A statistical theory of void growth and time-lag

Abstract

The Langevin method using the system-size expansion is applied to the nucleation and growth of voids in irradiated metals. The evolution of the average void size and the fluctuations are ordered with respect to the “system-size” inverse, where the system-size is defined as the concentration of nucleating centers. To the lowest order, the average void size satisfies the equations used for swelling calculations, and the fluctuations about the mean are Gaussian. The growth of critical sized clusters into voids is due to the higher order terms. Void growth under steady-state irradiation depends on the higher order non-Gaussian corrections until the voids become large enough. The cooling cycle of an ICFR is also considered. It is found that the non-Gaussian correction terms may play a significant role in the final void size at the end of the pulse period. The two-time cluster size correlation function φ(t, t') is evaluated near the critical size. φ(t, t') is exponentially increasing with an e-folding time, which is within a factor of about two of nucleation time-lag estimates using multistate kinetics. For sizes greater than the critical size, an exact equation is derived relating φ(t, t') to the void size current I(x, t).