Physico-Chemical nanomaterials science

Phase-field modeling precipitation and precipitates dissolution in Zr-Nb alloys under neutron irradiation

Dmitrii O.Kharchenko1, Vasyl O.Kharchenko1, Anna I.Bashtova1,
Viktor V.Kupriienko1,  Lu Wu2

1 Institute of Applied Physics, National Academy of Sciences of Ukraine, 58 Petropavlovskaya St., 40000 Sumy, Ukraine 
2 The First Sub-Institute, Nuclear Power Institute of China, 328, the 1st Section, Changshun Road, Shuangliu, Chengdu, China

A model to study microstructure transformations in binary Zr-Nb systems at thermal treatment and irradiation in the framework of the developed phase field theory is developed. This approach is generalized by taking into account thermodynamic CALPHAD potentials, misfit dislocations and dynamics of point defects, their elastic interactions and point defect sinks representing interstitial dislocation loops. Dynamics of beta-phase precipitates is studied at the thermal treatment of the solid solution. Stability of beta-Nb precipitates under neutron irradiation at different conditions is studied in details by considering local rearrangement of Nb concentration field, phase field, vacancy concentration field and effective misfit dislocation density field. By using dose dependencies of loop density, precipitate size and their density we estimate the associated hardening change. 
It was shown that at thermal treatment stage Niobium precipitates into the beta-phase of the mean size 11-12nm that relates well to experimental observations. It was shown that vacancies are mostly concentrated in the vicinity of interfaces. Misfit dislocation cores are localized in a vicinity of interfaces of large precipitates and inside small ones. It was shown that at 550K the fast precipitate growth at early stage related to inhomogeneous instability is changed by slow coalescence regime with quasi-stationary distribution of beta-phase particles over their size.
By studying stability of beta-phase precipitates at irradiation it was found that at large damage rate (10-4dpa/s) related to irradiation in accelerators a dissolution of precipitates, resulting in a decrease of the mean precipitate size is observed. This process is caused by ballistic mixing competing with thermal diffusion. It was found that misfit dislocations sustain an existence of Nb-enriched domains.  At low dose rate (10-5dpa/s) the thermal diffusion plays a major role in evolution of the microstructure. Here due to vacancy diffusion mechanism and misfit dislocations large beta-phase particles remain stable with dose accumulation, whereas small ones tend to dissolve. An increase in the temperature accelerates diffusion processes resulting in coagulation process accompanied by formation of large precipitates from interacting small ones by the Ostwald ripening scenario.  An increase in the precipitate size up to 1-2nm during dose accumulation at these conditions and a decrease of the Nb content inside precipitates are relevant to experimental data.