Effects of vacancies near substitutional implants on trapping and desorption of helium — a simulation

Trapping of He by vacancies and drainage of He from substitutional implants (Ag and Kr in W) to nearby vacancies are investigated using static lattice calculations. The calculations indicate that drainage of He will occur to vacancies within a radius of 2.5 lattice units from the implant. Furthermore the trapping probability of substitutional and interstitial random walkers on a bcc lattice by substitutional traps or vacancies is calculated. When implantation-produced vacancies are present in the vicinity of the observed trap a shielding effect occurs. Trapping constants are calculated with two random walk models for both the unshielded and the shielded defect. For the latter several configurations were taken. The results show that shielding of a defect by one vacancy at a distance of three lattice units leads already to a reduction of He trapping by that defect of 30% to 40%.     

Calculations of the trapping and migration of vacancies and nickel self-interstitials in the presence of rare gases and dislocations

Recent models of swelling, void growth, and solute segregation under irradiation all require knowledge of the trapping and migration of vacancies and self-interstitials in the presence of lattice defects. The present calculations include trapping of both vacancies and nickel self-interstitials to substitutional and interstitial rare gas atoms. The results show a systematic dependence on rare gas atom size. It is found for example, that a vacancy is bound to a small fixed rare gas interstitial (He) by ～0.5 eV and to a large fixed interstitial (Xe) by ≥3 eV. In addition, a fixed substitutional rare gas or rare gas interstitial is found to be a strong trap for a self-interstitial. It is found that a single vacancy can significantly affect the migration energy of another vacancy. For example, a 0.4 eV decrease in migration energy is found at a distance of three half-lattice constants. However, this interaction is of limited range; at distances greater than five half-lattice constants vacancy migration is unaffected. The migration of vacancies near the core of a partial dislocation was also investigated. This partial is found to provide a 1 eV (compared to 1.4 eV in the bulk) path for the pipe diffusion of vacancies. In addition, the activation energy for vacancy migration along the slip plane is reduced by as much as 0.2 eV.     

Theory of He trapping, diffusion, and clustering in UO2

We have performed ab initio total energy calculations to investigate the behavior of helium and its diffusion properties in uranium dioxide (UO₂). Our investigations are based on the density functional theory within the generalized gradient approximation (GGA). The trapping behavior of He in UO₂ has been modeled with a supercell containing 96-atoms as well as uranium and oxygen vacancy trapping sites. The calculated incorporation energies show that for He a uranium vacancy is more stable than an oxygen vacancy or an octahedral interstitial site (OIS). Interstitial site hopping is found to be the rate-determining mechanism of the He diffusion process and the corresponding migration energy is computed as 2.79 eV at 0 K (with the spin-orbit coupling (SOC) included), and as 2.09 eV by using the thermally expanded lattice parameter of UO₂ at 1200 K, which is relatively close to the experimental value of 2.0 eV. The lattice expansion coefficient of He-induced swelling of UO₂ is calculated as 9 × 10⁻². For two He atoms, we have found that they form a dumbbell configuration if they are close enough to each other, and that the lattice expansion induced by a dumbbell is larger than by two distant interstitial He atoms. The clustering tendency of He has been studied for small clusters of up to six He atoms. We find that He strongly tends to cluster in the vicinity of an OIS, and that the collective action of the He atoms is sufficient to spontaneously create additional point defects around the He cluster in the UO₂ lattice.     

Stability and migration property of helium and self defects in vanadium and V-4Cr-4Ti alloy by first-principles

The stability and migration behavior of helium and self defects in vanadium and V-4Cr-4Ti alloy are studied by first-principles calculations. The tetrahedral site is found as the most stable configuration for interstitial He, followed by the octahedral and substitutional sites. Among the self defects, the monovacancy has lower formation energy (1.71 eV for V and 2.14 eV for V-4Cr-4Ti alloy) than the self interstitial ones. The migration energies for He hopping between the tetrahedral sites are 0.06 and 0.09 eV for vanadium and V-4Cr-4Ti alloy, respectively. Our calculations reveal strong repulsion between two interstitial He atoms and strong attraction between He and vacancy, suggesting that vacancy acts as a trapping site for He impurity and a seed for further bubble formation.     

First principles modelling of oxygen impurities in UN nuclear fuels

We report results of first principles VASP supercell calculations of O impurity in UN fuels placed either at an interstitial tetrahedral position or as a substitution for a host N ion. In the latter case O perfectly fits into N site producing no lattice distortion. Such the O substitutional impurity only slightly affects the formation energies of U and N vacancies nearby. In both interstitial and substitutional positions O atom attracts the additional electron density and transforms into the negatively charged ion. Oxygen incorporation into pre-existing N vacancy is energetically more favourable than into the interstitial position. The O impurities produce an additional peak at the low energy side of N contribution to the DOS calculated for uranium mononitride which could be used for the O identification by means of the UPS spectroscopy. We compare also the DOS calculated for UN and hypothetical isostructural UO. Both O solution and incorporation energies are negative, indicating that O penetration into UN fuel is the energetically favourable. The migration energy of the interstitial O ion is estimated as 2.8 eV.     

Atomistic properties of helium in hcp titanium: A first-principles study

First-principles calculations based on density functional theory have been performed to investigate the behaviors of He in hcp-type Ti. The most favorable interstitial site for He is not an ordinary octahedral or tetrahedral site, but a novel interstitial site (called FC) with a formation energy as low as 2.67 eV, locating the center of the face shared by two adjacent octahedrons. The origin was further analyzed by composition of formation energy of interstitial He defects and charge density of defect-free hcp Ti. It has also been found that an interstitial He atom can easily migrate along 〈0 0 1〉 direction with an activation energy of 0.34 eV and be trapped by another interstitial He atom with a high binding energy of 0.66 eV. In addition, the small He clusters with/without Ti vacancy have been compared in details and the formation energies of He_nV clusters with a pre-existing Ti vacancy are even higher than those of He_n clusters until n ? 3.     

Positron simulations of defects in tungsten containing hydrogen and helium

An understanding of the behavior of defects containing hydrogen or helium in tungsten is an important issue. Here the properties of defects in tungsten containing hydrogen or helium atoms have been investigated by model positron lifetime quantum-mechanical simulations. The electron and positron wave functions have been obtained in the local density approximation to the two-component density-functional theory. The calculated values of the positron lifetime correlate with the magnitude of the electron density. The vacancy-clusters without hydrogen or helium are active positron traps. The lattice relaxation of atoms around vacancy reduces the effective vacancy volume and decrease the positron lifetime at a vacancy. The hydrogen and helium atoms are trapped in tungsten by lattice vacancies and nano-voids. It was established that positron lifetime depends on the density of gas atoms inside the nano-void. Hydrogen and helium presence in the larger nano-voids considerably decrease the positron lifetime.     

Atomic diffusion mechanism of Xe in UO2

We have investigated vacancy-assisted diffusion of Xe in uranium dioxide (UO₂) calculating incorporation, binding, and migration energies. All the energy values have been obtained using the density functional theory (DFT) within the generalized gradient approximation (GGA) and the projector-augmented-wave (PAW) method. Considering spin-polarization effect, we find that the computed migration energy is reduced by and agrees well with experimental data compared to those obtained from non-magnetic calculations. We also find that an oxygen vacancy lowers the migration energy of a uranium vacancy by about 1 eV, enhancing an effective movement of vacancy clusters consisting of both uranium and oxygen vacancies. Furthermore, the strain energy of Xe is large enough to contribute to the clustering of vacancies making it the driving force for the vacancy-assisted diffusion of Xe in UO₂. In summary all the calculated results suggest that the trivacancy is a major diffusion pathway of Xe in UO₂.     

Interaction of hydrogen isotopes with metals: Deuterium trapped at lattice defects in palladium

From an interplay between theory based on the effective-medium scheme and experiments, an extremely simple picture has evolved which is capable of describing a vast number of experimental quantities related to interaction of hydrogen with metals, especially the trapping of hydrogen at defects. It is shown that the trap strengths are determined mainly by the interstitial electron density, and any open structures in the lattice leads to a trap, with the vacancies and voids being the strongest traps. It is also found theoretically and experimentally that up to six hydrogen atoms can be accomodated in a vacancy, and the change in trap strengths with occupancy has been determined. Recent results for the trapping of deuterium to defects in Pd are discussed.     

Computer simulation on the interaction between vacancy and carbon impurity in α-Fe

Metals possessing a bcc lattice have been considered as materials with high resistance to irradiation swelling. The aggregation of vacancies is the main reason of the swelling and the interaction of carbon atoms with vacancies affects the mechanical properties of metals. The complex of vacancy-carbon atom in α-Fe is modeled by MD method using a pair inter-atomic potential. The defect formation energy of vacancy-carbon atom complex was obtained by MD method. The stable site of carbon near a vacancy in three dimensions was discussed.     

Study on C-W interactions by molecular dynamics simulations

By means of molecular dynamics simulations using bond-order potential (BOP), we have investigated the interactions between carbon (C) atoms and bcc tungsten (W). At finite temperature (T = 300 K) with incident energy of C atoms ranging from 0.5 to 100 eV at normal incidence, the projected range distribution as a function of incident energy and the average depth have been depicted. The properties of vacancy, vacancy migration, interstitial and substitutional C atoms in W have been determined. The most stable configuration for an interstitial C atom in W is in octahedral position and the lattice distortion around the C atom in octahedral interstitial configuration occurs along 〈1 0 0〉 and 〈1 1 0〉 directions. The mutual interaction between a vacancy and near interstitial C atom is also studied.     

Quantum mechanical calculations of uranium phases and niobium defects in γ-uranium

Depleted uranium (U) from fuel enrichment processes has a variety of applications due to its high density. With the addition of a small concentration of niobium (Nb), U becomes stainless. Nb is fully miscible with the high-temperature γ phase of U and tends to segregate upon cooling below 1050 K. The starting point of segregation is the configuration of Nb substitutional or interstitial defects. Using quantum mechanical calculations, the authors find that the formation energy of a single vacancy is 1.08 eV, that of Nb substitution 0.59 eV, that of Nb interstitial at octahedral site 1.58 eV, and that of Nb interstitial at tetrahedral site 2.35 eV in the dilute limit of isolated defects; all with reference to a reservoir of the pure γ phase U and pure Nb. The analysis of electronic structures reveals the correlation of formation energies of Nb defects with the local perturbations of electron distribution. Higher formation energy of Nb defects correlates with larger perturbation. Based on this study, Nb atoms thermodynamically prefer to occupy substitutional sites in the γ phase U.     

Basic mechanisms for the lattice-site occupation of metallic elements implanted into aluminium

In situ ion implantation combined with channeling spectroscopy was used to show that the most important parameter which determines the lattice site occupation of implanted atoms in Al is the size mismatch energy, ΔH_size. The lattice site occupation is governed by two basic processes: spontaneous recombination of the impurities with vacancies in the relaxation phase of the collision cascade and displacement from the substitutional site by trapping point defects in the cooling phase with a probability proportional to ΔH_size.     

Ab initio study of Kr in hcp Ti: Diffusion, formation and stability of small Kr-vacancy clusters

Ab initio electronic structure calculations have been performed to study the formation and migration of Kr impurities, and the stability of small Kr-vacancy clusters for clusters with up to four vacancies and four Kr atoms, in hcp Ti. Both the substitutional and the interstitial configurations of Kr are found to be stable. The octahedral configuration is however found to be more stable than the tetrahedral. Interstitial Kr atoms are shown to have attractive interactions and a low migration barrier, suggesting that, at low temperature, Kr bubble formation is possible, even in the absence of vacancies. We also find vacancy clusters to be stable. The binding energies of an interstitial Kr atom and a vacancy to a Kr-vacancy cluster are obtained from the calculated formation energies of the clusters. The stability of small-vacancy clusters is found to be dependent on Kr-vacancy ratio. The trends of the calculated binding energies are discussed in terms of providing further insights on the behaviour of Kr in implanted Ti.     

Formation and properties of defects and small vacancy clusters in SiC: Ab initio calculations

Large-scale ab initio simulation methods have been employed to investigate the configurations and properties of defects in SiC. Atomic structures, formation energies and binding energies of small vacancy clusters have also been studied as a function of cluster size, and their relative stabilities are determined. The calculated formation energies of point defects are in good agreement with previously theoretical calculations. The results show that the di-vacancy cluster consists of two C vacancies located at the second nearest neighbor sites is stable up to 1300 K, while a di-vacancy with two Si vacancies is not stable and may dissociate at room temperature. In general, the formation energies of small vacancy clusters increase with size, but the formation energies for clusters with a Si vacancy and nC vacancies (V_Si-nV_C) are much smaller than those with a C vacancy and nSi vacancies (V_C-nV_Si). These results demonstrate that the V_Si-nV_C clusters are more stable than the V_C-nV_Si clusters in SiC, and provide possible nucleation sites for larger vacancy clusters or voids to grow. For these small vacancy clusters, the binding energy decreases with increasing cluster size, and ranges from 2.5 to 4.6 eV. These results indicate that the small vacancy clusters in SiC are stable at temperatures up to 1900 K, which is consistent with experimental observations.     

Theory of the production and depth distribution of helium defect complexes by ion implantation

The complex defect formations and migrations occurring under helium ion bombardment of Cu have been modeled by a system of coupled equations, including diffusion. Atomistic binding and migration energies were determined from two-body calculations. A new mathematical scheme was developed in order to take diffusion into account in a self-consistent fashion. The calculations were applied to the low temperature implantation and annealing experiments of Bauer and also to the (proton backscattering) profiling experiments of Blewer. The calculations indicate that the ~0° C release peak of Bauer may be due to helium interstitial migration. When applied to the Blewer experiments, the calculations indicate that the dominant defect after room temperature implantation is six helium atoms in a vacancy (He₆V). The shape and position of the total helium distribution is not altered by isochronal annealing (because of the trapping of vacancies by the helium), but the helium is released directly from the damage which traps it.     

First-principles approach to the properties of point defects and small helium-vacancy clusters in palladium

First-principles calculations based on density functional theory (DFT) have been performed to study the properties of interstitial helium atoms, the vacancy, substitutional, and small helium-vacancy clusters He_mV_n (m, n = 0-4) in palladium. The result indicates that the vacancy has the strongest ability of capturing helium atoms and the octahedral interstitial configuration is more stable than the tetrahedral one, while the energy difference between them is very small. In the palladium crystal, helium atom will migrate from one octahedral interstitial site to another one through the O-T-O path. The formation energies and binding energies of an interstitial helium atom and an isolated vacancy to the helium-vacancy clusters are also determined in palladium. It is found that the formation energies increase with the increasing of helium atoms and the binding energies mainly depend on the helium to vacancy ratio of the clusters rather than the cluster size.     

Axial channeling by an intersecting plane potential

A model for 〈100〉 axial channeling based on the electrostatic potential of two mutually perpendicular sets of intersecting parallel planes is used to calculate the close-encounter probability between incident particles and planar lattice atoms. The development of the model was in the context of extending channeling calculations to octahedron clusters. Assumptions and geometrical constraints are discussed, and the results of the calculations are compared with recent experimental angular scans for the B atoms in LaB₆.     

Atomistic simulations of point defects in ZrNi intermetallic compounds

The properties of point defects, including stable configurations, formation and migration energies, and migration mechanisms, in the ZrNi and Zr₂Ni intermetallic compounds were simulated using molecular dynamics and statics, in conjunction with interatomic potentials derived from the Embedded Atom Method. We describe a method to calculate the formation energy of point defects from the program and apply the method to ZrNi and Zr₂Ni. The results showed that vacancies are most stable in the Ni sublattice, with formation energy of 0.83 and 0.61 eV in ZrNi and Zr₂Ni, respectively. Zr vacancies are unstable in both compounds; they spontaneously decay to pairs of Ni vacancy and antisite defect. The interstitial configurations and formation energies were also calculated, with similar behaviors. In ZrNi, vacancy migration occurs preferentially in the [0 2 5] and [1 0 0] directions, with migration energy of 0.67 and 0.73 eV, respectively, and is essentially a two-dimensional process, in the (0 0 1) plane. In Zr₂Ni, vacancy migration is one-dimensional, occurring in the [0 0 1] direction, with a migration energy of 0.67 eV. In both compounds, the presence of Ni antisite defects decreases the Ni vacancy migration energy by up to a factor-of-three, and facilitates three-dimensional motion.     

Interatomic potentials for simulation of He bubble formation in W

A new interatomic pair potential for W–He is described, which includes a short range modification to the Ackland–Thetford tungsten potential. Molecular dynamics simulations using these potentials accurately reproduce ab initio results of the formation energies and ground state positions of He point defects and self interstitial atoms in W. Simulations of larger He–vacancy clusters with up to 20 vacancies and 120 He atoms show strong binding of both He and vacancies to He–vacancy clusters for all cluster sizes. For small clusters, the qualitative agreement with ab initio results is good, although the vacancy binding energy is overestimated by the interatomic potential.