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.     

Molecular Statics Simulation of Hydrogen Defect Interaction in Tungsten

Hydrogen(H) defect interactions have been investigated by molecular statics simulations in tungsten(W),including H-H interactions and interactions between H and W selfinterstitial atoms.The interactions between H and small H-vacancy clusters are also demonstrated;the binding energies of an H,a vacancy and a self-interstitial W to an H-vacancy cluster depend on the H-to-vacancy ratio.We conclude that H bubble formation needs a high concentration of H in W for the H bubble nucleation and growth,which are also governed by the H-to-vacancy ratio of the cluster.The vacancy first combines with H atoms and a cluster forms,then the H-vacancy cluster goes through the whole process of vacancy capture,H capture,and vacancy capture again,and as a result the H-vacancy cluster grows larger and larger.Finally,the H bubble forms.     

Energetics of He and H atoms with vacancies in tungsten: First-principles approach

The formation energies of various defect configurations of He and H atoms in W were estimated based on the density functional theory. A special consideration was given to the coexistence of the He and H atoms at the presence of the vacancy and vacancy cluster in W. A single He atom favors a substitutional site, while a H atom spontaneously incorporates at an interstitial site with the negative formation energy. When He and H are present close to each other, they form an interstitial pair, occupying relaxed tetrahedral sites. When He, H and a vacancy coexist within a unit cell of W, however, He occupies the vacancy site then the He_sub-H_tet pair is predicted to be the lowest energy configuration. At the presence of a nearby vacancy cluster, He atoms occupy the vacant space while H atoms move slightly toward W.     

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.     

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.     

Molecular dynamics simulation of helium-vacancy interaction in plutonium

The formation energies of small He_nV_m clusters (n and m denote the number of He atoms and vacancy, respectively) in Pu have been calculated with molecular dynamics (MD) simulations using the embedded atom method (EAM) potential, the Mores potential and the Lennard-Jones potential for describing the interactions of Pu-Pu, Pu-He and He-He, respectively. The binding energies of an interstitial He atom, an isolated vacancy and a self-interstitial Pu atom to a He_nV_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. With the increase of the n/m ratio, the binding energies of a He atom and a Pu atom to a He_nV_m cluster decrease with the ratio, and the binding energy of a vacancy to a He_nV_m cluster increases. He atoms act as a catalyst for the formation of He_nV_m clusters.     

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.     

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.     

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.     

Atomistic behavior of helium-vacancy clusters in aluminum

We have performed a molecular dynamics (MD) technique to calculate the formation energies of small He_nV_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_nV_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_nV_m cluster decrease with the ratio, but the binding energy of a vacancy to a He_nV_m cluster increases with the ratio. The results indeed show that He atoms can increase the binding energy of a vacancy to a He_nV_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_nV_m clusters.     

Modelling of deposition processes on the TiO2 rutile (1 1 0) surface

Deposition of Ti_xO_y clusters onto the rutile TiO₂ (1 1 0) surface has been modelled using empirical potential based molecular dynamics. Deposition energies in the range 10-40 eV have been considered so as to model typical deposition energies of magnetron sputtering. Defects formed as a function of both the deposition energy and deposition species have been studied.The results show that in the majority of cases Ti interstitial atoms are formed, irrespective of whether Ti was contained within the deposited cluster. Furthermore that the majority of these interstitials are formed by displacing a surface Ti atom into the interstitial site. O surface atoms are also relatively common, with Ti and TiO₂ surface units often occurring when the deposited cluster contains Ti but becoming less frequent as the deposition energy is increased. Structures that would give rise to the growth of further layers of rutile are not observed and in the majority of the simulations the energy barriers for diffusion of the end-products is high.     

First-principles investigation on dissolution and diffusion of oxygen in tungsten

Using a first-principles method, we have investigated dissolution and diffusion properties of oxygen (O) in tungsten (W). Single O atom prefers to occupy the tetrahedral interstitial site (TIS). Two interstitial O atoms are attractive and tend to be paired up at two neighboring TIS with a distance of 0.228 nm and a large binding energy of 1.60 eV, which indicates a strong tendency of O clustering in W. O is preferred to diffuse between the most nearest neighboring TIS with a diffusion barrier of 0.17 eV. By the estimation of pre-exponential factor according to an empirical theory, the diffusion coefficient as a function of temperature has been determined, which is 1.50 × 10⁻⁹ m²/s at a typical temperature of 500 K. The results provide a good reference to understand the behavior of O in intrinsic W.     

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.     

The co-precipitation of vacancies and carbon atoms in quenched platinum

The geometry of secondary defect structures observed in quenched platinum containing various amounts of carbon is shown to be consistent with a simple model based on the premise of a strong impurity (carbon) atom/vacancy binding energy. When the ratio of carbon atoms to vacancies (C_c/C_v) is large, co-precipitation as platelets on {100} planes occurs; whereas when C_c/C_v is small, the effects of carbon are still manifest; the defect geometry is dominated by the vacancy behavior, and loops on {111} planes form. Consideration of the mechanism of defect formation on {100} planes leads to conclusions about the structure of the carbon atom/vacancy complex, its migration and stability. An electron microscopy analysis of the {100} defects is in excellent accord with the proposed model. Implications concerning the likely behavior of carbon atoms in a radiation environment are considered, and an interstitial impurity solute segregation effect to vacancy sinks is predicted.     

Ab initio study electronic structures of LiYF4 crystal containing interstitial oxygen atoms

The positions of the interstitial oxygen atoms in LiYF₄ crystal are simulated by computer technologies. It is found that the total energy of cluster is low when interstitial oxygen atoms exist around the Li⁺ ion. Basing on the computer results, the electronic structures of perfect LiYF₄ and the LiYF₄ containing interstitial oxygen atoms with the lattice structure optimized are studied within the framework of the density functional theory. By analyzing the calculated results it can be concluded that an interstitial oxygen atom could combine with formal lattice fluorine ions forming molecular ions, which cause the 260 nm absorption band.     

Molecular dynamics simulations of oxygen Frenkel pairs in cerium dioxide

Molecular dynamics simulations of oxygen Frenkel pairs (FPs) in cerium dioxide (CeO₂) were carried out in order to understand their kinetic behavior. The results show that an oxygen FP recombine with the vacancy and the interstitial after the vacancy jump preferentially along the 〈1 0 0〉 direction. When multiple oxygen FPs are introduced, the interstitials aggregate into a (1 1 1) plate-like cluster at relatively lower temperature lower than 600 K, while they recombine with vacancies at elevated temperatures higher than 900 K within 10 ps. Molecular mechanics calculations of oxygen FPs on a (1 1 1) plane show that the formation energy per a FP decreases with increase of the number of FPs. The theoretical results are consistent with the transmission electron microscopy observations of formation of 1/9〈1 1 1〉{1 1 1} oxygen interstitial platelets in CeO₂ under electron irradiation.     

First-principles investigation of energetics and site preference of He in a W grain boundary

We perform first-principles calculations based on density functional theory to investigate energetics and site preference of He in a bcc-W Σ = 5 grain boundary (GB). The segregation energy is calculated to be −1.37 eV, indicating that He prefers to segregate in the W GB. The formation energy of He in the W GB is positive and thus He is quite hard to dissolve in the W GB, similar to its behavior in the bulk. Because of its closed-shell electronic structure, He is shown to preferably occupy either interstitial or substitutional site with larger space provided by the GB, changing the GB electronic structure. Moreover, segregation of He gives rise to the W GB expansion. These structure variations can have a large effect on the mechanical properties of the W GB.     

Computer study of intrinsic defects in CaWO4

A computer simulation has been performed to study the intrinsic defects in CaWO₄. The inter-atomic interaction potentials are empirically fitted to the known crystal properties. The results reveal that the predominant intrinsic defects existed in the crystal should be oxygen Frenkel-type. Calculated formation energies of electronic defects suggest that the hole is easier to be trapped by oxygen ion than by calcium ion, and oxygen would prior to occupy the oxygen vacancy during the annihilation under oxidation atmosphere. An analysis of activation energy shows that oxygen vacancy migration is movable ionic defects in CaWO₄.     

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.     

Dependence of cluster ranges on target cohesive energy: Molecular-dynamics study of energetic Au402 cluster impacts

It has long been known that the stopping and ranges of atoms and clusters depends on the projectile-target atom mass ratio. Recently, Carroll et al. [S.J. Carroll, P.D. Nellist, R.E. Palmer, S. Hobday, R. Smith, Phys. Rev. Lett. 84 (2000) 2654] proposed that the stopping of clusters also depends on the cohesive energy of the target. We investigate this dependence using a series of molecular-dynamics simulations, in which we systematically change the target cohesive energy, while keeping all other parameters fixed. We focus on the specific case of Au₄₀₂ cluster impact on van-der-Waals bonded targets. As target, we employ Lennard-Jones materials based on the parameters of Ar, but for which we vary the cohesive energy artificially up to a factor of 20. We show that for small impact energies, E₀ ? 100 eV/atom, the range D depends on the target cohesive energy U, D ∝ U^−β. The exponent β increases with decreasing projectile energy and assumes values up to β = 0.25 for E₀ = 10 eV/atom. For higher impact energies, the cluster range becomes independent of the target cohesive energy. These results have their origin in the so-called ‘clearing-the way’ effect of the heavy Au₄₀₂ cluster; this effect is strongly reduced for E₀ ? 100 eV/atom when projectile fragmentation sets in, and the fragments are stopped independently of each other. These results are relevant for studies of cluster stopping and ranges in soft matter.