Calculation of Critical Nucleus Size and Minimum Energy Path of Cu-Riched Precipitates During Radiation in Fe-Cu Alloy Using String Method

As a pressure containment shell that supports all components in the nuclear reactor, reactor pressure vessel (RPV) is an irreplaceable core component during the whole life of nuclear power plant. Cu-riched particles precipitated in the early stage of radiation have significant effects on the mechanical property (such as radiation hardening and embrittlement) changes during the application of RPV steel. However, the Cu-riched precipitate with extremely small size (smaller than 2 nm) cannot be detected by the conventional experimental method, such as scanning electron microscope and transmission electron microscope. Hence, it is essential to calculate the critical nucleus size of Cu-riched precipitate under radiation in RPV steel. In this study, based on the constrained string method and phase-field theory, the critical nucleus size and minimum energy path of Cu-riched precipitate in Fe-Cu alloy under irradiation were calculated, and the minimum energy path, critical nucleus radius, and vacancy concentration distribution were also studied. The calculated results showed that both temperature and Cu concentration have a great influence on the energy path and critical nucleus cluster size of Cu-riched particles in Fe-Cu binary alloy. Temperature is the main factor influencing the energy path direction of the nucleus, while Cu concentration is the main factor influencing the growth rate of the nucleus radius. With the increase of temperature, the Cu concentration in the nucleus increases, while the time needed for the Cu-riched particles to reach its critical nucleus size decreases, and the energy barrier needed to be crossed also decreases. The distribution of Cu concentration also has a great influence on the distribution of vacancy during radiation. The vacancy concentration in the Cu-riched cluster is lower than that in the Fe-Cu matrix. The vacancy concentration decreased as the Cu concentration increased. The calculated results are consistent with the experimental results.

Automated summary

In this study, the critical nucleus size and minimum energy path of Cu-riched precipitate in Fe-Cu alloy under irradiation were calculated, and the effects of temperature and Cu concentration on the energy path and critical nucleus cluster size were studied. It was found that temperature mainly influences the energy path direction, while Cu concentration mainly affects the growth rate of the nucleus radius. The distribution of Cu concentration also impacts the distribution of vacancy during radiation.