Effect of one-dimensional diffusion on void nucleation

Nucleation of voids via the stochastic accumulation of vacancies is considered when one-dimensionally migrating self-interstitials are present. A system instability signaling a non-equilibrium phase transition is found to occur when the mean free path of the one-dimensionally moving self-interstitials becomes comparable with the average distance between the voids at a sufficiently high void-number density. At this point, due to the exponential dependence of void nucleation probability on the net vacancy flux, the nucleation of voids is much more favored at the void lattice positions. At the same time, voids initially nucleated at positions where neighboring voids are non-aligned will shrink away. The shrinkage of non-aligned voids is caused entirely by the stochastic fluctuations in point-defect fluxes received by the voids. These two processes leave the aligned voids to form a regular lattice. The formation of the void lattice in this way can be accomplished at a void swelling of below 1%, in agreement with experimental observation.