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.     

钚自辐照老化过程中氦效应理论研究进展

钚因放射性衰变而出现自辐照老化效应。钚中氦行为是理解钚自辐照老化效应的一个基础和前提。运用分子动力学模拟技术,计算研究了钚中缺陷行为、氦与缺陷的相互作用、氦泡的初始形核过程、氦泡的长大过程以及氦泡对钚材料宏观性能的影响等。其中,钚-钚、钚-氦和氦-氦相互作用势分别采用修正嵌入原子多体势（modifiedembeddedatommethod,MEAM）、Morse对势和Lennard-Jones对势。主要的计算结果表明,氦原子与空位的结合能较大,在钚的自辐照过程中,两者易于结合并形成氦-空位团簇,成为氦泡的前驱体;氦泡可通过冲出位错环的机制而长大;氦泡的压力在GPa量级,且氦泡引起的基体膨胀很小。     

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.     

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.     

Atomistic study of the thermodynamic equilibrium of nano-sized helium cavities in βSiC

The estimation of the number of inert gas atoms contained at equilibrium in microscale bubbles in a solid usually relies on a well-known formula equilibrating the internal pressure of He to the surface energy of the bubble. This approach evidences a strong variation with temperature of He content for a given bubble. At the opposite, at the Angstrom scale, ab initio calculations for He contained in vacancy assemblies neglect temperature effects. In this work, empirical potential molecular dynamics simulations are used to study, in the case of helium inserted in cubic silicon carbide, the variation of the He content of sub-nanoscale cavities with temperature. To do so free energy for He atoms inserted in cavities made of a few vacancies (up to 29) are calculated. One then evidences the existence of a sub-surface segregation in interstitial sites close to the surface of the cavity. The variation of the He content with temperature is observed to be negligible at the nanoscale, thus validating the ab initio approach.     

Phase-field modeling of gas bubbles and thermal conductivity evolution in nuclear fuels

A phase-field model was developed to simulate the accumulation and transport of fission products and the evolution of gas bubble microstructures in nuclear fuels. The model takes into account the generation of gas atoms and vacancies, and the elastic interaction between diffusive species and defects as well as the inhomogeneity of elasticity and diffusivity. The simulations show that gas bubble nucleation is much easier at grain boundaries than inside grains due to the trapping of gas atoms and the high mobility of vacancies and gas atoms in grain boundaries. Helium bubble formation at unstable vacancy clusters generated by irradiation depends on the mobilities of the vacancies and He, and the continuing supply of vacancies and He. The formation volume of the vacancy and He has a strong effect on the gas bubble nucleation at dislocations. The effective thermal conductivity strongly depends on the bubble volume fraction, but weakly on the morphology of the bubbles.     

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.     

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.     

Atomistic simulations of the elastic properties of helium bubble embedded aluminum

The helium bubble has significant consequence to the mechanical properties of irradiated materials. The influence of embedded helium bubble to the elastic properties of aluminum has been investigated by molecular dynamics (MD) simulations. The interaction between aluminum atoms and the interaction between helium atoms are described by an embedded-atom-method (EAM) many-body potential and a pair potential, respectively. Another pair potential, which is parameterized based on ab initio calculation, is used to describe the interaction between aluminum and helium atoms, and its validation under pressure up to 10 GPa is reasonable demonstrated by the electron density calculation. For the composite system consisting of 62,500 aluminum atoms and one helium bubble with various diameters, its elastic constants are calculated properly by stress-strain relation rather than by energy-strain relation. The results show that elastic constants c₁₁, c₁₂ and c₄₄ decrease with increasing of the volume of the helium bubble, and remain almost invariable with the internal pressure of the helium bubble. The main reason is under high-pressure the helium is softer than aluminum, and the soft effect overwhelms the hard effect of internal pressure of helium bubble.     

Thermal desorption of helium from defects in nickel

Helium atoms, introduced into materials by helium plasma or generated by the (n, α) nuclear reaction, have a strong tendency to accumulate at trapping sites such as vacancy clusters and dislocations. In this paper, the effects of dislocations, single vacancies and vacancy clusters on the retention and desorption of helium atoms in nickel were studied. Low energy (0.1-0.15 keV) helium atoms were implanted in nickel with vacancies or dislocations without causing any displacement damage. He atoms, interstitial-type dislocation loops, and vacancy clusters were also introduced with irradiation damage by 5.0 keV helium ions. Helium thermal desorption peaks from dislocations, helium-vacancy clusters and helium bubbles were obtained by thermal desorption spectroscopy at 940 K, in the range from 900 to 1370 K, and at 1500 K, respectively. In addition, a thermally quasi-stable state was found for helium-vacancy clusters.     

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.     

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.     

Positron simulations of defects in tungsten containing hydrogen and helium

An understanding of the behavior of defects containing hydrogen or helium in tungsten is an important issue. Here the properties of defects in tungsten containing hydrogen or helium atoms have been investigated by model positron lifetime quantum-mechanical simulations. The electron and positron wave functions have been obtained in the local density approximation to the two-component density-functional theory. The calculated values of the positron lifetime correlate with the magnitude of the electron density. The vacancy-clusters without hydrogen or helium are active positron traps. The lattice relaxation of atoms around vacancy reduces the effective vacancy volume and decrease the positron lifetime at a vacancy. The hydrogen and helium atoms are trapped in tungsten by lattice vacancies and nano-voids. It was established that positron lifetime depends on the density of gas atoms inside the nano-void. Hydrogen and helium presence in the larger nano-voids considerably decrease the positron lifetime.     

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.     

氦离子辐照烧结碳化硅损伤效应研究

利用中国科学院近代物理研究所320 kV高压平台提供的氦离子辐照烧结碳化硅,辐照温度从室温到1 000 ℃,辐照注量为1015~1017 cm-2。辐照完成后,进行退火处理,然后开展透射电子显微镜、拉曼光谱、纳米硬度和热导率测试。研究发现,烧结碳化硅中氦泡形核阈值注量低于单晶碳化硅。同时,氦泡形貌和尺寸与辐照温度、退火温度有关。另外,对辐照产生的晶格缺陷、元素偏析进行了研究。结果表明,辐照产生了大量的缺陷团簇,同时氦泡生长也会发射间隙子,在氦泡周围形成间隙型位错环。在晶界处,容易发生碳原子聚集。辐照导致材料先发生硬化而后发生软化,且热导率降低。     

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.     

Theory of the production and depth distribution of helium defect complexes by ion implantation

The complex defect formations and migrations occurring under helium ion bombardment of Cu have been modeled by a system of coupled equations, including diffusion. Atomistic binding and migration energies were determined from two-body calculations. A new mathematical scheme was developed in order to take diffusion into account in a self-consistent fashion. The calculations were applied to the low temperature implantation and annealing experiments of Bauer and also to the (proton backscattering) profiling experiments of Blewer. The calculations indicate that the ~0° C release peak of Bauer may be due to helium interstitial migration. When applied to the Blewer experiments, the calculations indicate that the dominant defect after room temperature implantation is six helium atoms in a vacancy (He₆V). The shape and position of the total helium distribution is not altered by isochronal annealing (because of the trapping of vacancies by the helium), but the helium is released directly from the damage which traps it.     

Pressure of stable He-vacancy complex in bcc iron: Molecular dynamics simulations

Molecular dynamic simulation was employed to study the stable state of He-vacancy (He-V) complex in bcc iron. The pressure of He-V complex was calculated using the concept of atomic-level stress. In the case of no initial vacancies introduced in the simulation box, self-interstitial atoms (SIAs) are emitted by the small He cluster. As the number of the He cluster is above a critical value, interstitial-type dislocation loops (I-loop) will be generated. After the interstitial-type defects (SIA or I-loop) were created, it is found that the ratio of He atoms to athermal vacancies keeps nearly constant in the He-V complex.     

含氦Ti膜的透射电镜研究

在氦气和氩气混合气氛中用磁控溅射法制备含氦Ti膜。应用透射电镜观察不同氦气和氩气流量比对Ti膜微观结构及氦泡形貌和分布的影响,并研究退火温度对氦泡聚集和长大行为的影响。研究观测到,Ti膜中氦泡的尺寸随氦流量的增加而增大,氦泡的密度随氦流量改变出现一最大值;温度低于0.5 Tm时,He泡以泡迁移和合并机制(MC)长大;温度高于0.5 Tm时,He从小泡离解,被大泡吸收,以OR机制长大,氦泡尺寸明显增加。     

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.