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 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.     

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.     

The interaction of defects in titanium: A molecular dynamics study

Behaviors and properties of helium in titanium were explored by molecular dynamics (MD) simulation in this study. The influence of He number, vacancy number and He density (ratio of helium to vacancy) on the thermal stability of HenVm clusters (where n and m denote the number of He atoms and vacancies) were investigated. Meanwhile, interactions among He atoms, SIA atoms and vacancies were discussed. The results demonstrate that the binding energies of an interstitial helium atom primarily depend on He and vacancy numbers rather than the helium-to-vacancy ratio (n/m). It is different from the previous report of other researchers. The binding energies of an isolated vacancy and a self-interstitial titanium atom depend on both the number of helium atoms and the helium-to-vacancy ratio (n/m) of clusters. The thermal stability of clusters is decided by the competitive processes among thermal emissions of vacancy, SIA and helium atom.     

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.     

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.     

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.     

Temperature accelerated dynamics study of migration process of oxygen defects in UO2

We studied the migration dynamics of oxygen point defects in UO₂ which is the primary ceramic fuel for light-water reactors. Temperature accelerated dynamics simulations are performed for several initial conditions. Though the migration of the single interstitial is much slower than that of the vacancy, clustered interstitial shows faster migration than those. This observation gives us important insight on the formation mechanism of high-burnup restructuring, including planar defects and grain sub-division (the rim structure), found in UO₂.     

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 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.     

The effect of alloying elements on the vacancy defect evolution in electron-irradiated austenitic Fe-Ni alloys studied by positron annihilation

The vacancy defect evolution under electron irradiation in austenitic Fe-34.2 wt% Ni alloys containing oversized (aluminum) and undersized (silicon) alloying elements was investigated by positron annihilation spectroscopy at temperatures between 300 and 573 K. It is found that the accumulation of vacancy defects is considerably suppressed in the silicon-doped alloy. This effect is observed at all the irradiation temperatures. The obtained results provide evidence that the silicon-doped alloy forms stable low-mobility clusters involving several Si and interstitial atoms, which are centers of the enhanced recombination of migrating vacancies. The clusters of Si-interstitial atoms also modify the annealing of vacancy defects in the Fe-Ni-Si alloy. The interaction between small vacancy agglomerates and solute Al atoms is observed in the Fe-Ni-Al alloy under irradiation at 300-423 K.     

金红石辐照损伤的分子动力学模拟

为了研究辐照条件下金红石的耐辐照损伤能力，采用GULP软件包拟合出了与实验值吻合的势函数，并采用LAMMPS软件包计算出了金红石的离位阈能和高能粒子反冲条件下的位移级联。通过统计球坐标系下266个出射方向的离位能，利用缺陷形成概率的定义得出Ti和O原子的离位阈能分别为(78.3±1.0) eV和(42.6±2.0) eV。采用VORONOI缺陷统计方法，计算了300 K、10 keV出射能量条件下缺陷数量随辐照时间演化信息，结果表明：Ti原子作为初始出射原子产生的缺陷数量整体高于O原子产生缺陷的数量，在最大无序阶段产生的空位、填隙和不同类型反位缺陷通过空位-填隙复合作用和kick-out机制逐渐减少，有效地降低了晶体的无序度，提高了基材耐辐照损伤性能。     

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.     

Interaction of displacement cascade with helium bubbles in α-iron: Computer simulation

Molecular dynamics (MD) method has been performed to study the interaction of displacement cascade with He bubbles with two sets of potentials. The results show that the stability of He bubbles depends much on the initial He–vacancy (He/V) ratio and the recoil energy. For an initial He/V ratio of 3, the cascade leads to the increase in the number of vacancies in the He bubble and the decrease in the He/V ratio. For an initial He/V ratio of 0.5, the interaction of a cascade with the He/V bubble results in the decrease in the number of vacancies and the increase in the He/V ratio. For an initial He/V ratio of 1, the stability of the bubbles slightly depends on the primary knock-on atom (PKA) energy. Furthermore, a large number of self-interstitial atom clusters are formed after cascade collision for the He/V ratio of 3, while large vacancy clusters are observed for the He/V ratio of 0.5. However, some differences of defect production and clustering between the two sets of potentials are observed, which may be associated the formation energies of He–V clusters, the binding energies of vacancies and He atoms to the clusters and the probability of subcascade formation.     

Trapping of helium atoms in aluminum

Using molecular dynamic simulation, the effect of vacancy clusters on the interstitial helium atoms was studied in the early stages of helium bubble formation in the vessel of fission reactor, aluminum. The simulation shows, that there is a slight propensity of helium interstitial clustering without initial vacancies in aluminum. When vacancy cluster was introduced, the behavior of interstitial helium atoms was strongly dependent on the ratio of vacancy to helium. The interstitial helium atoms will be attracted in the center of the vacancy cluster when the ratio of vacancy to helium is much larger than 1, and when the ratio approaches 1, the helium will recombine with the vacancies, and, form in substitutions. In the case of the ratio of vacancy to helium less than 1, some aluminum interstitials will be created. The result shows, that the vacancy cluster plays a role of a nucleation center for helium atoms to accelerate the helium bubble growth.     

Positron lifetime calculations of defects in fusion irradiated beryllium

Numerical quantum-mechanical positron lifetime calculations were performed for mono-vacancies, di-vacancies, tri-vacancies and small nano-voids containing helium and hydrogen in neutron irradiated beryllium. Helium and hydrogen atoms in the sample after the irradiation are considered as atoms forming interstitial O-type loops. Spherical clusters of vacancies are included in the calculations as a reference. It was found that the presence of He and H atoms significantly changes the positron lifetime in irradiated beryllium. A correlation between the positron lifetime and mutual position of vacancies in nano-voids and interstitial loops was established.     

An object Kinetic Monte Carlo Simulation of the dynamics of helium and point defects in tungsten

In the near surface of plasma facing materials, high concentrations of hydrogen and helium isotopes can build up, which will interact with the point defects resulting from the bombardment of the surface as well as with the impurities of the materials. It is important to develop an understanding of the evolution of W microstructure in such conditions and to be able to model this evolution. The task is very complex, as many elements have to be included in the model which must be all parameterized correctly. Isochronal annealings experiments are simple experiments which can help in the making of more complicated models. In this work, an object Kinetic Monte Carlo technique parameterized on ab initio calculations as been used to model He desorption in W. The He atoms and the self interstitial atoms have been found to be very mobile but they can bind quite strongly with impurities such as carbon or molybdenum atoms. The evolution of the number of defects in the Kinetic Monte Carlo simulation was found to be in good agreement with the resistivity changes observed during an He desorption experiment of above threshold He implantation in a thin wire of tungsten.     

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.     

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.