# A Comparison of the Relative Importance of Helium and Vacancy Accumulation in Void Nucleation

Abstract: Void nucleation in irradiated austenitic stainless steels generally requires the presence of either residual or transmutant gases. Classical nucleation rates are much too low to account for the number of voids observed attemperatures greater than about 450°C. An alternate path is generally believed to be responsible for void formation; namely, the growth of gas-stabilized bubbles until they reach a critical size beyond which further gas accumulation is not required to promote growth. Two limiting paths can be envisioned for void nucleation on a population of sub-critical helium/vacancy clusters; one is limited to growth by helium accumulation alone and the other to growth by stochastic fluctuations in the vacancy accumulation. As bubbles approach the critical size, stochastic processes could begin to contribute to the void nucleation rate. A comparison is made of nucleation rates along these two limiting paths as a function of the gas content of the clusters. The calculations indicate that the gas accumulation path is generally dominant, particularly at higher temperatures and for lower gas contents. The fraction of the critical size required for the vacancy path to contribute to the total nucleation rate increases with temperature. The results confirm the important role of transmutant helium in promoting void swelling.

## Summary (1 min read)

### Nucleation by Stochastic Fluctuations

- The method developed here is similar to that of Katz and Wiedersich (6) , Clement and Wood (26) and Mansur and Wolfer (27) .
- It should be pointed out that the void nucleation rate is quite sensitive to the dislocation density (see Fig. 3b below).
- The number of vacancies which correspond to this critical size will be designated n*.
- The values of the cluster concentrations in the constrained equilibrium distribution are elevated relative to the steady state distribution for n < n* also, this is accounted for in the theory by the introduction of the so-called Zeldovich factor.
- The term involving the products of the p. can safely be eliminated by noting two facts.

### Nucleation by Helium Accumulation

- The critical bubble size corresponding to n\u is in general not the same as the critical size associated with n discussed above.
- For a fixed value of the vacancy supersaturation, the family of curves shov/n in Figure 1 represent three different levels of helium.
- The curves labeled I and II contain a region in radius space for which the net growth rate is negative.
- Since the procedure used here is similar to that which has been discussed previously (20) only a brief summary will be given.

### He D He S? e

- G^ is the helium generation rate and D^e is the heliur.i diffusivity.
- Based on the foregoing helium partitioning model, the arrival rate of helium atoms at a bubble with a radius r(n,m) is EQUATION ) where N is the total number of bubbles among which the helium from the dislocations is partitioned.
- This bubble density is taken from Ref. 20 and reflects experimentally observed values.

### values of certain of these parameters listed in the table have been varied

- In the analysis and they will be discussed further in the text.
- These parameter values are similar to those which have been used previously in rate theory simulations of void swelling (18) (19) (20) .
- 2c where the ratio of the nucleation times has been plotted.
- For lower gas contents the nucleation time due to helium accumulation is always much less than that for the stochastic process.

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### Cites background from "A Comparison of the Relative Import..."

...There are two nucleation pathways for void formation under irradiation [18,20,21]....

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