Cluster dynamics simulation of reactor pressure vessel steels under irradiation

The distance between irradiated features (precipitates, clusters and atmospheres) exceeds significantly the size of them in neutron irradiated reactor pressure vessel (RPV) steels. Therefore, cluster dynamics (CD) that originally has been suggested for small clusters and that can be applied to any ideal gas of clusters is found to be very effective to investigate the long-term behavior of the neutron stimulated changes of the microstructure of RPV steels.
In the present paper CD simulation have been carried out for model iron alloys with small and high copper content as well as for VVER 1000 steels R16, R17 and D under neutron irradiation. For this case CD simulations are needed for two sets of input parameters. The first one relates to the description of the local material damage at the cascade stage when the local temperature increases to the melting point and then decreases to a temperature of about 300°C over a time of some ps and CD is not applicable. The cascade stage is investigated by molecular dynamics (MD) and kinetic lattice Monte-Carlo (KLMC) methods that provide the data on the neutron cascade efficiency, rate of the vacancies (interstitials) that form the clusters, the planar or spherical or another shape of clusters, content and distribution of them by size at the end of cascade stage. The second set of input parameters contains the energy of formation and energy of migration, pre-exponential factor of diffusivity for vacancy and interstitial, copper, manganese, silicon and other alloying elements in iron; recombination radius for pair vacancy-interstitial; dislocation density, capture efficiency of vacancies (interstitials) by dislocations, surface tension for boundary between cluster and iron matrix; binding energy dependence on cluster size; lattice parameters of iron and precipitates. Some of these characteristics are well-known with some accuracy from the experiment and can be considered as materials constants for RPV steels.
It was found that the coupling between copper rich precipitates (CRP) and point defects in neutron irradiated iron alloys and VVER steels can be investigated by CD simulations using LSODA code as a solver of the stiff ordinary differential equations system. The additional consideration of the strain energy effect on CRP kinetics as well as the application of the regular solution model for the case of different fixed copper contents of CRP improves quantitatively the simulation results for considered model alloys. The additional accounting of the Ni effect in CD simulation is needed to study the kinetics in the investigated VVER steels under irradiation.