A study of the self-organization of vacancy clusters in irradiated materials is presented. Using a continuum stochastic model we take into account dynamics of point defects and their sinks with elastic interactions of vacancies. Dynamics of vacancy clusters formation is studied analytically and numerically under conditions related to irradiation in both reactors and accelerators. We have shown a difference in patterning dynamics and studied the external noise influence related to fluctuation in a defect production rate. Applying our approach to pure nickel irradiated under different conditions we have shown that vacancy clusters having a linear size ≃ 6 nm can arrange in statistical periodic structure with nano-meter range. We have found that linear size of vacancy clusters at accelerator conditions decreases down to 20%, whereas a period of vacancy clusters reduces to 6.5%.
In the framework of rate theory, a generalized statistical approach has been proposed to describe the spatial organization of point defects of the vacancy type into clusters and pores in irradiated systems. The approach makes allowance for the generation of point defects by elastic fields, as well as for defect interaction. The model is applied to study the defect pattern formation in pure nickel. The conditions required for the pattern formation at actual irradiation regimes in reactors have been analyzed. The peculiarities of microstructure changes at various temperatures and dose accumulation rates have been obtained both analytically and numerically. The defect pattern period and the change of a characteristic pattern size have been studied by applying the statistical methods to analyze the obtained numerical data. The results are in good correspondence with well-known experimental observations of the defect microstructure formation in irradiated materials under reactor conditions. K e y w o r d s: rate theory, spatial organization of point defects of the vacancy type, clusters, pores, irradiated systems, defect pattern formation, irradiation in reactors, numerical simulation.
A phase field approach to study stability of β-Nb precipitates in Zr–Nb alloys is extended by taking into account local rearrangement of point defects and misfit dislocations. Kinetic properties of β-Nb phase formation are discussed at a heat treatment stage. Stability of secondary phase precipitates is studied at different irradiation temperatures and dose rates. It is shown that processes of dissolution/growth of precipitates are governed by the competition of ballistic mixing and thermal diffusion. It is found that at large values of dose rates and low temperatures, precipitates are dissolved due to a major role of ballistic mixing, whereas at low dose rate and elevated temperatures, β-niobium particles grow slowly by an Ostwald ripening scenario up to 1–2 nm due to the dominant role of thermal diffusion. Misfit dislocations sustain the existence of Nb-enriched domains of mixed symmetry. It is shown that growing dislocation loops and dissolving/growing precipitates result in the hardening change up to 0.01% at a dose rate of 10−5dpa/s and temperatures of 550–575 K. Obtained theoretical results are verified by experimental data.
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