Small-angle neutron scattering and rate theory applied to neutron-irradiation-induced clustering of defects and copper atoms in iron

Results of small-angle neutron scattering (SANS) experiments are presented for a low-Cu (0.015 wt%) and a high-Cu (0.42 wt%) iron-based model alloy as well as selected reactor pressure vessel (RPV) steels. In order to exclude a strong participation of nickel atoms in the cluster formation, the selection of RPV steels is restricted to either low Ni content or low Cu in connection with medium Ni content according to the present status of knowledge. These materials were irradiated at about the RPV service temperature up to two or more levels of neutron fluence each. A low-temperature irradiation (60°C) is also included. The results are analysed in terms of both measured cluster size distribution and ratio of magnetic and nuclear contributions to SANS intensities. The assumptions underlying the analysis (e. g. spherical vs. plane scatterers) are addressed.

Calculations are based on the direct solution of the master equation of rate theory for three special cases: (1) Long-term evolution of vacancy clusters (VCs) in the absence of copper atoms, (2) long-term evolution of copper clusters in the absence of vacancies but assuming irradiation-enhanced copper diffusion to occur, and (3) co-clustering of copper and vacancies. Assumptions and limitations are discussed and the results are compared with SANS results.

It turned out that pure VCs or pure copper clusters were never observed. The observations for the low-Cu model alloy and the high-Cu model alloy can be interpreted as being due to spherical vacancy-rich clusters and Cu-rich clusters, respectively. The mean radius is about 1 nm in both cases. The parameters of the rate theory models can be adjusted so as to correctly reflect some major observations. The remaining discrepancies are also discussed.