Formation of steady state size distribution of precipitates in alloys under cascade-producing irradiation

The effect of coherency loss on the development of precipitate size distribution under cascade-producing irradiation is considered. The nucleation of coherent precipitates, their growth followed by coherency loss and cascade-induced dissolution of large incoherent precipitates can occur simultaneously resulting in formation of a quasi-stationary size distribution of semicoherent precipitates. To describe this process we consider co-evolution of a mixed population of coherent, semicoherent and incoherent precipitates. Mathematically, the problem is formulated as a set of discrete rate equations of nucleation kinetics (the Master equation approach) which is also used for later stages of evolution. To solve the corresponding large set of equations (typically, more than 105 equations) an efficient numerical method is developed. The simulation results obtained for material parameters and irradiation conditions typical for nuclear reactors show that the coherency loss affects considerably evolution of the precipitate population. Under certain irradiation conditions, both in solution-annealed alloys and in aged ones, the mean precipitate size and the number density during prolonged irradiation tend to steady state values, whereas the size distribution function of large precipitates narrows. The width of the quasi-stationary size distribution is controlled by cascade parameters. It was found that the asymptotic quasi-stationary state of the precipitate population may depend on initial state of the alloy.