On density effects in point defect solutions under irradiation. II. Formation of interstitial dislocation loops

A model is presented for the simultaneous nucleation and growth of vacancy and interstitial loops in irradiated metals. The model is based on the homogeneous time-dependent rate theory. Conservation equations are developed for single defects as well as defect clusters. Defect-conservation equations include production by irradiation and thermal sources; and destruction by mutual recombination, migration to sinks as well as clustering into loops. Interstitial clustering is assumed to occur by diffusion of interstitial atoms. Vacancy loops, on the other hand, are assumed to form by an athermal cascade-collapse process. The density of such loops is determined as a result of the production of cascades and the finite loop lifetime. Cascade overlap and coalescence are also included in the model. The calculations are extended to the analysis of the radiation-induced changes in tensile properties due to formation of interstitial and vacancy loops. A simpe hardening model relates the microstructural calculations to predictions of changes in tensile strength. The results of this study show good agreement with hardening data for copper irradiated in RTNS-II at room temperature. The results also provide insight on differences in microstructural results observed in various experimental studies on copper. 7 figures.

In situ microstructural evolution in face-centered and body-centered cubic complex concentrated solid-solution alloys under heavy ion irradiation

Interstitial loops are one of the principal evolving defects in irradiated materials. The evolution of interstitial loops, including spatial and size distributions, affects both vacancy and interstitial accumulations in the matrix, hence, void formation and volumetric swelling. In this work, a phase-field model describing the growth kinetics of interstitial loops in irradiated materials during aging is developed. The diffusion of vacancies and interstitials and the elastic interaction between interstitial loops and point defects are accounted in the model. The effects of interstitial concentration, chemical potential, and elastic interaction on the growth kinetics and stability of interstitial loops are investigated in two and three dimensions. It is found that the elastic interaction enhances the growth kinetics of interstitial loops. The elastic interaction also affects the stability of a small interstitial loop adjacent to a larger loop. The model predicts linear growth rates for interstitial loops that is in agreement with the previous theoretical predictions and experimental observations.

Microstructure formation and its role on yield strength in AISI 316 SS irradiated by fission and fusion neutrons

Point defects and clusters in the hcp metals: their role in the dose transition

On the theory of dislocation loop nucleation in irradiated crystals

Vacancies and interstitial type dislocation loops of two fusion reactor candidate materials (V-4Cr-4Ti and F82H) after fission and fusion neutron irradiation were studied by positron annihilation lifetime spectroscopy. Fusion neutron irradiation was performed in the FNS of JAERI, and fission neutron irradiation was performed in the KUR of Kyoto University. The neutron irradiation dose was about 1×10−6–1×10−4 dpa, and the irradiation temperatures were room temperature and 673 K. In the irradiation at room temperature, the defects (mainly dislocation loops) in both alloys were detected even at a low irradiation dose of 10−6 dpa and the mean lifetime of positrons increased as the irradiation dose increased. The effects of the fission and fusion neutron irradiation on the point defect production were almost the same if they were compared at the same dpa. This can be explained by the fact that the number of subcascades, which is an important factor for the defect formation at room temperature, is proportional to dpa in these metals. In contrast, an effect of cascade size was found for the irradiation at 673 K. Dislocation loops were detected only in the fusion-neutron-irradiated F82H at 673 K.

Tungsten (W) is considered to be the most promising plasma-facing material in fusion reactors. During their service, severe irradiation conditions create plenty of point defects in W, which can significantly degrade their performance. In this work, we first employ the molecular static simulations to investigate the interaction between a 1/2[111] dislocation loop and a vacancy-type defect including a vacancy, di-vacancy, and vacancy cluster in W. The distributions of the binding energies of a 1/2[111] interstitial and vacancy dislocation loop to a vacancy along different directions at 0 K are obtained, which are validated by using the elasticity theory. The calculated distributions of the binding energies of a 1/2[111] interstitial dislocation loop to a di-vacancy and a vacancy cluster, showing a similar behavior to the case of a vacancy. Furthermore, we use the molecular dynamics simulation to study the effect of a vacancy cluster on the mobility of the 1/2[111] interstitial dislocation loop. The interaction is closely related to the temperature and their relative positions. A vacancy cluster can attract the 1/2[111] interstitial dislocation loop and pin it at low temperatures. At high temperatures, the 1/2[111] interstitial dislocation loop can move randomly. These results will help us to understand the essence of the interaction behaviors between the dislocation loop and a vacancy-type defect and provide necessary parameters for mesoscopic scale simulations.

The formation of small dislocation loops in size of 2.5 - 45 nm and a density of 1.4·1011 cm−2, as well as voids in size ≤10 nm in ZnS crystals were found by the transmission electron microscopy method (TEM). Samples were examined and irradiated in situ in a JEOL 4000EX-II electron microscope operated at energy of 400 keV and intensity of (1 - 4)·1019 e/cm2·s. Fine particles of a new phase in size ≤10 nm are formed also. These features can be identified from an analysis of moiré fringe contrast as phase of ZnO2. Similar defects in single crystals of ZnS formed in situ after irradiation in a transmission electron microscope JEM-100CX operated at energy of 100 keV and intensity of 3,5·1017 e/cm2·s. It was found that the formation of structural defects in ZnS under electron irradiation with above-threshold energy of defect formation (400 keV) is similar to the formation of structural defects in these crystals under electron irradiation with sub-threshold defect formation energy (100 keV).

The effect of temperature on the evolution of loops in nickel was investigated under 30 keV He+ irradiation. The size, Burgers vector, and nature of loops were analyzed by a transmission electron microscope (TEM). In addition, the Weibull statistical analysis was introduced to analyze the size distributions of the loops. The TEM results indicate that the sizes of loops increase with increasing irradiation temperature, where they are mainly in the range of 10–30, 20–50, and 30–80 nm at 300, 400, and 500 °C, respectively. In the irradiation temperature range of 300–500 °C, the size distributions of loops fit Weibull distribution very well, which suggests that the loops tend to grow larger and/or be merged. In addition, almost all the loops formed under He+ irradiation are the interstitial loops with Burgers vectors b = a2⟨110⟩, which is ascribed to the assistance of the He atom on the formation process of loops.

Electron microscope observations of interstitial loops in graphite have provided many examples of their interactions with basal plane dislocation lines. The two most important effects discussed in this paper are the motion of the loops due to the force of an approaching dislocation, and the pinning of these dislocation lines by a high density of small loops. Both effects are analysed in the light of a recent theoretical treatment of such interactions in anisotropic materials. Conditions under which loop movement occurs are examined and compared with theory and the process is shown to be unfavourable for loops of radius greater than 150 Å. Calculated criteria are obtained for the pinning of the dislocation lines by the introduction of a saturation pinning stress which is independent of irradiation temperature, and when combined with the theory of nucleation and growth of loops in graphite it is possible to calculate the irradiation dose for which saturation of elastic modulus is obtained as a function of irradiation flux and temperature. The application of these results to polycrystalline graphite is considered and a comparison made with experimental observations. Suggestions are made for further analysis and experiment.

Effects of concurrent irradiation with ions and electrons on the formation process of defect clusters in covalent and ionic crystals

A single point defect diffusion near a Cu (100) surface

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

Refractory tungsten-based medium- and high-entropy alloys form a promising class of strong, heat- and radiation-resistant materials for nuclear applications. Here, we systematically explore the radiation tolerance of Mo–Nb–Ta–V–W alloys using molecular dynamics simulations and a machine-learned interatomic potential. Going from pure W to W-based equiatomic binaries, ternaries, quaternary, and the quinary high-entropy alloy, we simulate the radiation damage accumulation up to 0.4–0.8 dpa through cumulative collision cascades. We find that the radiation damage and evolution are controlled by a combination of cascade-induced clustering, the balance in migration of vacancies and interstitials, and defect cluster binding energies. These mechanisms are strongly influenced by atom size, among which vanadium as the smallest atom is decisive. In pure W and alloys without V, the microstructure is characterised by large and growing interstitial dislocation loops. In stark contrast, in alloys containing V, vacancy dislocation loops are formed directly in collision cascades and the balanced migration rate of vacancies and interstitials promotes recombination and prevents growth of interstitial loops. The atom size differences also lead to clear segregation, with small atoms (V) in interstitial clusters and larger atoms (Ta, Nb) segregating around vacancy clusters. Furthermore, the small cluster sizes, formation of vacancy loops, segregation, and balanced migration in V-containing alloys lead to low swelling and an exceptionally efficient defect annealing compared to pure W and V-free alloys. Our results highlight WTaV as a promising low-activation material, where almost 90% of defects are annealed at 2000 K during 5 ns compared to <20% in pure W.