Philip Brohan

Grain Boundary Porosity And Gas Release In UO₂

Presented at the ANS-2000 Meeting, Park City, Utah, USA, April 2000.

Abstract

A campaign of power ramp and power cycling tests in the Halden reactor, and an intensive campaign of post-irradiation examination (PIE) on fuel from those tests, have provided a considerable collection of data on grain boundary bubble behavior. Analysis of this data has provided information on the conditions for grain boundary bubble nucleation, bubble pressures and growth rates, as well as the coalescence and spillage onto grain edges that leads to gas release.

Introduction

Fission gas release and gas bubble swelling are critical issues for light water reactor (LWR) fuel performance. Released fission gas can reduce the thermal conductivity of the fuel-clad gap and produce temperature increases in the fuel pellet; gas release can also produce high pressures in the fuel rod during operation, raising the possibility of clad lift-off. Swelling is an issue as fuel swelling may increase the contact pressure between fuel and clad, increasing the chances of clad damage or failure.

It has been well established that gas release is controlled by a strongly temperature dependent process of diffusion, however, negligible fission gas is released below a burnup dependent temperature threshold, and the existence of this threshold is interpreted as showing that gas release from the fuel is delayed while fission gas is accumulated in pores on the grain faces.

To understand and predict gas release, it is therefore necessary to be able to model the build up of grain face porosity. This paper describes some experimental data produced by PIE of grain face bubbles from UO₂ fuel ramped in a test reactor, and presents an analysis of the data with the aim of building a model for grain face porosity development.

Experimental Data

The AGR Ramp Program

Data on the development of grain boundary fission gas porosity was obtained by PIE of fuel ramped or power cycled in the Halden reactor.

Since the late 1980s British Energy (BE) have been mounting a program of experiments on Advanced Gas-Cooled Reactor (AGR) fuel (steel clad UO₂ with a hollow bore) in the Halden reactor^1-3. These experiments cover fuel at two different burnup levels (9-12 and 20-24 MWd/KgU), and include fast and slow power ramps with and without holds at high power, as well as the effects of power cycling.

The results of this program are of interest for LWR fuel modeling because some of the fuel was microscopically examined during PIE, producing data on grain boundary porosity growth that is relevant to any UO₂ fuel type.

The experiments for which this data is available are listed in the table below. Additional information on the fuel used in the experiments is given in the appendix.

Table 1: Experimental database for porosity data

Pin Number	Experiment Type	Burnup (MWd/KgU)	Peak Fuel Sample Temperature (C)	Hold Time(s)
IFA 576.4 rod 6	Slow ramp	9.2	1920	0
IFA 587.4 rod 2	Slow ramp	12.6	1800	0
IFA 587.4 rod 3	Fast ramp	12.6	1800	120
IFA 583.4 rod 3	Slow ramp	24	1870	0
IFA 583.2 rod 1	Fast ramp	22	1810	120
IFA 583.2 rod 4	Fast ramp	22	1810	120
IFA 583.2 rod 2	Fast ramp	22	1800	1800
IFA 619.2 rod 2	Power cycling (115 cycles)	20	1360	3600 per cycle
IFA 619.2 rod 4	Power cycling (115 cycles)	20	1520	3600 per cycle

PIE Program And Bubble Measurement

To characterize the fission gas bubble populations, a section was cut from each fuel pin at the axial location which saw the highest rating. From these sections, samples were taken at different radial positions (about every 0.5 mm) out from the central bore of the fuel pellet, thus covering a range of temperatures. Figure 1 shows a cross-section of an AGR fuel pin and an indication of the positions from which fuel samples were taken.

The fuel from each sample was fractured to provide a fresh surface which was examined in a Scanning Electron Microscope (SEM). Photo-micrographs were obtained of about six grain faces for each sample. Figures 2 and 3 are examples of these micrographs for a high and lower temperature sample respectively. Both examples come from the same fuel pin (IFA 583.2 rod 2), but the grain face in figure 2 was about 0.45mm out from the rod bore, while that in figure 3 was 1.95mm from the bore.

The effects of increased temperature are clear from the figures. At the higher temperature the bubbles are larger; and many have coalesced, forming serpentine, multilobed pores.

For each micrograph, the grain face porosity was measured by tracing each bubble. This provided data not only on the total porosity for each sample but also the distributions of bubble sizes and shapes^4,5.

Data Produced From The Ramp Tests And PIE Program

Typically five samples were examined from each of the nine rods in the experimental program. Six grain faces were examined from each sample. This gave detailed gas porosity and swelling data from almost 300 grain faces comprising 48 samples of UO₂, each with a different temperature history.

Data Analysis

From examination of the micrographs, it seems likely that as the fuel temperature increases past a threshold and gas arrives at the grain faces, initially small bubbles are nucleated across the grain face. These bubbles are circular in cross-section (lenticular in shape). As more gas is released to the grain faces the bubbles will grow, maintaining their shape until they get too large and start to coalesce.

To build a model for grain boundary swelling and gas release based on these assumptions it is necessary to know:

1. How many fission gas atoms are reaching the grain faces.
2. The threshold for bubble nucleation.
3. The number density at which bubbles are nucleated.
4. How the bubbles grow as more gas arrives at the grain faces.
5. When coalescence occurs and the bubble contents are vented to the grain edges.

Given this information a complete model for grain face swelling and release can be built. The data described above make it possible to address all these issues.

Gas Release To The Grain Faces

A model for release of fission gas to grain boundaries was developed by Booth⁶ and later refined by Speight⁷ and White⁸. Essentially this model considers the competing effects of single atom diffusion and irradiation induced resolution to predict the rate at which gas escapes from the grains.

The temperature and rating history for each sample can be calculated from the fuel rod power history using a fuel performance code. The gas release to the grain boundaries has been calculated from these histories using the model described above. The measured grain face porosity (total bubble volume fraction) is plotted against this calculated release in figure 4.

Threshold For Bubble Nucleation

Extrapolating to zero porosity from the low porosity data in figure 4 suggests that there is a threshold gas concentration on the grain boundaries of around 3.5x10²⁴ atoms/m³ (equivalent to 2x10¹⁹ atoms/m²) below which grain face bubbles do not appear.

Nucleation Number Density

The bubble number density for each sample can be measured from the micrographs, but many of the bubbles have coalesced, so the measured number density will be much lower than the nucleation density. To calculate the nucleation density, it is necessary to estimate the number of circular bubbles that were present on the grain face before coalescence began.

Equivalent Circular Bubbles.

Some of the bubbles on each grain face will be circular. From these the average area of a circular (uncoalesced) bubble can be calculated for each sample.

Assuming that bubble coalescence conserves area, the number of circular bubbles that joined up to make each large bubble can be estimated - see figure 5.

So for each sample the number of equivalent circular bubbles is the total bubble area divided by the mean area of a circular bubble. Figure 6 shows the equivalent circular bubble number density as a function of the fractional coverage of the grain faces with bubbles.

Figure 6 shows that there is no systematic trend in the ramp cases, with the average value being around 4-5 microns. Also there is no difference between the two burnup levels. The power cycling cases, however, show systematically lower number densities.

Figure 7 shows the variation in the mean circular bubble area.

The power cycling cases have much larger circular bubbles than the ramp cases, and this explains the systematically lower equivalent circular bubble number densities. The power cycling cases differ from the ramp cases in that, while the temperatures were lower, the fuel was at a high temperature for a long time (more than 100 hours, as against up to 0.5 hours for the ramp cases). It is likely that, over this long period, surface diffusion allowed some large bubbles produced through coalescence to change shape - becoming circular, and so the large circular bubbles in the power cycled samples have not grown from a single nucleation point.

The data shown in figures 6 and 7 support the hypothesis that grain face bubbles are nucleated at a density of 4-5 per square micron and that nucleation occurs rapidly when the density of fission gas atoms on the grain boundary exceeds a threshold; subsequent changes in the grain face porosity are due to bubble growth rather than the nucleation of additional bubbles. The difference between the ramp and power cycling data suggests that bubbles change their shape only slowly, over many hours.

Bubble Growth

The trend in circular bubble size for the ramp cases only is shown in figure 8.

Figure 8 shows a clear trend for the circular bubbles to increase in size as more gas arrives at the grain faces. As with the nucleation density there is no difference in the behaviour between the two burnup levels.

As bubbles are nucleated at a density of 4-5 per square micron, each bubble will collect the gas arriving over an area of about 0.22 square microns and grow as a result. So the number of gas atoms in each grain face bubble is the number released to 0.22 square microns of grain face after the threshold for bubble nucleation has been reached.

The volume of a grain face bubble can be calculated from the number of gas atoms using the ideal gas equation:

Where V is the bubble volume, p its pressure, T its temperature, R the gas constant, and n the number of gas atoms in the bubble.

The volume of the bubble therefore depends on its temperature and pressure.

Bubble temperatures

As an estimate of the peak temperature reached by each sample is available, it is straightforward to allow for temperature variations between the samples. Figure 9 is the same as figure 4 except that the pore volumes have been normalised to a temperature of 1700 C.

Bubble Pressures

If all the gas released to the grain boundaries ended up in the grain face bubbles, and the pressure in those bubbles were constant, then the data plotted in figure 9 should lie on a straight line. These two assumptions are reasonable for low release samples, where the bubbles are small and spillage of gas off the grain faces is negligible. The low release points can be reasonably well modeled by a straight line, and figure 10 shows the measured data at a calculated release of less than 2x10²⁵ atoms/m³ as well as the calculated porosities resulting from bubble growth at a pressure of 1MPa (plenum pressure) and 35MPa.

Figure 10 suggests that the pressure in the grain face bubbles is about 35 MPa and that it is the same for all the samples and thus independent of burnup. Although there is considerable uncertainty on this pressure estimate it is clear that the pressure in the bubbles is much greater than the plenum pressure of about 1 MPa.

The bubble pressure might be influenced by the compressive stress produced in the fuel by contact with the clad during the power ramps. However, calculations suggest that this stress is in the range 5-20 MPa for these experiments, again significantly lower than the bubble pressure.

These results are in agreement with previous experiments: in the Halden experiment IFA 558 it was demonstrated that variations of the plenum pressure between 0.2 and 4 MPa had no significant effect on the conditions for gas release^10, and Kashibe and Une¹¹ have shown that compressive stresses above 40 MPa have a significant effect in reducing gas release from irradiated fuel samples annealed out of pile.

Bubble Coalescence And Venting

The straight lines in figure 10 give the predicted porosity if all the gas reaching the grain faces is retained in bubbles. In fact as the bubbles grow some will come into contact with the grain edges and gas coming into those bubbles will be released from the grain faces. At the same time, bubble coalescence will greatly increase the bubble area open to the grain edges.

Bubble radius

Bubble coalescence depends on the bubble radius rather than its volume. As they are on a grain face the bubbles are lenticular rather than spherical⁹. The relationship between bubble volume and projected radius is:

Venting Probability For An Uncoalesced Bubble.

The probability that a circular bubble of radius r touches the grain edge is equal to the fraction of the grain face which is within r of the grain edge. So, if a grain face is modeled as a circle of radius R:

Venting Probability For A Bubble After Coalescence.

A bubble will also be vented if it touches another bubble which is touching the grain edge, so if m circular bubbles, each of radius r, coalesce to form one large, multilobed bubble (see figure 5), the large bubble will be vented if any of the circular bubbles touch the grain edge. The probability that the large bubble is not vented is therefore the probability that none of the circular bubbles is. Using the simplifying approximation that the venting probabilities for each of the m circular bubbles are independent, this gives:

Degree Of Coalescence.

To calculate vented fractions using equation 4 requires a model for bubble coalescence to calculate m. This calculation is difficult, but it is simple to estimate the mean value of m from the data.

Using the idea of equivalent circular bubbles introduced above, the mean value of m for each sample is the mean area of a bubble divided by the mean area of a circular bubble. Figure 11 is a plot of this result against grain face fractional coverage.

The data shown in figure 11 show a clear increase in the degree of coalescence as the grain face coverage increases, but the variation has no obvious functional form so it is most simply represented by a straight line. Figure 11 also shows a linear model for the data.

Calculation Of Grain Face Porosity And Gas Release.

The above analysis has produced models for bubble nucleation, growth, coalescence and venting, and these, together with a calculation of gas release to the grain faces, form a complete model for grain face porosity development and fission gas release.

The calculation has 4 steps:

1. Calculate the increment of gas release to the grain faces. Bubbles nucleate at 4-5 per square micron so the gas arriving over an area of 0.22 square microns is the source for each bubble.
2. From the bubble radius, calculate the venting probability. This gives the fraction of the gas which is retained in the bubbles, and the gas released.
3. Increase the amount of gas in each bubble by the amount calculated in step 1 multiplied by the probability the bubble is not vented.
4. From the bubble content, pressure and temperature, calculate the bubble volume and radius. This gives the grain face porosity.

Applying these steps iteratively gives the development of the grain face porosity as more gas arrives at the grain boundaries. Figure 12 shows the data from figure 9 as well as the calculated porosity at a temperature of 1700 C and pressure of 35 Mpa.

Figure 12 demonstrates that this model gives a good prediction of the grain face porosities of this dataset.

Conclusions

SEM of small samples from ramped and power cycled fuel has produced a comprehensive set of data on grain face porosity development in UO₂ fuel.

Analysis of this porosity data using a widely accepted model for the release of fission gas to the grain faces has produced a model for grain face porosity development.

The main conclusions from the analysis are:

1. Bubbles nucleate on the grain faces when the fission gas concentration there exceeds 2x10¹⁹ atoms/m².
2. The bubbles nucleate at a density of 4-5 per square micron.
3. The bubble pressure can be much higher than the rod plenum pressure. A pressure of 35 MPa is estimated for the data analysed here.
4. Bubble coalescence and the venting of bubbles to the grain edges becomes important when the coverage of the grain face by bubbles exceeds 25%, and increases linearly when the coverage grows beyond this value.
5. Large multilobed bubbles produced by coalescence of small circular bubbles can change shape to become circular, but the process is slow, taking many hours.
6. There is no difference in grain face bubble behavior between the two burnup levels studied (9-12 and 20-24 MWd/KgU).

References

1. C. Wise & P.A. Tempest, "Experiments on Pellet-Clad Interaction in Advanced Gas Cooled Reactor Fuel in the Halden BWR Facility", Enlarged Halden Program Group (EHPG) Meeting, Bolkesjø 1994, HPR 345/25
2. M.A. McGrath, "Advanced Gas-Cooled Reactor (AGR) Fuel Tests in Halden", EHPG Meeting, Loen 1996, HPR-347/25
3. C. Baker, R. Corcoran, A.T. Donaldson & R.J. White, "An Investigation of Intragranular Fission Gas Bubble Distributions in Commercial Advanced gas Cooled Reactor (CAGR Fuel, Following Power Ramps in the Halden Reactor", EHPG Meeting, Loen 1996, HPR 347/25
4. R.J. White, J. Chuter, T.C. Gilmour, M.J. Liddington, S. Mowles, K. Stook & J.M. Stump, "Swelling Measurements on AGR Fuel Ramped in the Halden Reactor", Nuclear Electric Report, EPD/AGR/REP/0050/96, 1996
5. R.J. White, "Swelling Measurements on AGR Fuel Ramped in the Halden Reactor: Part 2, IFA 587.4 & IFA 619.2", Nuclear Electric Report, EPD/AGR/REP/0454/98 1998
6. A.H. Booth, "A Method of Calculating Fission Gas Diffusion from UO₂ Fuel and its Application to the X-f-2 Loop Test", AECL Report No. 496, 1957
7. M.V. Speight, Nucl. Sci. and Engineering, 37, 180, 1969
8. R.J. White, "A New Mechanistic Model for the Calculation of Fission Gas Release, ANS International Topical Meeting on Light Water Reactor fuel Performance", April 1994
9. R.J. White, "Fission Gas Release and Swelling in Irradiated Uranium Dioxide", Nuclear Electric Report EPD/GEN/REP/0166/96, 1996
10. P.A. Tempest & R.J. White, "The Effect of Fill Gas Pressurization on Fission Gas Release and Thermal behavior in IFA 558 and its Prediction by the Fuel Performance Code ENIGMA", EHPG Meeting, Storefjell 1993, HPR 343/27
11. S. Kashibe & K. Une, "Effect of External Restraint on Density Change and Fission Gas Release in UO₂ Fuels", EHPG Meeting, Lillehammer 1998, HPR 349/20

Appendix - Fuel Characteristics

All the fuel pins used in the experimental program were of AGR design - UO₂ fuel pellets 14.5mm in diameter with a hollow bore and clad in stainless steel. However, they had different base irradiations and slight differences in their as-fabricated properties.

The fuel rods fall into three groups: IFA 576.4 used one batch of fuel which was both base irradiated and ramped in the Halden reactor, IFA 587.4 used a second batch base irradiated in Torness, and the other experiments used a third batch base irradiated in Hinkley Point B.

The table below summarises some fabrication data for each group.

	IFA 576.4	IFA 587.4	IFAs 583.2 583.4 619.2
Base Irradiated in	Halden	Torness	Hinkley Point B
Pellet radius (mm) inner/outer	3.175 / 7.255	3.175 / 7.255	3.175 / 7.255
Clad thickness (mm)	0.37	0.37	0.37
MLI grain size (microns)	11.7	12.2	13.0
Initial density (%)	98	98	98
Fill gas/pressure (MPa)	He / 0.136	He / 0.1	He / 0.1
Enrichment (%)	2.86	2.25	2.78