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.     

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.     

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.     

Simulating radiation damage in δ-plutonium

Radiation events in δ-Pu (fcc) have been simulated in an attempt to understand the fundamental mechanisms that contribute to the Pu ageing process. The Pu interactions are modelled using a potential based on the modified embedded atom method (MEAM). The energetics of point defects have been investigated using static calculations together with molecular dynamics (MD) to simulate radiation events. All MD simulations were carried out with Pu initially in the face-centred-cubic (fcc) structure, although this is not the lowest energy configuration for the pure metal.The point defect study suggests that the mono-vacancy has the lowest formation energy (0.46 eV), with interstitial defects favouring the - split orientation over occupation of the native fcc octahedral site. Displacement threshold energy calculations at room temperature give a minimum value of between 5 and 6 eV, increasing to 8-14 eV along the major crystallographic directions.Low energy collision cascades, initiated with energies in the range of 0.4-1 keV, show that the cascades form in a similar manner to other fcc metals with a vacancy rich zone at the cascade core, surrounded by isolated interstitial defects. Higher energy cascades show similar features but with occasional channelling of energetic atoms and sub-cascade branching which significantly reduces defect production. A common trait observed across all the cascades was the relatively slow annealing period, compared to cascades in other fcc metals, with simulations at energies above 5 keV requiring many 10’s of picoseconds before the ballistic phase was completed.     

Molecular dynamics simulation of interaction of H with vacancy in W

Molecular dynamics simulations were performed to investigate the interaction between H and vacancy in W using an analytical bond-order potential to describe the interactions between W-W, W-H and H-H. The most stable configuration for H in W is the tetrahedron interstitial site. We calculated the binding energies of an H and a vacancy to an H-vacancy cluster (H_nV_m) in W, respectively, where n and m ranged from 0 to 10. The binding energy was almost unchanged. The binding energy of a vacancy to H-vacancy cluster is about 0.4 eV, which is higher than the binding energy of an H to H-vacancy cluster. Vacancy is much easier to bond with H-vacancy cluster than H. And H is easier to stay in the tetrahedron interstitial site or octahedron interstitial site in bcc 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.     

Effect of He on the structure and bonding properties of W: A first-principles computational tensile test

Using a first-principles computational tensile test (FPCTT), we have investigated the effect of helium (He) on the structure and bonding properties of tungsten (W), which is a promising plasma-facing material in nuclear fusion Tokamak. Density of states results reveal the underlying reason that the substitutional site for He is the most energetically favorable, while the tetrahedral interstitial site is more favorable than the octahedral interstitial one. The FPCTT shows that the ideal tensile strength is 29.1 GPa at the strain of 14% along the [0 0 1] direction for intrinsic W, while it decreases to 28.2 GPa at the same strain when one impurity He atom is introduced. A local bond-breaking region around He forms in the tensile process due to the presence of He, which suggests He will have a large effect on the bonding properties of W.     

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.     

Channelling studies on the lattice location of B atoms in graphite

In order to obtain information on the lattice location of B atoms in graphite, channelling experiments have been performed at room temperature with a proton beam of an energy of 0.65-0.77 MeV for the 〈0 0 0 1〉 axial channel in highly oriented pyrolytic graphite (HOPG) crystals doped with 0.32 at.% B. The B atoms are detected by measuring α-particles which are emitted as a result of a nuclear reaction ¹¹B(p,α)αα. It is clearly demonstrated that most of B atoms are shadowed behind the 〈0 0 0 1〉 C atomic rows. Taking account of the already reported experimental results on a change of lattice parameters by B-doping, it is concluded that most of B atoms are located at substitutional sites. It is also observed that B-doping introduces lattice strain on the c-plane. In addition, the presence of a small portion of interstitial B atoms is suggested.     

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.     

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.     

Formation of dislocation loops in silicon by ion irradiation for silicon light emitting diodes

We have studied the influence of the ion species, ion energy, fluence, irradiation temperature and post-implantation annealing on the formation of shallow dislocation loops in silicon, for fabrication of silicon light emitting diodes. The substrates used were (1 0 0) Si, implanted with 20-80 keV boron at room temperature and 75-175 keV silicon at 100 and 200 °C. The implanted fluences were from 5 × 10¹⁴ to 1 × 10¹⁵ ions/cm². After irradiation the samples were processed for 15 s to 20 min at 950 °C by rapid thermal annealing. Structural analysis of the samples was done by transmission electron microscopy and Rutherford backscattering spectrometry. In all irradiations the silicon substrates were not amorphized, and that resulted in the formation of extrinsic perfect and faulted dislocation loops with Burgers vectors a/2〈1 1 0〉 and a/3〈1 1 1〉, respectively, sitting in {1 1 1} habit planes. It was demonstrated that by varying the ion implantation parameters and post-irradiation annealing, it is possible to form various shapes, concentration and distribution of dislocation loops in silicon.     

Post-annealing temperature dependence of blistering in high-fluence ion-implanted H in Si 〈1 0 0〉

This study examined the influence of post-annealing temperature on blister formation and growth in ion-implanted H in Si 〈1 0 0〉. Ion energy levels of 40 and 100 keV and fluences of 2 × 10¹⁶ and 5 × 10¹⁶ cm⁻² were investigated. Post-annealing treatments were performed using the furnace annealing (FA) method with temperatures ranging from 200 to 600 °C for a duration of 1 h. Raman scattering spectroscopy (RSS), optical microscopy (OM), secondary ion mass spectrometry (SIMS), atomic force microscopy (AFM), and cross-sectional transmission electron microscopy (XTEM) were employed to explore the mechanisms behind the smart cut technique. The results revealed that variations among the transformation of the VH₃ (or V₂H₆) defect complex phase into the Si(1 0 0):H bonding configuration phase (RSS results), the appearance of optically detectable blisters and craters (OM results), the average depth of craters (AFM results), the trapping of hydrogen atoms and gettering of oxygen atoms (SIMS results), and the damaged microstructures (XTEM results) against post-annealing temperature were in close correspondence. It was also found that the optimal post-annealing temperature for blister formation and growth was 550 °C.     

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.     

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.     

Confinement of motion of interstitial clusters and dislocation loops in BCC Fe-Cr alloys

This work is devoted to the study of the effect of Cr solutes on the mobility of self interstitial atom (SIA) clusters and small interstitial dislocation loops (of size up to a few nanometers) in concentrated Fe-Cr alloys. Atomistic simulations have been performed to characterize the variation of the free energy of interstitial loops in the Fe-15Cr alloy using the experimentally determined profile of Cr distribution along the path of a loop. It is shown that the presence of randomly distributed Cr in Fe leads to the creation of local trapping configurations for small SIA clusters. The strength (trapping energy) and density of these configurations depend on the Cr content. On the contrary, large SIA clusters (which can be described as 1/2〈1 1 1〉 dislocation loops) are strongly affected by the presence Cr-Cr pairs and larger Cr clusters, which act as barriers to their motion.     

Electronic structures of β-SiC containing point defects studied by DV-Xα method

The DV-Xα method was used to calculate the bond order between atoms in cubic silicon carbide (β-SiC) with a point defect. Three types of β-SiC cluster models were used: pure cluster, vacancy cluster and interstitial cluster. The bond order was influenced by the kind of defects. The bonds between C interstitial and neighboring C atoms were composed of anti-bonding type interactions, while the bonds between Si interstitial and neighboring C and Si atoms were composed of bonding type interactions. The overlap population of each molecular orbital was examined to obtain detailed information of the chemical bonding. It appeared more difficult to recombine interstitial atoms in a cluster with a C atom vacancy than in a cluster with a Si atom vacancy, due to the stronger Si–Si bonds surrounding the C atom vacancy. The C interstitial atom had C2s and C2p anti-bonding interactions with high energy levels. The Si interstitial had minimal anti-bonding interactions.     

Displacement per atom calculation in YBCO superconductors through Monte Carlo simulation

The results of the calculations of the displacements per atom distribution induced by the gamma irradiation up to 15 MeV on YBa₂Cu₃O_7−x superconducting slabs are presented. Firstly, a calculation procedure for the displacement cross sections and the displacement per atom distributions was applied using the Monte Carlo simulation through the MCNPX code system. Then, based on this algorithm, the displacement per atom in-depth distributions were calculated starting from the energy flux distributions obtained from the simulation process, taking into account the contribution from each atom, obtaining a predominance of the Cu-O₂ planar sites over yttrium and barium atoms and more specifically the oxygen atoms predominate at low energies and the copper atoms at higher energies. Finally, the linear correlation observed between the displacement per atom distributions and energy deposition profiles at each incident energy was analyzed.     

Interaction of 〈1 0 0〉 and ½〈1 1 1〉 dislocation loops with point defects in ferritic alloys

The interaction between dislocation loops of interstitial nature with ½〈1 1 1〉 and 〈1 0 0〉 Burgers vectors and point defects in Fe has been studied molecular dynamics. Comparative calculations have been carried out using two interatomic potentials for pure Fe ([G.J. Ackland, M.I. Mendelev, D.J. Srolovitz, S. Han, A.V. Barashev, J. Phys.: Condens. Mater. 16 (2004) 1; S. Dudarev, P. Derlet, J. Phys.: Condens. Mater. 17 (2005) 7097]). The results of this study are range and energy of the interaction as functions of size and mutual position of defects. The applied potentials predict somewhat different strain field structure for 〈1 0 0〉 loops and therefore different lengths of interaction. However, both potentials suggest that, contrary to common belief, the distance of cluster-defect interaction within the glide prism of a ½〈1 1 1〉 cluster is significantly longer than that of a 〈1 0 0〉 cluster of similar size, in spite of the longer Burgers vector in the latter case.