First-principles theory for helium and xenon diffusion in uranium dioxide

The diffusion properties of He and Xe in UO₂ have been investigated, using density-functional calculations employing the projector-augmented-wave (PAW) method and the generalized gradient approximation (GGA). The migration energies corresponding to both interstitial and vacancy-assisted mechanisms have been calculated and the results for the two noble gas atoms are compared with each other. We suggest that He likely diffuses by hopping through a single vacancy with computed low migration energies smaller than 0.79 eV and its diffusivity is much higher than that of Xe. Xe has a quite large migration energy compared to He; the strain energy plays a key role in Xe diffusion in UO₂.     

First-principles modeling of He-clusters in UO2

We have investigated the behavior of He in UO₂, using the projector-augmented-wave (PAW) method and the generalized gradient approximation (GGA) based on the density functional theory. Total energy calculations with atomic relaxation included have been performed in a 96-atom large supercell. We have found that He has a strong tendency to form a cluster in vicinity of an octahedral interstitial site (OIS) in the UO₂ matrix. In addition, the strain energy produced by a He-cluster was found to be sufficient to create point defects of the host atoms in UO₂. Our study suggests that He-clusters and He-induced point defects play an important role for the local mechanical properties of UO₂.     

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.     

An atomistic approach to self-diffusion in uranium dioxide

The formation and mobility of point defects in UO₂ have been studied within the framework of the Density Functional Theory. The ab initio Projector Augmented Wave method is used to determine the formation and migration energies of defects. The results relative to intrinsic point defect formation energies using the Generalized Gradient Approximation (GGA) and GGA+U approximations for the exchange-correlation interactions are reported and compared to experimental data. The GGA and GGA+U approximations yield different formation energies for both Frenkel pairs and Schottky trios, showing that the 5f electron correlations have a strong influence on the defect formation energies. Using GGA, various migration mechanisms were investigated for oxygen and uranium defects. For oxygen defects, the calculations show that both a vacancy and an indirect interstitial mechanism have the lowest associated migration energies, 1.2 and 1.1 eV respectively. As regards uranium defects, a vacancy mechanism appears energetically more favourable with a migration energy of 4.4 eV, confirming that oxygen atoms are much more mobile in UO₂ than uranium atoms. Those results are discussed in the light of experimentally determined activation energies for diffusion.     

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.     

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.     

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 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.     

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.     

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.     

Grain boundary influence on displacement cascades in UO2: A molecular dynamics study

The influence of grain boundaries on the primary damage state created by a recoil nucleus in UO₂ matrix is studied here by molecular dynamics simulations. This study is divided in two steps: (1) the study of the structural properties of several symmetrical tilt boundaries for different misorientation angles ranging from 12.7° to 61.9°; and (2) the study of displacement cascades near these grain boundaries. For all the grain boundaries studied, the structure around the interface up to about 2 nm presents a perturbed but stable fluorite lattice. The type of defect at the interface depends directly on the value of the misorientation angles. For the small angles (12.7° and 16.3°) the interface defects correspond to edge dislocations. For higher misorientation angles, a gap of about 0.3 nm exists between the two halves of the bicrystal. This gap is composed of Schottky defects involving numerous vacancies along the interface. About 10 keV displacement cascades were initiated with an uranium projectile close to the interface. In all the cases, numerous point defects are created in the grain boundary core, and the mobility of these defects increases. However, cascade morphologies depend strongly on the grain boundary structure. For grain boundaries with edge dislocations, the evolution of the displacement cascades is similar to those carried out in monocrystals. On the other hand, cascades initiated in grain boundaries with vacancy layer defects present an asymmetry on the number of displaced atoms and the number of point defects created.     

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.     

First-principles study of helium effect in a ferromagnetic iron grain boundary: Energetics, site preference and segregation

Using a first-principles method based on density functional theory, we have investigated energetics and site preference of helium (He) in a ferromagnetic bcc-iron (Fe) grain boundary (GB). We calculate the binding energies of He atom in the GB, which show that the substitutional He is energetically favored in comparison with the interstitial He with a small energy difference of 0.06 eV. The segregation energy is calculated to be ∼1.4 eV for the energetically favorable GB substitutional and interstitial sites, which is large enough for the He atoms to segregate to these sites, independent of the temperature and the bulk He concentration. This leads to the conclusion that all the He atoms will segregate into the GB at a typical temperature range of 573-1173 K.     

Helium behavior in oxide nuclear fuels: First principles modeling

UO₂ and (U, Pu)O₂ solid solutions (the so-called MOX) nowadays are used as commercial nuclear fuels in many countries. One of the safety issues during the storage of these fuels is related to their self-irradiation that produces and accumulates point defects and helium therein.We present density functional theory (DFT) calculations for UO₂, PuO₂ and MOX containing He atoms in octahedral interstitial positions. In particular, we calculated basic MOX properties and He incorporation energies as functions of Pu concentration within the spin-polarized, generalized gradient approximation (GGA) DFT calculations. We also included the on-site electron correlation corrections using the Hubbard model (in the framework of the so-called DFT + U approach). We found that PuO₂ remains semiconducting with He in the octahedral position while UO₂ requires a specific lattice distortion. Both materials reveal a positive energy for He incorporation, which, therefore, is an exothermic process. The He incorporation energy increases with the Pu concentration in the MOX fuel.     

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.     

First-principles study on electronic structures and absorption spectra for BaWO4 crystal containing barium vacancy

The electronic structures, dielectric function and absorption spectra for the perfect BaWO₄ (BWO) crystal and the BWO crystal containing barium vacancy () have been studied using density functional theory code CASTEP with the lattice structure optimized. The results indicate that the optical properties of the BWO crystal exhibit anisotropy and its optical symmetry coincide with lattice structure geometry of the BWO crystal. For the BWO crystal containing , there exhibit four absorption bands peaking at 0.71 eV (1751 nm), 1.85 eV (672 nm), 3.43 eV (362 nm) and 3.85 eV (322 nm), respectively. The origins of the 370 nm absorption band should be related to the .     

Cuboctahedral oxygen clusters in U3O7

When UO₂ is oxidised to U₃O₇, the positions in the crystal lattice of all the uranium atoms and of about 70% of the oxygen atoms are hardly affected. The remaining oxygen atoms occupy new sites which are located 310 pm along 〈1 1 0〉 vectors from the holes in the fluorite framework of UO₂. These results, which are based on the analysis of neutron diffraction powder data, are consistent with the concept that excess oxygen in U₃O₇ is accommodated in cuboctahedral anionic clusters.     

First-principles study of electronic structure and insulating properties of uranium and plutonium dioxides

First-principles density functional theory calculations were carried out to investigate the electronic structure and the degree of 5f states localization of the Mott-Hubbard type insulators UO₂ and PuO₂. We used the fully relativistic cluster discrete variational method (RDV) with the local exchange-correlation potential. The energies of one-electron transition between occupied and vacant 5f^5/2 states of neighboring actinide atoms were evaluated on the base of the ground state and the excited state calculations. It is found that in UO₂ and PuO₂ the energy difference between 5f^5/2 levels of nearest metal sites in the lattice are close to 1.0 eV and 0.9 eV, despite the results of conventional band structure approach predicting that both oxides are good conductors.     

The effect of vacancy created by ion irradiation on the ordering of FePt: A first-principle study

Ion irradiation has been used to promote ordering processes and to modify the magnetic properties of magnetic thin films. The major reason for ion irradiation reducing the ordering temperature is the introduction of a number of vacancies. The vacancy and its influence on the ordering temperature and magnetic properties in L1₀ ordered FePt are investigated by first-principle simulation. The vacancy formation energy for Fe and Pt in FePt alloy are 1.45 and 2.25 eV respectively. The calculated order-disorder transition temperature of Fe₅₀Pt₅₀ is 1680 K. The order-disorder transition temperatures for Fe vacancy and Pt vacancy models are about 50 K and 200 K lower than that of the stoichiometric Fe₅₀Pt₅₀ alloy respectively. The results suggested that the vacancy in FePt alloy favors the ordering process. The saturation magnetization of stoichiometric L1₀ FePt is 1070 emu/cc and these of Fe and Pt vacancy are 1027 and 1075 emu/cc, respectively.