Fission gas release during annealing

Two particular cases are of interest here. The first concerns a ramp from 1000°C at 1°C/s to a top temperature of 1900°C followed by a rapid quench. In this case, the entire anneal was complete in under 25 minutes. The predictions of the gas release model⁵ using the simplified bubble growth model are shown in Figure 6 using three separate values of the dislocation density. In this case the release was small and the predictions are equally good regardless of choice of dislocation density.

5 The gas release model incorporates a treatment of inter-granular bubble growth and grain face venting so the total release to the boundaries is much greater than the release shown here.

TABLE II. COMPARISON OF PREDICTED AND MEASURED SWELLINGS

0 200 400 600 800 1000 1200 1400

Temperature (o C) dislocation dens. = 1x10¹³ dislocation dens. = 5x10¹³ dislocation dens. = 10¹⁴

FIG. 6. Comparison of the measured fission gas release during a post-irradiation anneal with predictions for different dislocation densities.

In contrast, Figure 7 (see next page) shows the case of a much slower ramp at 0.2°C/s to 1650°C followed by a 30 hour hold at the top temperature. In this case the measured release exceeds 40% but predictions with a dislocation density of 3×10¹³ m^-2 saturate at about 20%

because most of the gas has been trapped by the bubbles. Consideration of the alternative calculations suggests that it is possible that the dislocation density started at this high value and gradually annealed to a final value of around or slightly less than 10¹³ m^-2 where the inhibition of bubble growth permits the gas release to rise to higher values.

Time (hours)

0 5 10 15 20 25 30

Temperature (o C)

600 800 1000 1200 1400 1600 1800

Fission Gas Release (%)

0 10 20 30 40 50 60

Temperature

Measured gas release dislocation dens. = 3x10¹² dislocation dens. = 1x10¹³ dislocation dens. = 3x10¹³

FIG. 7. Comparison of the measured fission gas release from a post-irradiation anneal held at 1700°C for thirty hours with predictions based on three different values of dislocation

density. The continued increase in the release may be a result of the annealing of the dislocation density during the extended anneal.

5. CONCLUSIONS

The issue of intra-granular bubble growth in post-irradiation annealed fuel has presented an obstacle to the understanding of fission gas release for many years. Recent experiments conducted under the auspices of the IMC - see footnote in §1 - in which pre-irradiated fuel has been subjected to out-of-pile thermal annealing followed by detailed SEM of the intra-granular bubbles⁶ have provided sufficient information to assist in the understanding of the growth phenomenon. The following conclusions have been drawn:

6 Note that a full study of the inter-granular pores was also made in which over 9400 pores on 84 grain boundaries were measured and catalogued according to morphology. These data will be published at a later date.

(i) There is no evidence of intra-granular bubble loss during post-irradiation anneals and although differences exist from specimen to specimen, these are probably within the experimental scatter. The concentration of grown bubbles is around 3.5×10²⁰ m^-3 which is much smaller than the concentration of nanometre sized bubbles present in low temperature irradiated fuel. It must be concluded that the grown bubbles are a small sub-population of the large low temperature seed-population.

(ii) The intra-granular bubble radii and swellings that are observed in out-of-pile anneals tend to be smaller than those observed in-pile.

(iii) The intra-granular bubble size distributions exhibit long exponential tails in which the largest bubbles are present in concentrations of four or five orders of magnitude lower than the average radius bubbles. These distributions are significantly different from those expected from a thermal re-solution mechanism. This, in conjunction with the invariance of the bubble populations during anneals is taken as evidence for lack of thermal re-solution of fission gas atoms from intra-granular bubbles.

An alternative model has been proposed to explain the slow growth of intra-granular fission gas bubbles. A detailed balance of the sources and sinks for vacancies in the fuel indicates that for most of the period of growth the intra-granular bubbles are starved of vacancies. This has two important consequences. The first is to attenuate the vacancy and fission gas diffusion rates. The second, and probably most important, is to create absorption difficulties at the matrix/bubble interface whereby a certain vacancy gradient is required to initiate absorption of vacancies and gas atoms. This mechanism operates as a selective absorption probability and, out of a large population of bubbles, a proportion may absorb gas and vacancies while the remainder may be unable to do so. This mechanism offers an explanation for the exponential tails on the distributions and for the fission gas release observed during post-irradiation anneals. The controlling parameter in this model is the dislocation density present at the end of irradiation period and the growth and release kinetics may change as this thermally anneals.

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