Helium-vacancy Clusters Research Articles

Interaction of helium–vacancy clusters with edge dislocations in α-Fe

Molecular static calculations were performed to evaluate the formation energies and binding energies of helium–vacancy (He–V) clusters in and near the core of an a/2<111>{110} edge dislocation in α-Fe with empirical potentials. The formation energies of these He–V clusters and their binding energies to the dislocation depend on the helium-to-vacancy ratio of the clusters. For the ratio equal to or larger than 1, the helium–vacancy clusters have negative binding energies on the compression side of the dislocation and strong positive binding energy on the tension side. However, for the ratio less than 1, the He–V clusters have positive binding energy on the both sides near the dislocation core. On the slip plane, the binding energies of the He–V clusters to the dislocation depend on not only the helium-to-vacancy ratio, but also the cluster size.

A Molecular Dynamics Study of Helium-Vacancy Clusters Production due to Cascades in α-Iron

Molecular dynamics (MD) methods are utilized to study the displacement cascades in α-Fe containing different concentrations of substitutional He atoms. Primary knock-on atom (PKA) energies, Ep, from o.5 keV to 20 keV are considered at a temperature of 100 K and 600 K, and the results are compared with those performed in pure α-Fe. There are distinct differences in the number and size of defect clusters within displacement cascades with and without substitutional helium atoms. Particularly, the number and size of helium-vacancy clusters generally increase with increasing helium concentration and PKA energy. However, the number of He-vacancy (He-V) clusters increases with increasing temperature, the mean size of He-V clusters is independent on temperature for the same He concentration and energy recoils.

Accumulation of helium in tungsten irradiated by helium and neutrons

Effects of helium on the microstructural evolution in tungsten were investigated using computer simulation based on a rate theory. Two cases were considered: helium with high energy (1 keV) and low flux (10 18/m 2s) and helium with low energy (30 eV, which cannot produce displacement damage) and high flux (10 22/m 2s). Neutron irradiation at 10 −6 dpa/s and 873 K was used in the calculations as a typical irradiation condition. Helium–vacancy clusters with high concentration were formed near the incident surface during neutron and helium irradiations. The formation of helium–vacancy clusters suppressed the helium diffusion deeper into the specimen. The results show that a helium plasma with low energy and high flux has a greater effect on the accumulation of helium–vacancy clusters near the incident surface than would a helium plasma with high energy and low flux.

Interaction between helium and self-defects in α-iron from first principles

The interaction between helium and self-defects in α-iron has been studied by means of density functional theory calculations. We show that the fast migrating interstitial helium atoms, which are known to strongly interact with vacancies, can also be weakly trapped by self-interstitial atoms, with a binding energy of about 0.3 eV. The small He n clusters, which can form as a result of the attractive interaction between interstitial helium atoms, induce strong lattice distortions and we predict that the emission of a self-interstitial atom is energetically favorable for n > 4. We also report on the structural and energetic properties of small helium–vacancy clusters (He n V m ) with n/ m ratio around the optimal value with respect to the emission of vacancy or helium ( n/ m ≃ 1.3). We suggest that helium dissociation from these clusters can be responsible for stages above 700 K (II and IV) observed in thermal helium desorption spectra.

Diffusion coefficients and thermal stability of small helium–vacancy clusters in iron

Recent studies of helium clustering kinetics in bcc iron have revealed noticeable mobility of small He–vacancy complexes, which are commonly thought of as immobile. Here, the lifetimes and diffusion coefficients of small He–vacancy clusters were quantified. These kinetic parameters were estimated for clusters of different sizes and compositions by lattice kinetic Monte-Carlo using ab initio data for helium and vacancy interactions energies. It is shown that nanosized He–vacancy clusters have high thermal stability. It is also found that the diffusion coefficients of some small clusters are indeed very high, being at 573K only 1–2 orders of magnitude lower than the diffusion coefficient of a monovacancy. Finally, it is demonstrated how the coupling of Monte-Carlo numeric experiments with the rate theory approach can be used for the estimation of the rate theory parameters, such as the defect and cluster agglomeration rates.

Kinetics of coarsening of helium bubbles during implantation and post-implantation annealing

To understand the effects of He on irradiated metals requires modeling of helium-vacancy cluster evolution. A new method of solving the two-dimensional master equation (ME) describing He-vacancy cluster evolution has been applied to calculate helium bubble evolution in a stainless steel irradiated with alpha particles near room temperature and annealed in the temperature range of 600–900°C. For the first time, the evolution of the helium bubble size distribution function was precisely calculated in 2-D phase space and good agreement with experimental results was obtained. The results indicate that Brownian motion of bubbles via surface vacancy diffusion provides a reasonable explanation for bubble evolution during annealing, most bubbles are found to be near the equilibrium state during the evolution at temperatures of 700°C and higher, lack of vacancies at temperatures lower than 700°C prevents bubble growth, and use of a non-ideal He equation of state (EOS) increases the bubble density and size relative to the case when the ideal EOS is used.

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.

Atomistic evaluation of the point defect capture efficiency of He-V clusters in α-Fe

The displacement field around a helium-vacancy (He-V) cluster in Fe is evaluated by molecular dynamics and molecular static calculations. When the He pressure of a He-V cluster is high, Fe displacements are compressive in the direction away from the cluster, but expansive in the azimuthal angle direction. When the pressure is much higher, Fe atoms on the cluster surface are pushed off from their regular lattice positions due to high pressures and such displaced Fe atoms prefer to be localized on the same side of the cluster rather than uniformly distributed over the cluster surface. With the displacement field thus obtained, the interaction energy of point defects with the strain field of a He-V cluster is evaluated using elasticity theory. Finally, a method is developed to obtain the capture efficiency of He-V clusters for point defects.

Defect production and formation of helium–vacancy clusters due to cascades in α-iron

Displacement cascades are simulated by molecular dynamics methods in α-Fe containing different concentrations of substitutional He atoms. Primary knock-on atom (PKA) energies, E p, from 0.5 to 5 keV are considered at the irradiation temperature of 100 K. The concentration of He in Fe varies from 1 to 5 at%, and the results are compared with the simulations performed in pure α-Fe. We find that the total number of point defects increases with increasing He concentration. The present studies reveal the formation and the configurations of He–vacancy clusters in the cascades of α-Fe. Furthermore, the production efficiency of He–vacancy clusters increases with increasing He concentration and PKA energy. The nucleation mechanisms of He–vacancy clusters in displacement cascades are discussed in detail.

Kinetic Monte Carlo simulations applied to irradiated materials: The effect of cascade damage in defect nucleation and growth

Kinetic Monte Carlo is used extensively in the field of radiation effects to understand damage accumulation and growth under irradiation. These calculations require previous knowledge on the formation of these defects, the relative stabilities of the different types of defects, their interactions and their mobilities. Many of these parameters can be extracted from molecular dynamics calculations using empirical potentials or from ab initio calculations. However, the number of parameters necessary for a complete picture is rather large. Kinetic Monte Carlo can be used as a tool to isolate those parameters that most influence the outcome of the calculations. In this paper, we focus on one aspect: the form of the damage after the collision cascade. We describe the effect of the form of the cascade as obtained from molecular dynamics simulations on damage accumulation. In particular, we demonstrate that the form of the cascade drastically changes the nucleation and growth of helium-vacancy clusters, possible precursors of voids and bubbles. Finally, we point to those open questions that need to be resolved to develop a truly predictive kinetic Monte Carlo model.

Atomistic behavior of helium–vacancy clusters in aluminum

We have performed a molecular dynamics (MD) technique to calculate the formation energies of small He n V m clusters in Al using the embedded atom method (EAM), the Baskes–Melius potential and the Lennard-Jones potential for describing the interactions of Al–Al, Al–He and He–He, respectively. The binding energies of an interstitial He atom, an isolated vacancy and a self-interstitial Al atom to a He n V m cluster are also obtained from the calculated formation energies of the clusters. All the binding energies mainly depend on the He–vacancy ratio ( n/ m) of clusters rather than the clusters size. The binding energies of a He atom and an Al atom to a He n V m cluster decrease with the ratio, but the binding energy of a vacancy to a He n V m cluster increases with the ratio. The results indeed show that He atoms can increase the binding energy of a vacancy to a He n V m cluster, and decrease the binding energies of a He atom and an Al atom to the cluster, namely, He atom acts as a catalyst for the formation of He n V m clusters.

The Formation Energies and Binding Energies of Helium Vacancy Cluster: Comparative Study in Ni and Pd

Molecular dynamics calculations are performed to calculate the formation energy for helium in Ni-vacancy and Pd-vacancy clusters. The binding energies of helium and metal self-interstitial atoms (SIA) to the helium-vacancy cluster are also determined. The comparison of these energies indicates that helium to vacancy ratio (He/V) for helium in Pd is much higher.

Ab initiostudy of helium inα−Fe: Dissolution, migration, and clustering with vacancies

Density functional theory calculations have been performed to study the dissolution and migration of helium in $\ensuremath{\alpha}$-iron, and the stability of small helium-vacancy clusters ${\mathrm{He}}_{n}{V}_{m}$ ($n$,$m=0$ to 4). Substitutional and interstitial configurations of helium are found to have similar stabilities. The tetrahedral configuration is more stable than the octahedral by 0.2 eV. Interstitial helium atoms are predicted to have attractive interactions and a very low migration energy (0.06 eV), suggesting that He bubbles can form at low temperatures in initially vacancy-free lattices. The migration of substitutional helium by the vacancy mechanism is governed by the migration of the ${\mathrm{HeV}}_{2}$ complex, with an energy barrier of 1.1 eV. The activation energies for helium diffusion by the dissociation and vacancy mechanisms are estimated for the limiting cases of thermal-vacancy regime and of high supersaturation of vacancies. The trends of the binding energies of vacancy and helium to helium-vacancy clusters are discussed in terms of providing additional knowledge on the behavior of He in irradiated iron, necessary for the interpretation of complex experimental data such as thermal He desorption spectra.

Helium-Charged La-Ni-Al Thin Films Deposited by Magnetron Sputtering

An advanced implantation of low energy helium-4 atoms during the La-Ni-Al film growth by adopting magnetron sputtering with Ar/He mixture gases is discussed. Both proton backscattering spectroscopy (PBS) and elastic recoil detection (ERD) analyses were adopted to measure helium concentration of the films and distribution in the near-surface region. Helium atoms with a high concentration incorporate evenly in deposited film. The introduction of the helium with no extra irradiation damage is expected by choosing suitable deposition conditions. It was found that amorphous and crystalline LaNi5-type structures can be achieved when sputtered with pure Ar and Ar/He mixture gases at room temperature, respectively. Thermal desorption experiments proposes that a part of hydrogen atoms are bound to trapped helium at crystal and releases together with helium. Only a small fraction of helium is released from the helium-vacancy clusters in lower temperature range and most of helium is released from small size helium bubbles in the high temperature range.

Defect production and formation of helium-vacancy clusters in cascades of α-iron with different concentration of helium

The low-temperature displacement cascades in α-Fe with different concentrations of substitutional He atoms are simulated by molecular dynamics (MD) methods. Primary knock-on atom (PKA) energy, Ep , from 500eV to 5keV is cons idered for irradiation temperature of 100K. The concentration of He in Fe varies from 1% to 5%. The results are compared with those obtained in pure α-Fe. We f ind the number of Frenkel pairs (NF) in Fe with low concentration of He atoms is nearly equal to those in pure Fe, but increases with increasing He c oncentration. The present study demonstrates for the first time that He-vacancy bubbles can be nucleated directly from displacement cascades, even at low tempe rature at which the vacancies are not mobile. However, the efficiency of He-vaca ncy clusters increases with increasing the concentration of He for the same ener gy recoils, and increases with increasing Ep for the same concentrati on of He. The mechanisms of He bubble nucleation in displacement cascades are di scussed in detail.

Dynamic Simulation of Multiplier Effects of Helium Plasma and Neutron Irradiation on Microstructural Evolution in Tungsten

Plasma-facing and high heat flux materials in a fusion reactor suffer two types of damage: displacement damage caused mainly by high- energy neutrons and surface damage, such as erosion, sputtering, and blistering, caused by hydrogen and helium plasma. Usually, these two kinds of damage are investigated separately. In the present study, multiplier effects of helium plasma and neutron irradiation on microstructural evolution in tungsten were investigated using computer simulations based on a rate theory. Neutron irradiation with 10 � 6 dpas � 1 at 873 K and a helium flux of 10 18 m � 2 � s � 1 with 10-keV energy were used as typical irradiation conditions. The effects of irradiation temperature and defect production rate on the interaction between helium and defects were also investigated. The simulation results revealed the rapid diffusion of helium in tungsten. The helium concentration was saturated in tungsten 0.067 mm thick within 0.01 s at 873 K, and the formation of helium- vacancy clusters was nearly uniform in the matrix except at the surfaces facing towards and away from the irradiation after 0.01 s. This meant that the 10-keV helium plasma could enhance formation of helium-vacancy clusters in the region without damage produced by helium. The concentration of 6He-V clusters reached a very high level (10 � 6 ) even after a 1-s irradiation with a defect production rate of 10 � 6 dpas � 1 at 873 K. The concentration of helium-vacancy clusters decreased with increasing irradiation temperature and decreasing defect production rate. The accumulation of helium and the formation of helium-vacancy clusters depended on not only the vacancy concentration, which was determined by the irradiation temperature and defect production rate, and helium concentrations, but also irradiation time.

MD and KMC modeling of the growth and shrinkage mechanisms of helium–vacancy clusters in Fe

A multiscale modeling approach, which is based on atomistic simulations, was applied to investigate the growth and shrinkage mechanisms of helium–vacancy (He–V) clusters in Fe. Firstly, a molecular dynamics technique with empirical interatomic potentials was used to determine energies for the formation and dissociation of clusters as a function of their size and He density. Both the number of He atoms and vacancies in a cluster ranged from 0 to 20. The dissociation energy of clusters showed a strong dependence on the He density, rather than the cluster size, indicating that the growth and shrinkage of clusters strongly depend on the He density. Secondly, these dissociation energies were employed in a kinetic Monte-Carlo (KMC) simulation, to explore long-time cluster behavior. The KMC simulation indicated that He can stabilize He–V clusters by suppressing thermal vacancy emission and by promoting thermal self-interstitial Fe atom emission. A preliminary KMC simulation to investigate the migration behavior of He–V clusters is also presented.

Thermal Stability of Helium-Vacancy Clusters and Bubble Formation - Multiscale Modeling Approach for Fusion Materials Development

The recent progress on our multiscale modeling to understand radiation damage processes in materials during irradiation is reviewed. The energies of He-V cluster formation in Fe were evaluated using a molecular dynamics (MD) simulation technique that employed interatomic potentials partially developed by first-principle (FP) calculations. Using the calculated energies, the longer timescale behavior of He-V clusters in Fe was investigated using a kinetic Monte-Carlo (KMC) simulation technique. The FP-MD-KMC scheme provided us significant information on the thermal stability of a He-V cluster in Fe as a function of the helium-to-vacancy ratio of the cluster.

Thermal stability of helium–vacancy clusters in iron

Molecular dynamics calculations were performed to evaluate the thermal stability of helium–vacancy clusters (He n V m ) in Fe using the Ackland Finnis–Sinclair potential, the Wilson–Johnson potential and the Ziegler–Biersack–Littmark–Beck potential for describing the interactions of Fe–Fe, Fe–He and He–He, respectively. Both the calculated numbers of helium atoms, n, and vacancies, m, in clusters ranged from 0 to 20. The binding energies of an interstitial helium atom, an isolated vacancy and a self-interstitial iron atom to a helium–vacancy cluster were obtained from the calculated formation energies of clusters. All the binding energies do not depend much on cluster size, but they primarily depend on the helium-to-vacancy ratio ( n/ m) of clusters. The binding energy of a vacancy to a helium–vacancy cluster increases with the ratio, showing that helium increases cluster lifetime by dramatically reducing thermal vacancy emission. On the other hand, both the binding energies of a helium atom and an iron atom to a helium–vacancy cluster decrease with increasing the ratio, indicating that thermal emission of self-interstitial atoms (SIAs) (i.e. Frenkel-pair production), as well as thermal helium emission, may take place from the cluster of higher helium-to-vacancy ratios. The thermal stability of clusters is decided by the competitive processes among thermal emission of vacancies, SIAs and helium, depending on the helium-to-vacancy ratio of clusters. The calculated thermal stability of clusters is consistent with the experimental observations of thermal helium desorption from α-Fe during post-He-implantation annealing.

Atomic mechanisms and energetics of thermally activated processes of helium redistribution in vanadium

Semi-empirical potentials of helium–helium and helium–vanadium interactions in vanadium are calculated based on the earlier developed theoretical model of a metal crystal which includes contributions of two-body components of atomic interactions and the s- and d-electrons into the binding energy of transition metals. Using the molecular dynamics (MD)-method the equilibrium properties (energies, entropies, relaxation volumes and others) are calculated and the atomic configurations of helium-vacancy clusters (He n V m , n⩽15, m⩽3) with the minimum free energy of formation are determined. The most probable mechanisms of helium clustering and diffusion are defined. Energetic criteria for realization of the main processes which contribute to the experimental helium thermal desorption spectra are investigated with reference to the experiments on thermal helium desorption spectroscopy (THDS).