Small Interstitial Clusters Research Articles

Influence of interstitial cluster families on post-synthesis defect manipulation and purification of oxides using submerged surfaces.

Injection of interstitial atoms by specially prepared surfaces submerged in liquid water near room temperature offers an attractive approach for post-synthesis defect manipulation and isotopic purification in device structures. However, this approach can be limited by trapping reactions that form small defect clusters. The compositions and dissociation barriers of such clusters remain mostly unknown. This communication seeks to address this gap by measuring the dissociation energies of oxygen interstitial traps in rutile TiO2 and wurtzite ZnO exposed to liquid water. Isotopic self-diffusion measurements using 18O, combined with progressive annealing protocols, suggest the traps are small interstitial clusters with dissociation energies ranging from 1.3 to 1.9eV. These clusters may comprise a family incorporating various numbers, compositions, and configurations of O and H atoms; however, in TiO2, native interstitial clusters left over from initial synthesis may also play a role. Families of small clusters are probably common in semiconducting oxides and have several consequences for post-synthesis defect manipulation and purification of semiconductors using submerged surfaces.

Spatially-resolved cluster dynamics modeling of irradiation growth

We develop here a spatially resolved, three-dimensional continuum model coupling cluster dynamics (SR-CD) and crystal plasticity to investigate irradiation growth in zirconium. The model uses scale separation to divide the population of the irradiation cluster into mobile and immobile families. Small interstitial and vacancy clusters are modeled using anisotropic reaction–diffusion equations. Among the immobile clusters, an atomistically-informed vacancy cluster to vacancy loop transition is taken into account. The coupling between the evolution equation of CD and the plastic deformation of the material is two-fold, with stress-informed bias factors and local inelastic strains computed from the evolution of the evolving cluster population. The numerical implementation of the model utilizes the finite element method to analyze both single-crystal and polycrystalline samples. The growth strains that are computed align well with the experimental data provided by Carpenter for single-crystal Zr. Furthermore, the transformation of a vacancy cluster into a complete vacancy loop, occurring at a size of 14 nm, is in agreement with experimental observations and atomistic simulations. The density, size, and growth rate of the dislocation loops, denoted as 〈c〉 and 〈a〉, also exhibit good agreement with transmission electron microscopy (TEM) analysis of irradiated Zr and its alloys. Our findings demonstrate that there is a spatial correlation between the growth of these dislocation loops and growth strains, significantly influenced by the crystal size. To explain the expansion of the 〈a〉 axis and the contraction of the 〈c〉 axis in irradiated Zr, it is necessary to consider the diffusion anisotropy difference (DAD) of mobile interstitial species. We show that the PWR Kearns parameters, specifically fr = 0.63, ft = 0.32, fa = 0.05, confer enhanced irradiation resistance to Zr along the principal directions when compared to single crystals. Additionally, reducing the grain size to nanograins further enhances the resistance to irradiation-induced growth, particularly along the direction with the highest volume fraction of basal poles [0001].

Energetics and diffusional properties of helium in W-Ta systems studied by a new ternary potential

In this paper, we present an interatomic potential for the ternary W–Ta–He system, which is an extension of our previous W–Ta potential. The new potential parameters for the W–He and Ta–He interactions are determined by fitting the results obtained from first-principles calculations. The formation energies of a single He atom at different sites, the binding energies of He–He and He–Vac (Vac = vacancy) in W/Ta, and the binding energies of a single He atom with a solute Ta atom in W are used as the fitting targets. Then, the binding energies of an additional interstitial He atom to existing HenVacm clusters in W/Ta are calculated, and the results reported correspond with the results from the first-principles. Furthermore, the effects of solute Ta on the diffusion and aggregation of He in bulk W are studied. We observed that small interstitial He atom clusters (NHe ≤ 4) were easy to diffuse in pure W, and their diffusion activation energies were less than 0.3 eV. However, the binding energies between Ta and these clusters were between 0.5 and 0.9 eV, which has a pinning effect on the He cluster diffusion. At high temperature, the solute Ta cannot qualitatively hinder the agglomeration of He atoms, however, due to the pinning effect compared with pure W, solute Ta in W has a certain delay effect on the agglomeration of He atoms in time.

Small uranium and oxygen interstitial clusters in UO[formula omitted]: An empirical potential study

The aggregation of defect clusters in UO2 under irradiations creates dislocation loops and cavities, which in turn contribute to swelling of the fuels, leading to detrimental pellet-clad mechanical interactions. The kinetics of the defect clusters, however, have received less attention and are not well understood. Using two interatomic potentials, the Morelon potential and a many-body model by Cooper, Rushton, and Grimes (CRG), the energetics and kinetics of small uranium interstitial clusters, with and without bound oxygen interstitials, are investigated with molecular dynamics and accelerated molecular dynamics simulations. For the single bound anti-Schottky interstitial cluster (Ui2Oi), both potentials find the interstitialcy migration mechanism to be a low barrier migration mechanism. However, for the CRG potential, an oxygen Frenkel pair assisted interstitial cluster migration mechanism with a lower migration barrier is identified during accelerated molecular dynamics simulations. For the Morelon potential, the interstitial clusters have geometrically compact structures, and small interstitial clusters (two and three anti-Schottky clusters) are more mobile than the single bound anti-Schottky interstitial cluster; for the CRG potential, the interstitial clusters have geometrically non-compact structures, yielding a more complex energy landscape. The rapid migration of interstitials and interstitial clusters are important for the irradiation response of UO2 and correlates well with the very low barriers reported in a few historic experimental studies.

The effect of rhenium on the diffusion of small interstitial clusters in tungsten

In this work, we use atomistic simulations to investigate the mobility and stability of self-interstitial atom (SIA) clusters of size 1–5 in W-Re alloys. We apply molecular statics and molecular dynamics (MD) simulations to determine the dimensionality of diffusion of the clusters, the activation energy of translation and rotation, and the energy of dissociation. The results show a strong effect of Re on the diffusion properties of SIA clusters, but not on its stability. The diffusion mechanism of the single SIA changes from 1-D migration with on-site rotations to full 3-D diffusion on the MD time and length scale due to the addition of Re. Further, the mobility of the SIA clusters is greatly reduced by the addition of Re. The obtained results can be readily used to parameterize coarse grain models such as object kinetic Monte Carlo and rate theory models.

Dimensional changes and thermal conductivity by annealing and its relation to the defect concentration and stored energy release of neutron-irradiated graphite

ABSTRACT The dimensional changes and thermal conductivity with the annealing of fine-grained isotropic graphite IG-110U and ETP-10 irradiated to 0.02 and 0.25 dpa (1.38 x 1023 and 1.92 x 1024 n/m2, E > 1MeV) at a design temperature of <200°C were studied. The irradiated graphite exhibited a small volume expansion and large degradation in thermal conductivity. Post-irradiation annealing experiments were carried out on dimensional changes and thermal conductivity up to 1700°C, and the results were analyzed in terms of changes in the defect concentration of graphite crystals. The rapid recovery of thermal conductivity observed below 200°C in the graphite irradiated to 0.02 dpa was attributed to the annihilation of Frenkel defects, whereas the recovery observed in both dimension and thermal conductivity above 200°C in the graphite irradiated to 0.02 dpa and 0.25 dpa was caused by the annihilation of small interstitial clusters of 4 ± 2 atoms. The role of large clusters of interstitials and vacancies in the changes to smaller dimension than pre-irradiation at high annealing temperatures are discussed. The temperature dependence of stored energy release was estimated from the changes in defect concentration calculated from the recovery of thermal conductivity.

Atomistic-object kinetic Monte Carlo simulations of irradiation damage in tungsten

We describe the development of a new object kinetic Monte Carlo (kMC) code where the elementary defect objects are off-lattice atomistic configurations. Atomic-level transitions are used to transform and translate objects, to split objects and to merge them together. This gradually constructs a database of atomic configurations- a set of relevant defect objects and their possible events generated on-the-fly. Elastic interactions are handled within objects with empirical potentials at short distances, and between spatially distinct objects using the dipole tensor formalism. The model is shown to evolve mobile interstitial clusters in tungsten faster than an equivalent molecular dynamics (MD) simulation, even at elevated temperatures. We apply the model to the evolution of complex defects generated using MD simulations of primary radiation damage in tungsten. We show that we can evolve defect structures formed in cascade simulations to experimentally observable timescales of seconds while retaining atomistic detail. We conclude that the first few nanoseconds of simulation following cascade initiation would be better performed using MD, as this will capture some of the near-temperature-independent evolution of small highly-mobile interstitial clusters. For the 20keV cascade annealing simulations considered here, we observe internal relaxations of sessile objects. These relaxations would be difficult to capture using conventional object kMC, yet are important as they establish the conditions for long timescale evolution.

Insights from atomistic models on loop nucleation and growth in α-Fe thin films under Fe+ 100 keV irradiation

The question of how loops nucleate and grow in α-Fe under irradiation is addressed using object kinetic Monte Carlo with parameters from molecular dynamics and density functional theory calculations. Two models are considered for the formation of <100> loops, both based on recent atomistic simulations. In one model <100> loops are formed by the interaction between ½<111> loops. In a second model small interstitial clusters, nucleated in the collision cascade, can grow as <100> or ½<111> loops. Comparing results from the calculations to experimental measurements of loop densities, ratios and sizes produced by Fe+ 100 keV irradiation of UHP Fe thin films at room temperature, the validity of the models is assessed. For these experimental conditions, the reaction model does not seem to be very efficient in the production of <100> loops due to the fast recombination of ½<111> loops to surfaces. Therefore, in our thin film simulations (at very low carbon concentrations) most <100> loops are a result of the nucleation model. In bulk simulations this effect could change since the probability of interactions between ½<111> loops would increase. Moreover, simulations show that total visible cluster concentration depends strongly on sample thickness and carbon content, while crystal orientation does not seem to have a significant role. Finally, the ratio of <100> to ½<111> visible clusters changes with increased carbon concentration.

Annihilating vacancies via dynamic reflection and emission of interstitials in nano-crystal tungsten

Radiation damage not only seriously degrades the mechanical properties of tungsten (W) but also enhances hydrogen retention in the material. Introducing a large amount of defect sinks, e.g. grain boundaries (GBs) is an effective method for improving radiation-resistance of W. However, the mechanism by which the vacancies are dynamically annihilated at long timescale in nano-crystal W is still not clear. The dynamic picture for eliminating vacancies with single interstitials and small interstitial-clusters has been investigated by combining molecular dynamics, molecular statics and object Kinetic Monte Carlo methods. On one hand, the annihilation of bulk vacancies was enhanced due to the reflection of an interstitial-cluster of parallel crowdions by the GB. The interstitial-cluster was observed to be reflected back into the grain interior when approaching a locally dense GB region. Near this region, the energy landscape for the interstitial was featured by a shoulder, different to the decreasing energy landscape of the interstitial near a locally loose region as indicative of the sink role of the GB. The bulk vacancy on the reflection path was annihilated. On the other hand, the dynamic interstitial emission efficiently anneals bulk vacancies. The single interstitial trapped at the GB firstly moved along the GB quickly and clustered to be the di-interstitial therein, reducing its mobility to a value comparable to that that for bulk vacancy diffusion. Then, the bulk vacancy was recombined via the coupled motion of the di-interstitial along the GB, the diffusion of the vacancy towards the GB and the accompanying interstitial emission. These results suggest that GBs play an efficient role in improving radiation-tolerance of nano-crystal W via reflecting highly-mobile interstitials and interstitial-clusters into the bulk and annihilating bulk vacancies, and via complex coupling of in-boundary interstitial diffusion, clustering of the interstitial and vacancy diffusion in the bulk.

Simulation of radiation damages in molybdenum by combining molecular dynamics and OKMC

In this paper, radiation defects in bcc molybdenum with the primary knock-on atom (PKA) energies of 2–40 keV are simulated by the molecular dynamics. The binding energy of single point defect-to-defect clusters increases with the cluster size. The stability and mobility of point defects and defect clusters are analyzed. The interstitial-type clusters are found to be easily migrating along the direction with low barriers (0.01–0.10 eV). Then, the object kinetic Monte Carlo is used to gain insight into the long-term defect evolution in the cascade. The simulation results indicate that Stage I almost occurs at annealing temperature of 100 K, which corresponds to the correlated recombination resulting from the motion of small interstitial clusters (n ≤ 2). The formation of substage partly as result of the small vacancy clusters motion. At about 460 K, the Stage II starts because of uncorrelated recombination due to an emitting mechanism of larger clusters. Size distribution of the clusters at the cascade quenching stage is positively correlated with the PKA energies, affecting notably the subsequent annealing process.

Towards understanding the differences in irradiation effects of He, Ne and Ar plasma by investigating the physical origin of their clustering in tungsten

While inert gas seeding to improve energy confinement has been successfully applied in many tokamak experiments, questions remain as to the irradiation effects of inert gases on tungsten. In this paper, we have systematically investigated the clustering behaviors of the inert gas atoms He, Ne and Ar in plasma-facing tungsten using first-principles calculations. Small interstitial clusters, Hem, Nem, and Arm, can form due to the attraction between the atoms and tend to expand along the (1 1 0) planes. The inert gas clusters induce strong lattice distortions and so it is energetically favorable for a self-interstitial atom to be emitted from the clusters when the numbers of atoms are above six, three, three for Hem, Nem, and Arm respectively. The clustering behaviors can be well explained by the intrinsic repulsive interaction between the inert gas atoms and the attractive interaction coming from the reduced valence-electron density by interstitial inert gas atoms. Compared to He, the much greater attraction between the Ne/Ar atoms and the lower trigger condition of ‘self-trapping process’ for Ne/Ar clusters provide a reasonable explanation for the difference of irradiation effects on tungsten between He and Ne/Ar plasmas, i.e. Ne/Ar plasmas cannot result in the formation of holes/bubbles and fiber-form nanostructures on tungsten surface under the same irradiation conditions as He plasma.

Ion irradiation induced disappearance of dislocations in a nickel-based alloy

Under Xe ion irradiation, the microstructural evolution of a nickel based alloy, Hastelloy N (US N10003), was studied. The intrinsic dislocations are decorated with irradiation induced interstitial loops and/or clusters. Moreover, the intrinsic dislocations density reduces as the irradiation damage increases. The disappearance of the intrinsic dislocations is ascribed to the dislocations climb to the free surface by the absorption of interstitials under the ion irradiation. Moreover, the in situ annealing experiment reveals that the small interstitial loops and/or clusters induced by the ion irradiation are stable below 600°C.

Inert gas bubbles in bcc Fe

The properties of inert gas bubbles in bcc Fe is examined using a combination of static energy minimisation, molecular dynamics and barrier searching methods with empirical potentials. Static energy minimisation techniques indicate that for small Ar and Xe bubbles, the preferred gas to vacancy ratio at 0 K is about 1:1 for Ar and varies between 0.5:1 and 0.9:1 for Xe. In contrast to interstitial He atoms and small He interstitial clusters, which are highly mobile in the lattice, Ar and Xe atoms prefer to occupy substitutional sites and any interstitials present in the lattice soon displace Fe atoms and become substitutional. If a pre-existing bubble is present then there is a capture radius around a bubble which extends up to the 6th neighbour position. Collision cascades can also enlarge an existing bubble by the capture of vacancies. Ar and Xe can diffuse through the lattice through vacancy driven mechanisms but with relatively high energy barriers of 1.8 and 2.0 eV respectively. This indicates that Ar and Xe bubbles are much harder to form than bubbles of He and that such gases produced in a nuclear reaction would more likely be dispersed at substitutional sites without the help of increased temperature or radiation-driven mechanisms.

Role of nickel and manganese in recovery of resistivity in iron-based alloys after low-temperature proton irradiation

This study investigates the recovery of electric resistivity in pure iron, Fe–0.6Ni and Fe–1.5Mn as related to isochronal annealing following 1 MeV proton irradiation at lower temperature than 70 K, focusing on the relationship between solute atoms and irradiation defects. Both nickel and manganese prevent stage ID recovery, which corresponds to correlated recombination. Stage II recovery is also changed by the addition of a solute, which corresponds to the migration of small interstitial clusters. In both pure iron and Fe–0.6Ni, no evident difference was observed in the stage III region, which corresponds to the migration of vacancies. In contrast, two substages appeared in the Fe–1.5Mn at a higher temperature than stage IIIB appeared in pure iron. These substages are considered to represent the release of irradiation-induced defects, which was trapped by manganese.

Genetic algorithm optimization of defect clusters in crystalline materials

A real-space genetic algorithm for the optimization of defect structures embedded in bulk crystalline materials is developed. The purpose of this method is to enable automated prediction of stable structures for a range of embedded clusters, including radiation induced defect clusters, dopant clusters, and small precipitates. The method is applied to the prediction of small interstitial clusters in cubic SiC, BCC Fe, and BCC Fe–Cr random alloys for radiation damage applications. The performance of the method is analyzed and compared to alternative techniques such as basin hopping. The technique is able to reproduce small-size defects that had been previously identified as stable or metastable structures as well as predict new mid-size defects. The structure optimization program (StructOpt) developed in this study is available under open source licensing as part of the MAterials Simulation Toolkit (MAST) and can be obtained from https://pypi.python.org/pypi/MAST.

An ab initio-based Er–He interatomic potential in hcp Er

We have developed an empirical erbium–helium (Er–He) potential by fitting to the results calculated from the ab initio method. Based on the electronic hybridization between Er and He atoms, an s-band model, along with a repulsive pair potential, has been derived to describe the Er–He interaction. The atomic configurations and the formation energies of single He defects, small He interstitial clusters (Hen) and He–vacancy (HenV) clusters obtained by ab initio calculations are used as the fitting database. The binding energies and relative stabilities of the HnVm clusters are studied by the present potential and compared with the ab initio calculations. The Er–He potential is also applied to study the migration of He in hcp Er at different temperatures, and He clustering is found to occur at 600 K in hcp Er crystal, which may be due to the anisotropic migration behavior of He interstitials.

Electrical and optical characterization of extended defects induced in p‐type Si after Si ion implantation

AbstractIn this work we present the analysis of small interstitial clusters (ICs) introduced in p‐type Si after ion implantation using deep level transient spectroscopy (DLTS) and photoluminescence. Silicon ions with energy 380 keV and fluence of 1.0 x 1012 cm‐2 have been implanted into bulk p‐type Si and post‐implant annealing at temperatures between 500 oC and 800 oC specifically to create small interstitial cluster (ICs) defects. In the samples annealed at 500 oC, DLTS spectra show deep level hole traps at EV + 0.20 eV, EV + 0.25 eV, EV + 0.36 eV, and EV + 0.50 eV. The hole traps EV + 0.36 eV and EV + 0.50 eV have been attributed to the small Si self‐interstitial clusters. After increasing the post‐implant anneals to 600 oC there is a significant decrease in defect concentration and all the defects are annealed‐out at 700 oC. Photoluminescence (PL) spectroscopy of the samples reveals optical band levels, at 1218 nm (1.019 eV), and 1233 nm (1.007 eV) which have both been attributed to interstitial cluster defects. The interstitial cluster‐related optical band levels have been observed in the samples annealed at 500 oC which correlate well with DLTS measurements. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Structures and stabilities of small carbon interstitial clusters in cubic silicon carbide

Knowledge of the configurations and stabilities of defect clusters in SiC is important for understanding radiation damage in this material, which is relevant to its nuclear and electronic applications. Such information is, however, often difficult to obtain experimentally. In this study, we perform Monte Carlo basin-hopping simulations with both empirical potential and density functional theory (DFT) calculations to search for the ground state (GS) configurations of small carbon interstitial clusters and carbon–antisite-based defects in cubic SiC (3C–SiC). Educated guesses of possible GS configurations have also been made. Our new approach can successfully identify many hitherto unknown GSs and energetically highly competitive metastable structures. For carbon penta- and hexa-interstitials, the GS structures predicted by DFT and empirical potential differ, and the plausible origin of this discrepancy is discussed from the chemical bonding point of view. Surprisingly, the GS structures of large carbon interstitial clusters in SiC are disjointed and composed of di- and tri-interstitial clusters as fundamental building blocks. Based on the present results, a possible mechanism for the carbon tri-interstitial defect to grow into the extended {111} planar interstitial defects observed in neutron-irradiated 3C–SiC is proposed. Furthermore, we show that C interstitial clusters can get trapped at a carbon antisite and form very stable complexes in SiC.

Electrical characterisation and predictive simulation of defects induced by keV Si+ implantation in n-type Si

In this work, we focused on the analysis of implantation-induced defects, mainly small interstitial clusters (ICs) and {311} defects introduced in n-type Si after ion implantation using deep level transient spectroscopy (DLTS). Silicon ions (at 160 keV or 190 keV) of fluences ranging from (0.1–8.0) × 1013 cm−2 have been implanted into n-type Si and annealed at temperatures between 500 °C and 800 °C specifically to create small ICs or {311}s rod-like defects. In samples dominated by small ICs, DLTS spectra show prominent deep levels at Ec − 0.24 eV and Ec − 0.54 eV. After increasing the fluence and temperature, i.e., reducing the number of small ICs and forming {311} defects, the peak Ec − 0.54 eV is still dominant while other electron traps Ec − 0.26 eV and Ec − 0.46 eV are introduced. There were no observable deep levels in reference, non-implanted samples. The identity and origin of all these traps are interpreted in conjunction with recently developed predictive defect simulation models.

Diffusion of small He clusters in bulk and grain boundaries in α-Fe

The diffusion properties of He interstitials and He clusters in the bulk and grain boundaries (GBs) of α-Fe have been studied using molecular dynamics with a newly developed Fe–He potential. The low migration energy barrier for a single He interstitial in the bulk is consistent with that obtained using ab initio methods. Small He clusters can migrate at low temperatures, but at higher temperatures they will kick out a self-interstitial atom (SIA) and become trapped by the vacancy, forming an He-vacancy complex. It is of great interest to note that small Hen-vacancy clusters (n<5) in the bulk are able to absorb an SIA, and the clusters become mobile again. Trapping and de-trapping of He clusters by emitting and absorbing an SIA represent an important dynamic process that provides a mechanism for the diffusion of He clusters and the nucleation of He bubbles in bulk Fe, particularly under irradiation in which numerous SIAs and vacancies are constantly being produced. A single He interstitial can migrate one-dimensionally or two-dimensionally within GBs, depending on the GB structure. Small interstitial Hen clusters (n∼1–10) can easily kick out an SIA, and become trapped by the vacancy, while the SIA quickly diffuses away from the clusters, disappearing into the GB, such that de-trapping of the He clusters by absorbing an SIA is less likely to occur. This suggests that small He clusters may be treated as relatively immobile defects in GBs. The different behavior of He clusters in the bulk compared to their behavior in GBs may explain the different He bubble sizes experimentally observed in the bulk and in GBs in reduced activation ferritic/martensitic steels that have been simultaneously neutron irradiated and He implanted.