Helium effect on temperature-displacement rate equivalence in radiation-induced swelling of iron: A study by improved stochastic cluster dynamics

In nuclear energy systems, understanding material behavior (e.g., swelling) under irradiation is critical for ensuring long-term stability and safety. While direct neutron irradiation experiments pose significant challenges, ion irradiation serves as an alternative accelerating method for simulating neutron-induced damage. However, fundamental differences exist between neutron and ion irradiation in terms of substantial helium (He) induced by transmutation and significantly lower displacement rate in neutron irradiation than that of ion irradiation experiments. The equivalence between the two irradiation approaches in swelling, as well as the role of He, thus remains poorly understood. This study presents an optimized stochastic cluster dynamics (SCD) framework that combines dynamic rate table updating with a dual-regime strategy of pre-storing properties of small defect clusters while computing large clusters in real time, thereby resolving the persistent memory efficiency trade-off in conventional SCD approaches and meanwhile improving simulation efficiency for high-dose irradiation damage evolution (up to 10 dpa). By using the enhanced methodology, we systematically investigated the effects of temperature, displacement rate, He and vacancy migration energy barrier ($E_V^m$) on swelling behavior. The results reveal that these factors significantly influence swelling. Specifically, the swelling of pure iron initially increases and then decreases with rising temperature, with the peak swelling temperature positively correlated with the logarithm of the displacement rate. High displacement rates considerably widen the temperature range for swelling. Increasing the cluster resolution size (i.e., accounting for larger vacancy clusters in swelling calculations) shifts the peak swelling temperature to higher values, whereas higher irradiation doses reduce it. He-induced synergistic damage promotes the formation of large vacancy clusters, expanding the temperature range for swelling and meanwhile resulting in a higher swelling compared to pure displacement damage. Additionally, an increase in $E_V^m$ (the migration energy of vacancies enhanced by helium and solute effects) leads to a higher peak swelling temperature and a reduced swelling. This study also explores the temperature shifts required to achieve equivalent irradiation damage at different displacement rates, providing insights into temperature selection criteria for ion irradiation equivalence in simulating neutron irradiation. The findings elucidate the mechanisms underlying swelling and establish a foundation for temperature control in neutron and ion irradiation equivalence.