiency for fusion relevant elements

Accurate computational modeling of fusion reactors depends upon precise figures of merit for radiation damage. The Norgett-Robinson-Torrens displacements per atom (NRT-dpa) model, a gold standard parameter for characterizing primary damage in solids, has been shown to overestimate surviving Frenkel defects in materials under high-energy irradiation. Here, we investigate the NRT-dpa model at higher primary knock-on atom (PKA) energies for six pure metals of interest in fusion. We compute updated defect production efficiency values and athermal recombination corrected (ARC)-dpa efficiency parameters for each element, which can be used for increased accuracy in neutronics simulations and fitting other extensions to the NRT-dpa.

Prediction of threshold displacement energies in TiC by ab initio molecular dynamics simulation method

The ab-initio molecular dynamics (AIMD) simulation method is used to compute the threshold displacement energies (Ed) of the Ti atom and the C atom in TiC. The Ed is calculated along the three high symmetric crystallographic directions, namely, [100], [110], and [111] and the weighted average of Ed is found to be 33 eV and 32 eV for Ti and C sublattice, respectively. The effect of small deviations from the high symmetry directions is also studied and the weighted average value of Ed along the 2° off-symmetric directions is found to be 35 eV for both the Ti atom and the C atom. Furthermore, the values of Ed are calculated in the presence of vacancies in C sites, which are often encountered in TiCx. In this case, small increases in the magnitude of weighted average values of Ed are observed, and these are found to be 39 eV and 34 eV for Ti and C, respectively. Anti-site defects are formed in all cases of Ti primary knock-on atom (PKA), however, no anti-site defect is formed along the high symmetry direction for C PKA. The calculated Ed values are explained by the structural and chemical properties of TiC. The projected values of Ed would be valuable parameters for modeling irradiation damage in TiC.

Molecular Dynamic Simulation of Primary Damage with Electronic Stopping in Indium Phosphide.

Indium phosphide (InP) is an excellent material used in space electronic devices due to its direct band gap, high electron mobility, and high radiation resistance. Displacement damage in InP, such as vacancies, interstitials, and clusters, induced by cosmic particles can lead to the serious degradation of InP devices. In this work, the analytical bond order potential of InP is modified with the short-range repulsive potential, and the hybrid potential is verified for its reliability to simulate the atomic cascade collisions. By using molecular dynamics simulations with the modified potential, the primary damage defects evolution of InP caused by 1-10 keV primary knock-on atoms (PKAs) are studied. The effects of electronic energy loss are also considered in our research. The results show that the addition of electronic stopping loss reduces the number of point defects and weakens the damage regions. The reduction rates of point defects caused by electronic energy loss at the stable state are 32.2% and 27.4% for 10 keV In-PKA and P-PKA, respectively. In addition, the effects of electronic energy loss can lead to an extreme decline in the number of medium clusters, cause large clusters to vanish, and make the small clusters dominant damage products in InP. These findings are helpful to explain the radiation-induced damage mechanism of InP and expand the application of InP devices.

Establishing the temperature and orientation dependence of the threshold displacement energy in ThO2 via molecular dynamics simulations

ThO2 is a promising fuel for next-generation nuclear reactors. As a critical quantity measuring its radiation tolerance, the dependence of the threshold displacement energy on temperature and crystal orientation in ThO2 is unclear and established using comprehensive molecular dynamics simulations in this work. For both Th and O primary knock-on atoms (PKAs), the thresholds, denoted as EdTh and EdO, respectively, are calculated using two different interatomic potentials. Similar temperature and orientation dependence are observed, albeit with some quantitative differences. While on average over all orientations, higher energy is required for Th PKAs than O PKAs to displace atoms, the polar-averaged EdTh is significantly lower than that for EdO. Further, EdTh and EdO show different crystal orientation dependence and temperature dependence. Notably, the cubic symmetry in the fluorite structure is followed by EdTh, but does not hold for EdO because of the existence of two sublattices. The much higher average EdO than EdTh and their different temperature dependence are interpreted by the distinct recombination rates of Th and O Frenkel pairs in thermal spikes, resulting from the substantially lower migration barriers of O vacancies and interstitials. The recombination of O vacancies and interstitials, both of which are charged, is further enhanced by the Coulomb interaction at small Frenkel pair separations. The new findings are discussed for their generality in fluorite-structured oxides by comparing the results in ThO2 and UO2.

Local Strain Effects on Lattice Defect Dynamics and Interstitial Dislocation Loop Formation in Irradiated Tungsten-Molybdenum Alloys: A Molecular Dynamics Study.

In this study, molecular dynamics (MD) simulations were used to investigate how alloying tungsten (W) with molybdenum (Mo) and local strain affect the primary defect formation and interstitial dislocation loops (IDLs) in W-Mo alloys. While the number of Frenkel pairs (FPs) in the W-Mo alloy is similar to pure W, it is half that of pure Mo. The W-20% Mo alloy, chosen for further analysis, showed minimal FP variance after collision cascades induced by primary knock-on atoms (PKAs) at 10 to 80 keV. The research examined hydrostatic strains from -1.4% to 1.6%, finding that higher strains correlated with increased FP counts and cluster formation, including IDLs. The following two types of IDLs were identified: majority ½ <111> loops as well as <100> IDLs that formed within the initial picoseconds of the simulations under higher tensile strain (1.6%) and larger PKA energies (80 keV). The strain effects also correlated with changes in threshold displacement energy (TDE), with higher FP formation under tensile strain. This study highlights the impact of strain and alloying on radiation damage, particularly in low-temperature, high-energy environments.

On the Use of a Chloride or Fluoride Salt Fuel System in Advanced Molten Salt Reactors, Part 3; Radiation Damage

Structural materials in fast reactors with harsh radiation environments due to high energy neutrons—compared to thermal reactors—potentially suffer from a higher degree of radiation damage. This radiation damage can change the thermophysical and mechanical properties of materials and, as a result, alter their performance and effective lifetime, in some cases leading to their disintegration. These phenomena can jeopardize the safety of fast reactors and thus need to be investigated. In this study, the effect of radiation damage on the vessels of molten salt fast reactors (MSFR) was evaluated based on two fundamental radiation damage parameters: displacement per atom (dpa) and primary knock-on atom (pka). Following the previous part of this article (Parts 1 and 2), an iMAGINE reactor core design (University of Liverpool, UK—chloride-based salt fuel system) and an EVOL reactor core design (CNRS, Grenoble, France, fluoride-based salt fuel system) with stainless steel and nickel-based alloy material vessels, respectively, were considered as case studies. The SPECTER and SPECTRA-PKA codes and a PTRAC card of MCNPX, integrated with a module which has been developed in MATLAB, named PTRIM and SRIM-2013 (using binary collision approximation), were employed individually to calculate and compare dpa and PKA (this master module containing all three tools has been appended to the iMAGINE-3BIC package for future use during reactor operations). Additionally, SRIM-2013 was applied in a 3D simulation of a radiation damage map on a small sample of vessels based on the calculated PKA. Our results showed a higher degree of radiation damage in the iMAGINE vessel compared to the EVOL one, which could be expected due to the harder neutron flux spectrum of the iMAGINE core compared to EVOL. In addition, the nickel alloy vessel showed better radiation damage resistance against high energy neutrons compared to the stainless steel one, although more investigations are required on thermal neutrons and alloy corrosion mechanisms to determine the best material for use in MSFR vessels.

Study on the Irradiation Evolution and Radiation Resistance of PdTi Alloys.

Medium-entropy alloys (MEAs) exhibit exceptional mechanical properties, thermal properties, and irradiation resistance, making them promising candidates for aerospace and nuclear applications. This study utilized molecular dynamics simulations to examine the defect behavior in PdTi alloys under various irradiation conditions. Simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) with the modified embedded-atom method (MEAM) potential to describe interatomic interactions. Various temperatures, primary knock-on atom (PKA) energies, and elemental ratios were tested to understand the formation and evolution of defects. The results show that compared to pure Pd, PdTi alloys with increased entropy exhibit significantly enhanced irradiation resistance at higher temperatures and PKA energies. This study explored the impact of different elemental ratios, including Pd, PdTi1.5, PdTi, and Pd1.5Ti. Findings indicate that increasing the Pd concentration enhances the alloy's irradiation resistance, improving mobility and recombination rates of defect clusters. A one-to-one Pd-to-Ti ratio demonstrated optimal performance. Temperature analysis revealed that at 300 K and 600 K, PdTi alloys exhibit excellent irradiation resistance at a PKA energy of 30 keV. However, as the temperature rises to 900 K, the irradiation resistance decreases slightly, and at 1200 K, the performance is likely to decline further. This study offers some useful insights into the irradiation evolution and radiation resistance of PdTi medium-entropy alloys, which may help inform their potential applications in the nuclear field and contribute to the further development of MEAs in this area.

Molecular dynamics simulations of high-energy radiation damage in hcp-titanium considering electronic effects

Abstract Titanium and its alloys are widely used as structural materials under extreme conditions due to their exceptional specific strength. However, comprehensive studies on their high-energy radiation damage remain limited. Considering electronic effects, molecular dynamics (MD) simulations were performed to explore high-energy radiation damage in hcp-titanium (hcp-Ti), focusing on displacement cascades induced by primary knock-on atoms (PKAs) with energies ranging from 1 to 40 keV. This study investigates the generation and evolution of point defects resulting from collisional cascades, particularly examining the influence of PKA energy. Additionally, the distribution and morphology of clustering defects from these events were quantitatively investigated and qualitatively visualized. The results show a significant dependence of surviving defects on PKA energies, highlighting a critical range that exhibits a shift in cascade morphology. Furthermore, it is demonstrated that PKA energy significantly influences the formation and growth of defect clusters, with both interstitials and vacancies showing increased cluster fraction and sizes at higher PKA energies, albeit with different tendencies in their formation and aggregation behaviors. Morphological analysis emphasizes the role of subcascades and provides further insights into the mechanisms of defect evolution behind high-energy radiation damage. Our extensive study across a broad range of PKA energies provides essential insights into the understanding of high-energy radiation damage in hcp-Ti.

Description of Short-Range Interactions of Carbon-Based Materials with a Combined AIREBO and ZBL Potential.

An accurate description of short-range interactions among atoms is crucial for simulating irradiation effects in applications related to ion modification techniques. A smooth integration of the Ziegler-Biersack-Littmark (ZBL) potential with the adaptive intermolecular reactive empirical bond-order (AIREBO) potential was achieved to accurately describe the short-range interactions for carbon-based materials. The influence of the ZBL connection on potential energy, force, and various AIREBO components, including reactive empirical bond-order (REBO), Lennard-Jones (LJ), and the torsional component, was examined with configurations of the dimer structure, tetrahedron structure, and monolayer graphene. The REBO component is primarily responsible for the repulsive force, while the LJ component is mainly active in long-range interactions. It is shown that under certain conditions, the torsional energy can lead to a strong repulsive force at short range. Molecular dynamics simulations were performed to study the collision process in configurations of the C-C dimer and bulk graphite. Cascade collisions in graphite with kinetic energies of 1 keV and 10 keV for primary knock-on atoms showed that the short-range description can greatly impact the number of generated defects and their morphology.

Radiation induced athermal diffusivity in uranium mononitride

Uranium mononitride (UN) is one of the ceramic nuclear fuel alternatives to oxide fuel considered for light water reactors and advanced reactor designs. Properties like self- and fission gas diffusivity need to be better understood, given that they influence key fuel performance phenomena such as fission gas swelling and release. In particular, the radiation induced athermal (D3) diffusivity remains challenging to accurately predict and has only been sparsely characterized in UN, despite its importance as it likely governs diffusion at the low temperatures this high-thermal-conductivity fuel form may operate. Molecular Dynamics simulations are used to estimate the mean square displacement induced by a primary knock-on atom (PKA) with a given kinetic energy. These results are combined with the PKA energy distributions obtained from binary collision approximation calculations to obtain the displacement due to a particular fission fragment. Finally, this is combined with experimental fission fragment yields to determine the displacement due to an average fission event and, thus, express the athermal diffusivity as a function of the fission rate density. These results are in excellent agreement with available experimental data. A particular importance is given to the understanding and the quantification of the variability of these results.

First-principles study on the microstructure, band structure, mechanical and optical properties of AB-stacked bilayer graphene under constant neutron irradiation with different electric field magnitudes and directions

Carbon-based devices have superior performance and lower power consumption compared to silicon-based devices. However, graphene and related two-dimensional materials are easily influenced by radiation due to their extremely high surface-to-volume ratio. Under constant neutron irradiation conditions, there have been no studies on the effects of the magnitude and direction of an external electric field on various properties of the AB system. This study systematically investigated the neutron irradiation effects on the AB system and the influence of the different electric fields on the properties of the AB system under constant irradiation conditions using the density functional theory and ab initio molecular dynamics method that assigns energy to the primary knock-on atom. The results indicate that under constant neutron irradiation with different electric fields, the changes in system configuration dominate the influence on band structure, while the impact of surface ripples is relatively limited. Reducing the interlayer spacing of the system can make the configuration more stable, which makes the band structure under the electric field more stable. The primary factors influencing the Young's modulus (Y) of the system are changes in the microstructure and the appearance of surface ripples, while the influence of system configuration is relatively limited. Under the irradiation conditions, the electric field can to some extent accurately modulate the band gap of the system. However, it will also correspondingly reduce the system's Y to a certain extent, causing negative impacts on the electrical and thermal conductivity.

Threshold displacement in the tungsten-carbon system

ABSTRACT Threshold displacement energies (Ed) of carbon and tungsten in tungsten carbide (WC), W2C, tungsten and diamond are predicted using molecular dynamics. The spatial dependence of Ed is probed by considering a geodesic projection of a symmetrically distinct arc of crystallographic directions for each lattice site. Further, the definition of threshold displacement is explored by making the distinction between atomic displacement ( E ¯ d disp ) and defect formation ( E ¯ d def ). Predicted values of E ¯ d def compare favourably to experimental observations for tungsten and tungsten carbide. Results confirm that E ¯ d def and E ¯ d disp are strongly structure dependent. Differences between E ¯ d disp and E ¯ d def are commensurate with rapid defect recombination within the timeframe of the simulations for some species and structures but not universally. The probability of displacement and defect formation as a function of primary knock-on energy is also reported. Previously developed models for the average displacement of the primary knock-on atom based on kinetic energy and momentum-dependent drag terms are generally found to provide a useful level of approximation. Anisotropy is investigated and results highlight differences due to structures.

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.

Enhanced irradiation tolerance of the body-centered cubic structured FeCrW medium-entropy alloy as revealed from primary damage process

Multi-principal element alloys have attracted much attention in the development of nuclear reactor materials due to their potentially excellent irradiation resistance. Here, we employed Molecular Dynamics (MD) simulations to investigate displacement cascades resulting from Primary Knock-on Atoms (PKA) energies ranging from 10 to 50 keV in body-centered cubic structured FeCrW, FeCr and α-Fe. The analysis encompasses irradiation-induced defect generation and evolution, aiming to elucidate mechanism of irradiation tolerance. The simulations results indicate that FeCrW medium-entropy alloys generate more Frenkel defects during the thermal spike stage compared to α-Fe, yet fewer residual defects are observed in FeCrW at the end of the cascade. The suppression of the increase in defects number in FeCrW compared to α-Fe is significantly enhanced with the increasing PKA energies. It is foreseeable that the number of residual defects in FeCrW will be much smaller than that of α-Fe with a dramatic increase of PKA energy, which will be attributed to the improved defect self-self-healing ability in FeCrW. Moreover, the mechanism of enhanced defect self-self-healing is attributed to the size of the defect cluster, the formation and distribution of defects, the enhanced thermal spike, and the chemical disorder caused by the increase in composition leading to low thermal conductivity. The spectral energy density (SED) curves spikes of α-Fe, FeCr and FeCrW reveal an important role in the enhanced phonon scattering in improving defect self-repairing ability due to chemical disorder. Our research provides valuable insights for guiding the development of advanced multi-principal element alloy structural materials in nuclear industry, particularly for the fourth-generation fast reactor.

Investigations on structure and optical properties of neutron irradiated nanocrystalline La2Zr2O7 pyrochlores

This research work investigates the response of nanocrystalline lanthanum zirconium oxide (LZO) under neutron irradiation, emphasizing grain size-dependent structural stability. LZO samples were synthesized with the chemical precipitation method and the LZO pellets were annealed at two different temperatures (1200 °C and 1400 °C) to obtain two different grain size samples, namely LZO-1200 and LZO-1400. The samples were exposed to neutrons at different doses (ranging from 1.63 × 1012 n/cm2 to 5.68 × 1014 n/cm2) and the effects were studied with X-ray diffraction, scanning electron microscopy, Raman scattering and optical characterization. The structural characterization results reveal that, the grain size and strain are significantly modified in LZO-1400 samples, and such changes are absent inLZO-1200 samples. The band gap and photoluminescence intensity are reduced significantly in LZO-1400 samples, however, this effect is not observed in LZO-1200 samples. The experimental results reveal that in LZO-1200 samples, the grain boundaries act as a sink for irradiation-induced defects and there is no significant change in the grain size, strain and band gap. However, in the case of the LZO-1400 sample, the grain size is larger than the cascades induced by primary knock-on atoms (PKAs) and it results in disorder-driven fast grain growth and changes in band gap and PL intensity. The LZO-1200 samples with small grain sizes are radiation resistant.

Molecular dynamics simulations of interaction of cascade damage with self-interstitial atom-loaded grain boundaries in tungsten

In this study, we conducted systematic molecular dynamics simulations to investigate the radiation resistance of grain boundaries (GBs) in tungsten with/without self-interstitial atoms (SIAs) loaded on them. The simulation results show that the presence of SIAs can extend the width of the Σ3<110>{112} twin GB compared to the SIA-free GB. When cascade damage occurs near Σ3, the presence of SIAs at Σ3 enhances radiation resistance. Specifically, it inhibits producing residual defects, particularly vacancies and prevents their aggregating into clusters. The radiation-resistant performance is most excellent when the SIA concentration at Σ3 is approximately 5 %. The influence of temperature and primary knock-on atom energy on radiation damage is also discussed. However, SIA-loaded high angle GBs and low angle GBs do not significantly enhance their radiation-resistant performance compared to their SIA-free counterparts. This study provides valuable insights into the radiation damage behaviors near GBs and contributes to understanding their radiation-resistant mechanisms.

Coupling Nuclear Predictions into Damage Simulations with SPECTRA-PKA

Modern nuclear physics software is well validated, providing advanced capabilities to support the engineering of the future generations of fission and fusion reactors. Transport simulators can model the transport of neutrons through reactor geometries, and inventory codes can accurately predict transmutation and activation. Meanwhile, material modeling applies a variety of techniques to understand how structural damage and composition changes will alter the properties of materials, ultimately limiting their usable lifetime in a reactor. Bridging the gap between nuclear simulation tools and materials modeling is a necessary step if these lifetimes are to be accurately predicted, which, for fusion, is critical to provide the necessary assurance of commercial viability. SPECTRA-PKA is a tool developed to compute the rates of structural damage source events, i.e. the primary knock-on atoms (PKAs), using the same nuclear data as used by transport and inventory simulations. Now, it has been interfaced with the binary collision approximation code SDTrimSP, allowing those PKA events, distributed spatially and temporally in an atomic system, to be converted into damage cascades. This computational infrastructure provides insight into the variation in damage distributions between different materials under the same nuclear environment. Example simulations for materials under fusion reactor conditions demonstrate how the rich detail of the nuclear environment can be applied directly to modeling, without the need for integral-average measures that omit those details.

A modified two temperature molecular dynamics (2T-MD) model for cascades

Two-Temperature molecular dynamics (2T-MD) is a common approach for describing how electrons contribute to the evolution of a damage cascade by addressing their role in the redistribution of energy in the system. However, inaccuracies in 2T-MD’s treatment of the high-energy particles have limited its utilisation. Here, we propose a reformulation of the traditional 2T-MD scheme to overcome this limitation by addressing the spurious double-interaction of high-energy atoms with electrons. We conduct a series of radiation damage cascades for 30, 50, and 100 keV primary knock-on atoms in increasingly large cubic W cells. In the simulations, we employ our modified 2T-MD scheme along with other treatments of electron–phonon coupling to explore their impact on the cascade evolution and the number of remnant defects. The results suggest that with the proposed modification, 2T-MD simulations account for the temperature time evolution during the ballistic phase and remove arbitrary choices, thus providing a better description of the underlying physics of the damage process.