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.     

Helium-implanted CLAM steel and evolutionary behavior of defects investigated by positron-annihilation spectroscopy

China Low Activation Martensitic (CLAM) steel has been chosen as the primary candidate structural material for the first wall/blanket for fusion reactor. The excessive helium irradiation induced damage of CLAM steel at high temperatures and the evolution of defects were investigated in this paper. The samples were homogeneously implanted with 1e + 17 ions/cm² and 100 keV of helium at room temperature, 473, 673, and 873 K. Irradiation induced damage of CLAM steel and the annealing behavior of defects were probed by slow positron beam Doppler broadening technique. Helium implantation produced a large number of vacancy-type defects which bound with helium and formed helium–vacancy complexes. Target atoms’ displacement capacity was strengthened with rising irradiation temperatures, so the S parameter increased with increasing irradiation temperatures, and helium–vacancy complexes were main defects after helium implantation at damage layers. Helium bubbles would be unstable and the desorption of helium bubbles would promote the density of defects above 673 K. By analyzing the curves of S–W and annealing tests of irradiated specimen, it suggested that there werenot only one type of defect in damage layers. Though helium–vacancy complexes were primary defects after helium implanted, introducing excessive helium might also generated other point defects or dislocation loops in the material.     

Helium desorption in He implanted tungsten at low fluence and low energy

The behaviour of helium in polycrystalline ³He implanted tungsten at low energy (60 keV) and low fluence (2 × 10¹³ cm⁻²) has been studied as a function of post-implantation annealing temperature until 1873 K by means of Nuclear Reaction Analysis. Helium desorption has been observed only from ∼1500 K, suggesting a helium trapping at mono-vacancies. Only ∼75% of the implanted helium has been released after the annealing during 1 h at high temperature (1873 K); besides, the desorption rate decreased from 1673 K. The presence of a second type of helium trapping site is likely to explain this strong helium retention.     

Nuclear reaction analysis of helium migration in silicon carbide

4H-SiC and 6H-SiC single crystals were implanted at room temperature with 3-MeV ³He ions at a fluence of 1 × 10¹⁶ cm⁻². Analysis of helium migration was carried out with the ³He(d, p)⁴He nuclear reaction. No clear thermally-activated migration in the end-of-range (EOR) region is found below 1100 °C, meaning that helium is strongly trapped probably in helium-vacancy clusters. At 1100 °C and above, a fraction of ³He atoms remains trapped in the clusters, but a significant fraction is detrapped into a broad distribution, which is slightly shifted towards the sample surface. Helium detrapping from the EOR region increases with increasing annealing time and temperature. Moreover, the helium content is not conserved, since a significant fraction of ³He atoms is released out of the sample. Helium out-gassing actually increases with increasing annealing time and temperature, up to about 40% at 1150 °C. No clear difference is found between the 4H-SiC and 6H-SiC polytypes.     

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.     

Thermal helium desorption spectrometry on plastically deformed molybdenum

Thermal helium desorption spectrometry (THDS) has been applied to study the effect of plastic deformation on the trapping of low energy helium implanted into molybdenum single crystals. The analysis of the desorption spectra shows the presence of monovacancies at a concentration of 1.6 appm per % strain, which anneal out in the recovery stage III. No contribution of single helium atoms bound to the dislocations was observed. The high temperature part of the spectra might contain a contribution of helium clusters bound to dislocations. However, after an anneal beyond stage III the main contribution to the desorption spectra is ascribed to helium desorbing from vacancy clusters.     

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.     

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.     

Thermal effects in 10 keV Si PKA cascades in 3C-SiC

We present a molecular dynamics study of the influence of temperature on defect generation and evolution in irradiated cubic silicon carbide. We simulated 10 keV displacement cascades, with an emphasis on the quantification of the spatial distribution of defects, at six different temperatures from 0 K to 2000 K under identical primary knock-on atom conditions. By post-processing the simulation results we analyzed the temporal evolution of vacancies, interstitials, and antisite defects, the spatial distribution of vacancies, and the distribution of vacancy cluster sizes. The majority of vacancies were found to be isolated at all temperatures. We found evidence of temperature dependence in C and Si replacements and C_Si antisite formation, as well as reduced damage generation behavior due to enhanced defect relaxation at 2000 K.     

Deuterium retention of boron-titanium and reduction of deuterium retention after helium ion irradiations

Deuterium ion irradiations with an ion with energy of 1.7 keV were conducted for boron-titanium (B-Ti) film prepared by electron beam evaporation and hot pressed titanium-boride, TiB₂. The amount of retained deuterium was measured for these materials using a technique of thermal desorption spectroscopy. The amount of deuterium retained in TiB₂ was comparable with that in B-Ti. Desorption peaks of deuterium in B-Ti were 470 K and 620 K, corresponding to a desorption in the low temperature regime observed in boron (B) and a desorption in titanium (Ti), respectively. The desorption peaks in TiB₂ were 620 K and 750 K, which correspond to the desorption in Ti and that in the high temperature regime in B, respectively. The desorption temperature in B-Ti was approximately 100 K lower than that in TiB₂. This difference is discussed based upon chemical bindings and amorphous/crystal structures of B-Ti and TiB₂. Irradiation of helium ion with energy of 5 keV was conducted for B-Ti after the deuterium ion irradiation. The amount of retained deuterium decreased and the desorption temperature shifted to the lower temperature regime, as the helium ion fluence increased. The shift to the low temperature regime is due to the enhancement of amorphous structure of B in B-Ti.     

Helium and deuterium implantation in tungsten at elevated temperatures

High temperature helium and deuterium implantation on tungsten has been studied using the University of Wisconsin inertial electrostatic confinement device. Helium or deuterium ions from a plasma source were driven into polished tungsten powder metallurgy samples. Deuterium implantation did not damage the surface of the specimens at elevated temperatures (∼1200 °C). Helium implantation resulted in a porous surface structure above 700 °C. A helium fluence scan, ion energy scan, and temperature scan were all completed. With 30 keV ions, the pore formation started just below 4 × 10¹⁶ He⁺/cm². The pore size increased and the pore density decreased with increasing fluence and temperature. The energy scan from 20 to 80 keV showed no consistent trend.     

Helium diffusion coefficient measurements in R7T7 nuclear glass by He(d,α)H nuclear reaction analysis

The immobilization of fission products and minor actinides by vitrification is the reference process for industrial management of high-level radioactive wastes generated by spent fuel reprocessing. Radiation damage and radiogenic helium accumulation must be specifically studied to evaluate the effects of minor actinide alpha decay on the glass long-term behavior under repository conditions.A specific experimental study was conducted for a comprehensive evaluation of the behavior of helium and its diffusion mechanisms in borosilicate nuclear waste glass. Helium production was simulated by external implantation with ³He ions at a concentration (≈1 at.%) 30 times higher than obtained after 10,000 years of storage. Helium diffusion coefficients as a function of temperature were extracted from the depth profiles after annealing. The ³He(d,α)¹H nuclear reaction analysis (NRA) technique was successfully adopted for low-temperature in situ measurements of depth profiles. Its high depth resolution revealed helium mobility at temperatures as low as 253 K and the presence of a trapped helium fraction. The diffusion coefficients of un-trapped helium atoms follow an Arrhenius law between 253 K and 323 K. An activation energy of 0.55 ± 0.03 eV was determined, which is consistent with a process controlled by diffusion in the glass free volume.     

Computer simulation of primary damage creation in displacement cascades in copper. I. Defect creation and cluster statistics

Atomic-scale computer simulation has been used to investigate the primary damage created by displacement cascades in copper over a wide range of temperature (100 K ? T ? 900 K) and primary knock-on atom energy (5 keV ? E_PKA ? 25 keV). A technique was introduced to improve computational efficiency and at least 20 cascades for each (E_PKA, T) pair were simulated in order to provide statistical reliability of the results. The total of almost 450 simulated cascades is the largest yet reported for this metal. The mean number of surviving point defects per cascade is only 15-20% of the NRT model value. It decreases with increasing T at fixed E_PKA and is proportional to (E_PKA)^1.1 at fixed T. A high proportion (60-80%) of self-interstitial atoms (SIAs) form clusters during the cascade process. The proportion of clustered vacancies is smaller and sensitive to T, falling from 30% to 60% for T ? 600 K to less than 20% when T = 900 K. The structure of clusters has been examined in detail. Vacancies cluster predominantly in stacking-fault-tetrahedron-type configurations. SIAs tend to form either glissile dislocation loops with Burgers vector b = 1/2<1 1 0> or sessile faulted Frank loops with b = 1/3<1 1 1>. Despite the fact that cascades at a given E_PKA and T exhibit a wide range of defect numbers and clustered fractions, there appears to be a correlation in the formation of vacancy clusters and SIA clusters in the same cascade. The size and spatial aspects of this are analysed in detail in part II [unpublished], where the stability of clusters when another cascade overlaps them is also investigated.     

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.     

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.     

Effects of Fe-He potential on primary damage formation in Fe-1%He

The effects of different Fe-He interatomic potentials on primary damage formation in Fe-1%He are investigated using molecular dynamics (MD) methods. Simulations of cascades produced by primary knock-on atoms (PKA) of energy E_p = 0.5-10 keV were performed at an irradiation temperature of 100 K. It is found that the Fe-He potentials have significant effects on the point defect creation and the formation of Fe-He interstitial clusters, whereas small effects on the formation of He-vacancy clusters.     

Temperature dependence of dislocation bias factors in metals

Recently, it has been shown that edge dislocations are not stable sinks for vacancies. Trapping and detrapping of vacancies occur as a thermally-activated process. In this paper, the temperature dependence of vacancy absorption coefficient of edge dislocations under irradiation was calculated by using rate equations in Fe and Ni. The temperature dependence was almost the same in both Fe and Ni and did not depend on the damage rate between 10⁻¹⁰ dpa/s and 10⁻⁶ dpa/s. At low temperatures such as room temperature, the coefficient was low and with increasing irradiation temperatures, it had a peak (500 K) and decreased.     

Multiple-interactions of displacement cascades with He-vacancy clusters in α-iron: Computer simulations

Multiple-interactions of displacement cascades with He-vacancy (He-V) clusters are investigated using molecular dynamics simulations. The effects of a single displacement cascade on the stability of a He-V cluster depend on the He-to-vacancy (He/V) ratio and the primary knock-on atom (PKA) energy. Initial He-V clusters consist of 10 and 20 vacancies with He/V ratios ranging from 0.2 to 3 and the PKA energy, E_p, varying from 2 keV to 10 keV. The size of He-V clusters was found to generally increase with increasing He/V ratios for the same PKA energy, but the stability of He-V clusters decreases with increasing PKA energy. The results are compared with those for voids impacted by collisional cascades. During multiple 5 keV, cascade events, the final size of He-V clusters depends on only the initial He/V ratios. It is of interest to notice that the number of vacancies in a He-V cluster is determined by the first cascade event, while subsequent cascade overlap has a significant effect on its stability. These results are discussed in terms of the internal pressure of He-V clusters, the mobility of He atoms, the number of vacancies produced by cascades and the He/V ratio.     

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。     

The annealing behaviour of vanadium,previously irradiated with 210 keV helium at 625°C to high fluences

Helium induced damage is one of the major contributing factors leading to projected loss of integrity of the first wall in fusion reactor systems. Previous electron microscopy investigations of the surface and bulk damage induced by energetic He⁺ bombardment of vanadium revealed that only a small fraction of the total implanted helium could be accounted for after irradiation. This fraction was contained in observable bubbles with diameters, $\text{d > 4 nm}$. In this study transmission electron microscopy techniques were used to establish the development of a new population of small diameter bubbles ($\text{d < 4 nm}$) after post-irradiation annealing treatments. A characteristic bimodal distribution function for the bubble population was found after annealing. This distribution has a strong peak at small diameters induced by growth of helium-vacancy clusters from the available thermally created vacancies.