On a stochastic description of precipitation phenomena in supersaturated solutions

Void nucleation at elevated temperatures under cascade-damage irradiation

“…͑7͒ to ͑9͒, the superscripts s, c, and e refer to the stochastic fluctuations due to the random migratory jumps, random cascade initiation, and random vacancy emission, respectively. Note also that D e is proportional to the void surface area, 17,18 instead of to the void radius, as usually assumed in most other studies. The dependence of D e on the void size was discussed in detail in Ref.…”

“…͑4͒ governs the ''diffusive spread'' of P V due to stochastic fluctuations in the point-defect fluxes received by the void, including vacancy emission from the void. It depends on the average point-defect fluxes and the cascade properties, with expressions derived previously: 15,16,18 D͑n ͒ϭD…”

“…17, and corresponding statistical characteristics of the fluctuations in the rate of emission from the new-phase embryo had been obtained in Ref. 18, but have not been applied to void nucleation theories. The effect of these fluctuations on the rate of void nucleation under irradiation is also included in the present investigation.…”

Classical nucleation theory of microstructure development under cascade-damage irradiation

“…For temperatures at which the vacancy emission from voids is not negligible, the critical void size n cr , at which the drift velocity V ðn cr Þ vanishes, is much larger than n min According to [21], expression (9) for the probability of void nucleation can be approximated by (14) is proportional to the surface area of the void [18,22], as it is natural to expect in the case of emission.…”

“…Physically, the stochastic growth of the microstructure components is the manifestation of the Ôdiffusive spread'. DðnÞ depends on the average point-defect fluxes, the cascade properties, and can be expressed in the following form [8,9,18]:…”