Application of the Langevin method to void growth

Abstract

The Langevin method using system-size expansion is applied to the growth of voids in irradiated metals. The evolution of the mean vacancy cluster size is calculated to the first two orders in the ’’system-size’’ inverse ε, for supercritical clusters. The system size is taken to be the vacancy cluster concentration. To the lowest order, the fluctuations of the cluster size are Gaussian and the mean satisfies the growth law used for swelling calculations. The non-Gaussian correction is shown to be negligible except for arrival-rate ratios DiCi/DvCv on the order of unity. The two-time cluster size correlation Φ (t,t′) is then evaluated near the critical size y*, which is an unstable equilibrium point. It is found that Φ (t,t′) is exponentially increasing, with an e-folding time τ*, which is within a numerical factor of the nucleation time-lag estimates using multistate kinetics. This suggests a definition of the time lag based on the cluster-size fluctuations. The supersaturated vapor is also discussed.