Journal of Nuclear Materials 206 (1993) 22-34 North-Holland
Formation and growth of intragranular fuels with burnup of 6-83 GWd/t
fission gas bubbles in UO,
S. Kashibe, K. Une and K. Nogita Nippon Nuclear Fuel Development Co., Ltd., 2163 Narita-cho, Oarai-machi, Higashi Ibaraki-gun, Ibaraki-ken, 311-13 Japan
Received 12 January 1993, accepted 10 May 1993
The detailed characteristics of intragranular fission gas bubbles in UO, fuel pellets (burnup: 6-83 GWd/t) before and after posti~adiation annealing at 1600 and 1800°C have been examined by TEM and SEM fractography. In the base-irradiated fuels, a high density of small bubbles of about 2 nm in diameter precipitated uniformly in the matrix. When increasing burnup above 44 GWd/t, larger bubbles of lo-20 nm newly appeared in addition to the small bubbles. On heating at high temperatures, bubble growth was saturated within a few minutes. Enhanced coarsening of bubbles was found preferentially near the grain boundaries in the middle burnup fuels of 16-28 GWd/t and throughout the grains in the high burnup fuels of 44 and 83 GWd/t. The bubble growth during annealing was associated with a remarkable decrease of the bubble number density, and the relationship between bubble density A$ and mean diameter d, was expressed as A$, a d;2.6. The coarsening was attributed to coalescence via bubble migration for moderately large bubbles of up to SO-60 nm, and to Ostwald ripening accompanied by a sufficient vacancy supply from external vacancy sources such as free surfaces, grain boundaries or irradiation-induced sub-grain boundaries for huge bubbles above 100 nm.
1. Jntroduction Fission gas atoms (Xe and Kr) generated in UO, lattice have a strong tendency to precipitate into bub-
bles at locations of many radiation defects and grain boundaries, because of their low solubility. Small intragranular gas bubbles are partially or completely destroyed by close-passing fission fragments and some of the gases in the bubbles are resolved into the matrix during irradiation [l]. Namely gas atoms in grains diffuse from grain interiors to boundaries through repeated trapping by the bubbles and resolution into the matrix, and finally fission gases trapped in the grain boundaries are released via interlinked grain boundary tunnels [2,3]. Consequently the formation and growth kinetics of intragranular bubbles are closely related to the effective diffusion rates of fission gases in grains. Moreover the precipitation of intragranular bubbles as well as intergranular bubbles swells fuel pellets during transient conditions, which brings about a severe pellet-cladding mechanical interaction (PCMI) at high burnups [4,5]. The detailed characteristics (mean diameter and number density) of intragranular bubbles in UO, fuels base-irradiated to 6-45 GWd/t have been examined ~ZZ-31~5/93/$~.~
by a transmission electron microscope (TEM), in which the small bubbles of l-3 nm in diameter observed in low burnup fuels (l-18 GWdft) [6,7] appear to grow to 7-8 nm in high bumup fuel with 45 GWd/t . Migration and growth of bubbles during postirradiation annealing has also been studied by TEM in the temperature ranges of 1400-1500°C for Kr-ion implanted UO, fuel , 1500-~6~‘~ for 4 GWd/t fuel [lo], 1300-1570°C for 8 GWd/t fuel [ll] and 1250-1660°C for 38 GWd/t fuel . Among the former three studies, quite different bubble size dependencies on the root-mean-square movement of bubbles were found. The derived bubble diffusivity, D,, varied as -3 -rp 191, lb’ [lo] tr g bubble radius) or there was lb no clear relationship between them fll]. Furthermore in these experiments with low burnup fuels of 4 and 8 GWd/t, strongly suppressed bubble growth was reported. By contrast, in annealing experiments with middle and high burnup fuels of 38 GWd/t by Baker and Killeen , and 25 and 44 GWd/t by us , significant growth of small bubbles of several nm began to occur at 1520 and 145O“C, respectively. Although there have been many experimental studies on the behaviour of intragranular bubbles so far, systematic investigations of burnup dependence on the formation
0 1993 - Elsevier Science Publishers B.V. All rights reserved
S. Kashibe et al. / Formation and growth of fission gas bubbles
and growth of bubbles are limited, especially at higher burnups above 40 GWd/t and at higher temperatures above 1600°C in connection with intragranular bubble swelling during power transients. In another previous paper , we examined the detailed characteristics of intergranular bubbles in base-irradiated and out-of-pile annealed UO, fuels and discussed the growth mechanism. In the present study, the corresponding data for intragranular bubbles in UO, pellets before and after postirradiation annealing at 1600 or lSOO”C, which had been irradiated to 6-83 GWd/t in light water reactor (LWR) conditions, were obtained by transmission (TEM) and scanning electron microscopies (SEMI. From the correlation between bubble diameter and bubble density and the kinetic data of bubble growth, the growth mechanism was discussed. In addition, intra- and intergranular bubble swelling, which was brought about by annealing at high temperatures, was individually evaluated, and the significance of intragranular bubble swelling at higher burnups was pointed out.
2. Experimental 2.1. Fuel specimens
The specimens examined in the present experiments were taken from UO, fuel pellets irradiated to 6-44 GWd/t in a commercial BWR, or to 83 GWd/t under PWR conditions in a test reactor. The fuel burnups and design characteristics of the pellets and rods are given in table 1. The density of the former fuel pellets was 95% TD, a little larger than the value of 93% TD for the latter. The latter fuel pellet was hollow with a pellet hole of 2.5 mm. Small discs (about
Table 1 Fuel pellet and rod design characteristics Fuel Burnup (GWd/t) Pellet density (%TD) 235U enrichment (%) Grain size (pm) Pellet diameter (mm) Pellet hole diameter (mm) Pellet-cladding gap (mm) He fill gas pressure (MPa) Active stack length (mm) Cladding material Cladding outer diameter (mm)
BWR 6-44 95 1.5 9 10.6 0.23 0.1 3660 Zircaloy-2 12.5
1.5 mm in diameter, 1 mm thick and weighing 30 mg) for the examinations were punched from the pellets at a point between the fuel rim and mid-radius, using an ultrasonic disc cutter. Experienced maximum temperatures at the location of the specimens were estimated to be about 800°C from their maximum linear heat generation rates. Local burnups and retained fission gas at that region were examined from radial distributions of soluble fission products of Zr and Ce, and Xe measured with an electron probe microanalyzer (EPMA). The local burnups of the specimens were very close to the above pellet average burnups, and most of fission gases generated during base-irradiation were retained there. The EPMA data for the high burnup pellets of 44  and 83 GWd/t  have been reported previously. Therefore fission gas concentrations in the fuel specimens range from 0.14 to 2.0 at%. The average grain size, after base-irradiation, was S-10 p,rn for the BWR fuel pellets and 12-14 km for the PWR-type fuel pellet according to ceramographs of each specimen, and no grain growth during base-irradiation occurred. In addition to the base-irradiated fuels, out-of-pile annealed fuels were also examined. The annealing conditions were as follows: for ramp heating tests, the specimens were heated up to 1800°C at various rates of 0.03-lo”C/s, and immediately cooled down to room temperature at the rate of 1.7”C/s. However for the slowest test of O.O3”C/s, temperature was first raised to 1200°C at 1.7”C/s and then to 1800°C at O.O3”C/s. For isothermal annealing tests, they were heated up to 1600 or 1800°C at 1.7”C/s, and held there for 5 h. The cooling rate was 1.7”C/s. The annealing atmosphere was high purity He/2%H, mixed gas at a flow rate of 60 cm3/min. The annealing apparatus and the experimental procedure were described in detail previously [17,18]. 2.2. Bubble observations
PWR-type 83 93 7.0 13 8.2 2.5 0.17 2.9 1017 Zircaloy-4 9.5
Intragranular bubbles in the base-irradiated and annealed fuels were observed by TEM and SEM. The TEM sample was prepared by a crushing technique. Small discs of the base-irradiated fuels were crushed into powder in an alumina mortar. The powder was suspended in n-propyl alcohol and the suspension was dropped on the TEM microgrids with a syringe. A 200 kV TEM was used and magnifications were from 100 000-300 000. The intragranular bubble concentration per unit volume of fuel, Nb, was calculated by
S. Kashibe et al. / Formation and growth of fission gas bubbles
where n is the number of bubbles obtained by image analysis based on TEM micrographs, A the observed area, and t the thickness of TEM sample. The value of t‘ was about 5-35 nm, which was evaluated by the thickness fringe. The error in bubble concentration due to uncertainty in the thickness was about rf:30%. SEM observations were carried out on a fractured surface of the fuel specimens, which was prepared by a diamond scratch method. The Nb was calculated by V
where d, is the three-dimensional mean diameter of bubbles, which was obtained by multiplying the two-dimensional diameter obtained from image analysis by 1.5  and V is the fractional volume in the fuels occupied by bubbles. The quantitative image analysis was applied to fractographs with magnifications of 5000-100000.
3. Results 3.1. Bubble morphology Figs. la-lc base-irradiated
show bright-field TEM images for the fuels with various burnups of 23, 44
and 83 GWd/t. There is a high density of small intragranular bubbles, of a few nm size, in the fuel matrix. The bubble size in the middle burnup fuel of 23 GWd/t (fig. la) is 2.2 nm in diameter, and they are homogeneously distributed with a high density of 9 X 102” m-3. In the high burnup fuels of 44 and 83 GWd/t, larger bubbles of about lo-20 nm newly appear, besides the 2 nm bubbles. The mean diameter and number density are 3.9 nm and 7 X 1O23 mm3 for the 44 GWd/t fuel, and 4.7 nm and 4 x 1O23 ms3 for the 83 GWd/t fuel. When increasing fuel burnup, the mean bubble size increases and bubble concentration decreases slightly. The density of the larger lo-20 nm bubbles increases cfearly with higher burnup. Finally, bubble size distribution changes from a monomodal shape for the middle burnup fuel of 23 GWd/t to a bimodal one for the highest burnup fuel of 83 GWdft. The bimodal distribution observed is attributed to (a) geometrical coalescence of adjacent small bubbles because of the increased bubble concentration at high burnups, and/or (b) bubble growth due to biased capture of radiation-induced supersaturated vacancies into the bubbles containing solid fission products precipitate. In fact, in larger bubbles above several nm in the high burnup fuels of 44 and 83 GWd/t, solid fission products precipitate, which are presumably composed of molybdenum, technetium, ruthenium, rhodium and palladium.
Fig. 1. Bright-field electron micrographs of base-irradiated fuels: (a) 23 GWd/t; (b) 44 GWd/t; (c) 83 GWd/t.
S. Kashibe et ai. / Formation and growth
Cornell 161 has reported small bubbles of 2-3 nm size with densities of l-3 x 10z3 mS3 in base-irradiated UO, fuels of l-18 GWd/t, irrespective of irradiation temperature of 800-1600°C. On the other hand, Baker  has found two categories of small bubbles in UO, fuels of 8-9 GWd/t, depending on irradiation temperature, i.e. 1 nm bubbles with a higher density of 9 x 10z3 mm3 at 1000°C and 2 nm bubbles with a lower density of 4 X 10z3 me3 at 1600-1800°C. Their bubble sizes are almost equivalent to the value f = 2 nm) obtained in the present study for the middle burnup
of assign gas bubbles
fuel of 23 GWd/t with irradiation temperatures below 8OO*C,as shown in fig. la. Our bubble concentration of 9 x 10z3 mm3 is consistent with the values (4-9 X 1O23 me31 by Baker . Recently Ray et al. 181examined intragranular bubbles in high burnup UOz fuels, which had been irradiated to 45 GWd/t in a commercial PWR. They prepared TEM specimens from different locations in the pellet, i.e. fuel periphery and center, at which estimated irradiation temperature was about 500 and 12OO”C,respectively. The reported bubble size and density were - 8 nm and 1-2 X 102’ rne3, apparently
Fig. 2. SEM fractographs of the fuel with burnup of 23 GWd/t after annealing at 1600°C X 5 h.
S. Ku&be er al. / Formaf~~~and growthoff~s~~ gas bubbles
independent of irradiation temperature. Compared with the present results (fig. lb) for the high burnup fuel of 44 GWd/t, they did not observe the 2 nm bubbles in addition to the 8 nm bubbles with a narrow monomodal distribution. The reason why Ray et al. reported a bubble density of about l-2 orders of magnitude smaller than the value (7 x 1O23 me31 obtained in the present fuel is probably due to no enumeration for the 2 nm bubbles. Figs. 2 and 3 show SEM fractographs of the fuels with 23 GWd/t after annealing at 1600 or 1800°C for 5 h, respectively. In both fra~tographs, coarsened intragranular bubbles are found only within limited regions
near the grain boundaries, i.e. about 1 ym for the case of 1600°C x 5 h of fig. 2 and about 3 km for the case of 1800°C x 5 h of fig. 3, in contrast to smaller bubbles of 45-55 nm in the central region of the grains. Near the boundaries no smaller bubbles precipitate. The enhanced coarsening near the grain boundaries clearly indicates that a substantial vacancy supply from open grain boundaries or free surfaces due to the formation of grain boundary tunnels plays an important role in the coarsening of bubbles. In the grain interiors, a sufficient supply of vacancies may be suppressed due to the distance from vacancy sources, such as grain boundaries or free surfaces. The observed mean bub-
Fig. 3. SEM fractographs of the fuel with burnup of 23 GWd/t after annealing at 180O”C~5 h.
S. Kashibeet al. / Formation and growthof fision gas bubbles Temperature T
o- -.& /
J HA *.
apen~bols~ce~ solid symbole.neer
from TEM and SEM fractography. The burnup dependence of mean bubble diameter and number density observed in the central region of the grains after annealing at 1800°C for 5 h, is given in fig. 6. The final bubble size in the annealed fuels is 110 nm for the lowest bumup fuel of 6 GWd/t, about 60 nm for the middle bumup fuels of 16-28 GWd/t, and 550 and 800 nm for the high burnup fuels of 44 and 83 GWd/t, respectively. The corresponding bubble number density has the opposite tendency: the smaller bubbles have the larger number densities, which vary over three orders of magnitude from 10” to 10” m-3.
Fig. 4. Mean diameter and number density of bubbles near grain boundaries and in the central region of a grain for the 23 GWd,/t fuels as a function of the annealing temperature.
ble size and bubble density near the grain boundaries and in the grain center are plotted against the inverse of absolute temperature in fig. 4, indicating different temperature dependencies of bubble size and density. An apparent activation energy, for the annealing duration of 5 h, obtained from the temperature dependence of the mean diameter is 0.4 eV in the grain center and 1.3 eV near the grain boundaries. Figs. 5a and 5b show fracture surfaces of the high burnup fuels of 44 and 83 GWd/t after annealing at 1800°C for 5 h, respectively. The bubble sizes of both fuels are larger than that in the middle burnup fuel of 23 GWd/t. Furthermore, even in the central region of the grains, very large bubbles of several 100 nm to pm size are formed. The 45-55 nm bubbles, which were observed in the 23 GWd/t fuel of figs. 2 and 3, are not found in these fuels. The absence of small bubbles below several 10 nm was also confirmed by TEM on the annealed high burnup fuels. Some of the huge bubbles in the 83 GWd/t fuel of fig. 5b show a peanut-shape, indicating coalescence of nearest neighbor bubbles with each other during heat treatment. The mechanism of bubble coarsening is detailed in section 4. The characteristics of bubbles for the base-irradiated and annealed fuels with various burnups and temperature histories are summarized in table 2. These were obtained by image analysis based on micrographs
The relationship between bubble number density and mean diameter for the base-irradiated and annealed fuels with various burnups of 6-83 GWd/t and various annealing histories (temperature: 1600-1800°C; heating rate: 0.03-lO”C/s; holding time: O-5 h) is given in fig. 7. A good linear relationship can be expressed by the following least square fitted equation for the bubble diameter range of Z-800 nm: log N,, = -2.6
logd, + 25.1,
where Nb is the bubble number density in me3 and d, is the mean bubble diameter in nm. The solid line in the figure represents the fitted line of eq. (3), and the chain line corresponds to the condition of geometricai coalescence of nearest neighbor bubbles. Baker and Killeen’s data  for annealed fuels (annealing temperature: 1250-1660°C; holding time: 50 s-24 hf, which had been base-irradiated to 38 GWd/t in a commercial PWR, appear to be in good agreement with the fitted equation. On the other hand, Small’s bubble densities  of 10’7-1019 mm3 for 20-200 nm bubbles in the annealed fuels (1500-19OO”C, 300-1900 s) with burnup of 18 GWd/t are about two orders of magnitude lower than the present data. Regarding bubbles in base-irradiated fuels, our bubble densities are a little larger than the values reported by other investigators [6-81 at a given bubble size. The relationship between bubble number density N,, and bubble diameter d, can be theoretically expressed as Nt, a db3 for dense gas with a constant density in smaller bubbles below about 20 nm and as Nb a db2 for ideal gas with the~od~amic equilibrium densities at p = 2-y/r, (p: gas pressure; y: surface energy) in larger bubbles above about 200 nm 1211. In the range of 20 d d, < 200 nm, gases in a spherical bubble may be regarded as a mixture of the two states. The present relationship of N,, a d;2.6 in a 2
S. Kashibe et al. / Formation and growth of j&ion gas bubbles
Fig. 5. SEM fractographs of the high burnup fuels after annealing at 1800°C for 5 h: (a) 44 GWd/t; (b) 83 GWdft.
Table 2 Mean diameter and number density of intragranular bubbles for base-irradiated
Mean diameter (nm)
Number density (mw3)
23 44 83 6a 16 b 16 a 23 b 23 a 23 a 23 h 23 a 28 ’ 28 = 28 b 28 a 28 b 28 a 28 = 44 b 44 a 83 =
base-irradiated base-irradiated base-irradiated lSOo”Cx5 h 18oo”Cx5 h 18OOYZx5h 16OO”Cx5 h 16OO”Cx5 h 1800°C (lO”C/s ramp) 18oo”CxS h 18OO”Cx5 h 16oo”Cx5 h 16OO”Cx5 h 1800°C (O.O3”C/s ramp) 1800°C (O.O3”C/s ramp) 1800°C (1.7”C/s ramp) 1800°C (1.7”C/s ramp) 1800°C (lO”C/s ramp) 18OO”CxS h 18OO”Cx5 h 18OO”Cx5 h
2.2 3.9 4.7 113 107 47 77 44 33 164 55 55 42 83 59 83 54 44 516 551 805
9.0 x 6.7 x 4.4x 3.4x 1.2x 3.6 x 1.6x 4.7 x 6.3 x 3.2x 4.9x 2.5 x 5.3 x 1.5 x 2.9x 4.7 x 3.6 x 6.5 x 1.0x 8.0 x 7.1 x
a Grain center ’ Near grain boundaries
1023 10”” 102” 10’9 1020 10” 10” 1020 10” lOI9 1020 1020 1020 1020 102’ 1020 10” 10zo IO’” 10’7 1017
S. Kashibe et al. / Formation and growth of fission gas bubbles
‘j: .5 5 10” 0 &
E x .Z g 1 1o’9 Q) n 8
2 z’ :
10” open symbols: solid symbols:
base- irradiated annealed
10” 1 10’ 0
800 nm range for the base-irradiated and annealed fuels lies on an intermediate situation of constant density and equilibrium densities of gas atoms, suggesting that initially overpressurized small bubbles of p * 2y/r, would approach equilibrium pressures as bubbles coarsen. In fact, solid or near-solid xenon-krypton particles of 20-100 nm were first found in LWR fuels of about 30-40 GWd/t by Thomas . The densities of the fission gas-solids measured by energy-dispersive
ramp of 28 GWd/t
Fig. 7. Correlation between bubble number density and mean for base-irradiated and annealed fuels. (0, 0) present work; (0 ) Cornell ; ( n ) Baker and Killeen ; ( v ) Baker 171; (A) Ray et al. . diameter
Fig. 6. Burnup dependence of mean diameter and number density after annealing at 1800°C for 5 h. (*) Annealed at 1700-1800°C for - 60 min.
Fig. 8. SEM fractographs
X-ray spectrometry (EDS) ranged from approximately 2 to 4 g/cm3, which are roughly equal to the density of solid face-centered cubic xenon of 4 g/cm3 . In order to obtain the coarsening rate of small bubbles, temperature ramp tests up to 1800°C with various heating rates of 0.03, 1.7 and lO”C/s were conducted. Figs. 8a-8c show fractographs of the ramp tested fuels with the burnup of 28 GWd/t. For the fastest heating rate of lO”C/s (cumulative heating duration above 1700°C: = 1 min), mean bubble size is 44
up to 1800°C at various
ramp (c) O.O3”C/s.
et al. / Formation
nm, while bubble sizes are 54 and 59 nm for the heating rates of I.7 (= 2 min) and O.O3”C/s (= 60 min), respectively, with no significant difference between them. The dependence of heating duration on mean bubble diameter is shown in fig. 9, when the base-irradiated fuels of 6-2X GWd/t were heated at high temperatures above 1700°C. The bubble sizes are distinctly saturated at the sizes of 50-60 nm within a few minutes for the middle burnup fuels of 16-28 GWd/t. By contrast, the bubble size of the lowest burnup fuel of 6 GWd/t becomes larger ( = 110 nml by a factor of 2 than the values (= 60 nm) for the middle burnup fuels of 16-28 GWd/t. According to the Greenwood-Speight model WI, which treated bubble migration and coalescence controlled by surface diffusion on the assumption of a fixed number of gas atoms in the bubbles during annealing, bubble diameter becomes larger in proportional to heating duration to the fifth power, and is expressed by
and growth offission gas bubbles
Fig. 10. Burnup dependence of bubble swelling for baseirradiated and annealed (18OO”CXS h) fuels. (*I Annealed at 1700-1800°C for _ 60 min.
d, = 3(~~D~~kT/~)i’~f1/5,
where M is the gas atoms per unit fuel volume which are contained in bubbles, a, the lattice constant, k Boltzmann’s constant, t the time, T the absolute temperature, and 0, the self-surface diffusion coefficient. The calculated growth curves for the two different burnups of 6 and 28 GWd/t by using reported D, values  are also given in fig. 9. Although a very fast growth of bubbles in a few minutes at the beginning of heating can be explained by the model, the experimental data, except for the value of about 110 nm in the lowest burnup fuel of 6 GWd/t, are suppressed to a size of about 60 nm. This saturation of bubble growth at high temperatures may be ascribed to pinning of 1 Bumup
16 23 :
:Greenwood- Speight model
I: I: .
Fig. 9. Bubble growth transients at 1700-1800°C for the fuels of 6-28 GWd/t.
mobile bubbles at dislocations and ~ntamination of the bubble surface by the solid fission products [21,25]. In fact, larger fission product precipitates are clearly observed in larger bubbles of several 10 nm, as shown in figs. 8a-8c. 3.3. Intrugranular bubble swelling Fuel swelling due to the precipitation of intragranular bubbles was calculated by mean bubble diameter and number density (table 2). The swelling for the base-irradiated UO, fuels is 0.5% at 23 GWd/t, 2.0% at 44 GWd/t and 2.5% at 83 GWd/t. As shown in figs. 3 and 5, small intragranular bubbles of 2-20 nm in the base-irradiated fuels grow remarkably after annealing at 1800°C for 5 h, and, in the high burnup fuels of 44 and 83 GWd/t, unusualIy coarsened bubbles above several 100 nm even in their grain centers appear. The burnup dependence of intragranular bubbie swelling before and after annealing at 1800°C for 5 h is given in fig. 10. The intragranular swelling in the annealed fuels increases progressively from 2 to 8% in the burnup range of 6-44 GWd/t. By contrast, in the highest burnup fuel of 83 GWd/t, the swelling becomes significantly large, 24%, due to the unusual coarsening of bubbles. Although kinetic data on bubble growth for the high burnup fuels of 44 and 83 GWd/t were not obtained in the present experiments, the bubble growth for the middle burnup fuels of 16-28 GWd/t (fig. 9) is certainly saturated in a few minutes. Therefore fuel
S. Kashibe et al. / Formation and grow6h of fission gas bubbles
swelling generated on high temperature transients must be expected to develop within a few minutes. In addition to intragranular bubble swelling, intergranular bubble swelling was also obtained from the difference in grain boundary porosity based on scanning electron micrographs of the polished surface taken before and after annealing. The porosity measurements were carried out by quantitative image analysis. The obtained burnup dependence of intergranular bubble swelling is also given in fig. 10. The intergranular bubble swelling is about 8-9% for the fuels of 6-28 GWd/t, and lo-11% for the high burnup fuels of 44 and 83 GWd/t, almost independent of fuel burnup. This saturation is due to the geometrical condition of the grain boundary or the limited grain boundary area. The theoretical saturated swelling, at which grain boundary bubbles begin to interlink with each other, is proportional to the bubble size and inversely proportional to the grain size . When using the most frequently observed radius of intergranular bubbles of 0.7-0.8 pm and the grain size of the present UO, fuels of 9 and 13 Frn (table l), the theoretical saturated swelling is 8-ll%, which is in good agreement with observed ones. By contrast, the theoretical saturated swelling by intragranular bubbles becomes much larger, being llO%, irrespective of grain size . When comparing the intragranular bubble with the intergranular bubble swelling, the latter one is predominant in the burnup range of 6-44 GWd/t. However, the ~ntribution of intragranular bubble swelling in the total swelling becomes progressively larger with increasing burnup, in contrast to the saturated intergranular swelling of about 10%. Finally the value of intragranular bubble swelling in the highest burnup fuel of 83 GWd/t is approximately double that of intergranular bubble swelling. In the present study, of course, all swelling data were obtained under an unrestrained condition. Large compressive loads have been reported to suppress bubble growth and to reduce fuel swelling . Furthermore, fission gas release as well as fuel swelling during power ramping and power cycling conditions are strongly dependent on cladding restraint or PCMI [4,29]. Accordingly the data for restrained bubble swelling, which can be obtained in high pressure and high temperature annealing experiments, are desired to evaluate fuel swelling under PCMI on power transients.
words, on annealing at high temperatures bubble number density decreases markedly in the course of bubble coarsening. This indicates that possible bubble growth mechanisms are (a> coalescence via s~ntaneous bubble growth or bubble migration [23,30,31], or (b) Ostwald ripening via resolution and reabsorption of gas atoms and vacancies [32,33]. First we consider the mechanism of bubble coalescence. The relation between the present data and the condition for geometrical coalescence of nearest neighbor bubbles is shown in fig. 7. The chain line in the figure corresponds to the condition for geometrical coalescence, which was calculated from the relation of d, = NC]/3 for regularly arranged bubbles in a simple cubic lattice. For example, if small bubbles of N,, = 10” me3 and d, = 2 nm observed in the base-irradiated fuel of 23 GWd/t grow up spontaneously to about 10 nm by absorbing vacancies, geometrical coalescence occurs and then the bubble number density is reduced to half its original number. Thereafter, bubble density and size must be reduced along the chain line during bubble coarsening via geometrical coalescence. The observed bubble densities for the bubble sizes of 2-100 nm, however, are certainly about l-2 orders of magnitude lower than the geometrical coalescence condition. Consequently, for this range, geometrical coalescence is not a reasonable coalescence mechanism. Only huge bubbles in the annealed highest burnup fuel of 83 GWd/t may have a possibili~ for geometrical coalescence, since its bubble density is close to the condition of d, = NE-‘j3. In fact, coalesced huge bubbles with a peanut-like shape appear in fig. 5b. On the other hand, in the absence of a temperature gradient small bubbles in solids can migrate by Brownian motion rate-controlled by surface diffusion, volume diffusion or vapor transport [23,30,31]. Although the data [9-ll] on bubble diffusivity in irradiated UO, fuels do not always support a fast surface diffusion mechanism for bubble migration, many sophisticated models [34-361 have adopted that mechanism. Accordingly we also assume the same mechanism in the following discussion. Then a simple condition for coalescence via bubble migration is given by
where x is the root-mean-square movement of bubbles; D,, the bubble diffusion coefficient; and the others, as described before. Using the values of D, reported by Maiya 1241, bubbles smaller than 74 and
As shown in fig. 7, the larger bubbles have a strong tendency to have smaller bubble densities. In other
&+2x&5* x = (4D,t)*‘2,
and D, = -, 2nr,4
S. Kashibe et al. / Formation and growth of fission gas bubbles
120 nm for the cases of 1600°C x 5 h and 1800°C x 5 h may have possibilities of coalescence via bubble migration, respectively. In the present results on bubble growth transients in the middle burnup fuels of 16-28 GWd/t at high temperatures above 1700°C (fig. 9>, the bubble size is completely suppressed at 50-60 nm in a few minutes. For this bubble immobilization, pinning of bubbles at dislocation lines and contamination of the bubble surface by solid fission products can be suspected [21,25], as described before. In contrast to the suppressed bubble growth in the grain interiors, an enhanced coarsening of bubbles is preferentially found near the grain boundaries of the middle burnup fuel of 23 GWd/t, as shown in figs. 2 and 3. The mean bubble size near the boundaries is 77 and 160 nm for annealing conditions of 1600°C x 5 h and 1800°C x 5 h, respectively, while the corresponding bubble size in the grain center is 55 and 47 nm. Since the coarsened bubble sizes near the boundaries may not be explained even by a fast surface diffusioncontrolled migration of bubbles, we must assume another coarsening mechanism, i.e. Ostwald ripening via thermal resolution and reabsorption of fission gas atoms and vacancies from smaller bubbles to larger ones. If Ostwald ripening is operative, the slower of the two processes (fission gas atoms or vacancies) is the rate controlling one. Whereas vacancy dissociation from a bubble becomes more difficult with increasing internal pressure, gas dissociation becomes easier . Therefore, for the smaller bubbles with excess pressures, it is difficult to consider the Ostwald ripening mechanism as possible. Then, we may be able to consider a substantial relaxation of initially overpressurized bubbles by sufficient vacancy supplies from external vacancy sources, such as grain boundaries or free surfaces, as suggested in coarsened helium bubbles near surfaces in nickel . The existence of overpressurized small bubbles has been indicated by the present slope of -2.6 in the log N,, and log d, plots of fig. 7 and EDS measurements of the fission gas densities . As one piece of evidence for distinct coarsening mechanisms near the surfaces and in the bulk for helium implanted nickel, Chernikov et al.  have examined temperature dependence of bubble size after annealing in each region, and found a highly activated one for fast bubble coarsening close to the surface controlled by Ostwald ripening, and a weakly activated one for slow bubble coarsening in the bulk controlled by bubble migration and coalescence. Also in the present results of fig. 4 for the 23 GWd/t fuels annealed at 1600 or 1800°C for 5 h, two different temperature
dependencies of bubble size near the grain boundaries and in the grain interiors are recognized. A strong temperature dependence with a high activation energy of 1.3 eV is found near the grain boundaries, where sufficient vacancy supply would relax the overpressures in small bubbles to trigger fast Ostwald ripening. On the contrary, a weak temperature dependence with a low activation energy of 0.4 eV is found in the grain interiors, where the high pressure in small bubbles would not relax substantially because of suppressed vacancy supply, and the bubbles remain relatively small and keep their overpressure. To examine the above idea on Ostwald ripening, we estimated the width of the region having the coarsened bubble structure near the grain boundaries for the annealed 23 GWd/t fuels. Assuming that vacancy absorption is restricted to a distinctly defined moving front where swelling changes abruptly from one to another constant value, the temporal evolution of the width of the grain boundary regions is given by ref.  e= (2D,t/AS)“’
(6) where D, is the volume self-diffusion coefficient and AS is the difference in swelling near the boundaries and in the grain center. Using D, = 6 x 10-20 m2 s-l  and AS = 2 X lo-* for 1600°C X 5 h, and D, = 2 x lo-l8 m2 s-l  and AS = 4 X lo-* for 1800°C X 5 h, we find e= 0.3 and 1 km for the former and latter conditions, roughly in agreement with the experimental results in figs. 2 and 3. Compared to the bubble sizes of 50-60 nm in the grain interiors of the middle burnup fuels of 16-28 GWd/t (fig. 9), larger sizes of about 110 nm in the lowest burnup fuel of 6 GWd/t would be interpreted as partly due to lower gas pressures in the bubbles, because of lower contents of fission gas, which would bring about thermally easier resolution of vacancies from small bubbles and faster Ostwald ripening. In the high burnup fuels of 44 and 83 GWd/t, intragranular bubbles coarsen unusually to around 500-800 nm by annealing at 1800°C for 5 h, even in the grain interiors (figs. 5a and 5b). Their bubble sizes are roughly equivalent to the largest bubbles just adjacent to the grain boundaries in the middle burnup fuel of 23 GWd/t (fig. 3b). As a possible substantial vacancy source for the extremely enhanced coarsening of bubbles in the high burnup fuels, two mechanisms can be considered. First supersaturated excess vacancies, which were induced by fission damage during baseirradiation, would flow into overpressurized small bubbles along steep gradients of vacancy potential on high temperature annealing. The supersaturated vacancy fraction during irradiation becomes higher with lower
S. Kashibe et al. / Formation and growth of fission gas babbles
temperatures, and its values at several 100°C would be approximately equal to the~alIy-activated equilibrium vacancy fractions at high temperatures /211. However, once the excess vacancies are consumed, there are no more vacancies in the fuel matrix. Furthermore, very large volume fractions of intragranular bubbles of 824% for the annealed high burnup fuels (fig. 10) cannot be explained by the excess vacancy fractions of even 10-3-10-4. The second possible mechanism is that another external vacancy source as well as grain boundaries would already exist in the matrix of the high burnup fuels. Actually, extremely developed subdivided grains with high tilt angles 1161 and recrystallized grains 1391have been found in high burnup fuels above 45 GWdft. These newly created boundaries in as-fabricated grains may act as a substantial vacancy source as original grain boundaries or act as an extremely fast diffusion path of vacancies (i.e. pipe diffusion). The bubbles pinned at these extra boundaries might coarsen unusually, with a sufficient vacancy supply, to huge sizes of 1000-2000 nm. Finally no significant difference between the intragranular and intergranular bubble sizes is recognized.
5. Conclusions The detailed characteristics of intragranular fission gas bubbles in UO, fuels before and after postirradiation annealing at 1600 or 1800°C were examined by TEM and SEM fractography. The fuel specimens were taken from the peripheral region of pellets, which had been irradiated to 6-83 GWd/t in LWR conditions. The conclusions obtained in the present study were as follows: (1) In the base-irradiated UO, fuels with maximum irradiation temperatures being around SOO”C, a high density of small bubbles (about 2 nm in diameter) precipitated uniformly in the matrix. When increasing fuel burnup, larger bubbles (about lo-20 nm) appeared in addition to the small bubbles, and bubble number density decreased slightly. The bubble size distribution changed from a monomodal to a bimodal shape with increasing burnup. In larger bubbles above several nm, solid fission products precipitated. (2) When heating the middle burnup fuels of 16-28 GWd/t at a high temperature of 18OO”C,in the central region of the grains, the 2 nm bubbles rapidly grew within a few minutes to about 50-60 nm, and the bubble growth was saturated at that size. In the region near the grain boundaries, preferential bubble coarsening was recognized for the above fuels. For high bum-
up fuels of 44 and 83 GWd/t, huge bubbles of 550-800 nm were formed after heat treatment of 1800°C X 5 h, even in the grain interiors. (3) The bubble growth during annealing at temperatures above 1600°C was associated with a remarkable decrease of the bubble density. The relationship between bubble number density Nt, in rnT3 and mean diameter d, in nm for the base-irradiated and annealed fuels was expressed in the range of bubble size of 2-800 nm by log Nb = -2.6
log d, + 25.1.
From the slope of -2.6, it was demonstrated that initially over-pressurized small bubbles grew by absorbing thermally activated vacancies to relax the overpressure, and finally became thermod~amic equilibrium sizes. (4) The bubble coarsening during annealing was attributed to coalescence via bubble migration for moderately large bubbles of up to SO-60 nm observed in the grain center of the middle burnup fuels of 16-28 GWd/t, and to Ostwald ripening accompanied by a sufficient vacancy supply from external vacancy sources for huge bubbles above 100 nm, which were observed near the grain boundaries of the middle bumup fuels and also throughout the grains in the high bumup fuels of 44 and 83 GWd/t. The unusual coarsening of bubbles observed in the high burnup fuels was closely related to the fuel mj~rost~~tural change of subdivided grain structure in as-fabricated grains, which would act as a sufficient vacancy source as well as free surfaces or grain boundaries. (5) Intragranular bubble swelling for the baseirradiated fuels calculated by the bubble diameter and size increased from 0.5 to 2.5% when increasing fuel burnup from 23 to 83 GWd/t. The swelling due to the coarsening of bubbles on heating at 1800°C for 5 h increased progressively from 2 to 8% in the burnup range of 6-44 GWdft. In the highest bumup fuel of 83 GWd/t, significantly large swelling of 24% appeared. In contrast to the strong bumup dependence of intragranular bubble swelling by heating at the high temperature, intergranular bubble swelling was saturated around lo%, almost independent of fuel burnup, which was in accordance with the theoretical prediction.
References 111J.A. Turnbull, J. Nucl. Mater. 38 (1971) 203. 121 J.R. Matthews and M.H. Wood, Eur. App. Res. Rept.Nucl. Sci. Technol. 5 (1984) 1685.
S. Kashibe et al. / Formation and growth of fission gas bubbles
 R.J. White and M.O. Tucker, J. Nucl. Mater. 118 (1983)
 k. Mogensen, C.T. Walker, I.L.F. Ray and M. Coquerelle, J. Nucl. Mater. 131 (1985) 162.  M. Imamura and K. Une, unpublished data.  R.M. Cornell, J. Nucl. Mater. 38 (1971) 319. (71 C. Baker, Eur. App. Res. Rept.-Nucl. Sci. Technol. 1 (19791 19.  I.L.F. Ray, H. Rhiele and Hj. Matzke, in: Fundamental Aspect of Inert Gases in Solids, eds. SE. Donnelly and J.H. Evance (Plenum, New York, 1991) p. 457.  R.M. Cornell and G.H. Bannister, Proc. Brit. Ceram. Sot. 7 (1967) 355. [lo] R.E. Gulden, J. Nucl. Mater. 23 (1967) 30. [ll] C. Baker, J. Nucl. Mater. 71 (1977) 117.  C. Baker and J.C. Killeen, BNES Conf. on Materials for Nuclear Reactor Core Applications, paper 24, London (1987).  K. Nogita and K. Une: to be published in J. Nucl. Sci. Technol.  S. Kashibe and K. Une, J. Nucl. Sci. Technol. 28 (1991) 1090.  S. Koizumi, H. Umehara and Y. Wakashima, Proc. IAEA Technical Committee Meeting on Fuel Performance at High Burnup for Water Reactors, Nykoping (1990) p. 102.  K. Une, K. Nogita, K. Kashibe and M. Imamura, J. Nucl. Mater. 188 (1992) 65.  K. Une and S. Kashibe, J. Nucl. Sci. Technol. 27 (1990) 1002.  K. Une and S. Kashibe, J. Nucl. Mater. 189 (1992) 210.  MI. Mendelson, J. Amer. Ceram. Sot. 52 (1969) 443.  G.J. Small, UKAEA Rept. AERE-R11773 (1987).
 D. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements, TID26711-Pl (1976) pp. 199-264.  L.E. Thomas, in: Fundamental Aspect of Inert Gases in Solids, eds. S.E. Donnelly and J.H. Evance (Plenum Press, New York, 1991) p. 431.  G.W. Greenwood, M.V. Speight, J. Nucl. Mater. 10 (1963) 140. (241 P.S. Maiya, J. Nucl. Mater. 40 (1971) 57.  Hj. Matzke, Radiat. Eff. 53 (1980) 219.  K. Une, J. Nucl. Mater. 158 (1988) 188.  D. Olander, Fundamental Aspects of Nuclear Reactor Fuel Elements, TID26711-Pl (1976) pp. 287-332.  H. Zimmermann, J. Nucl. Mater. 75 (19781 154.  T. Kogai and Y. Iwano, J. Nucl. Sci. Technol. 27 (1990) 1017.  F.A. Nichols, J. Nucl. Mater. 30 (19691 143.  L.J. Perryman and P.J. Goodhew, Acta Metall. 36 (1988) 2685.  G.W. Greenwood and A. Boltax, J. Nucl. Mater. 5 (1962) 234.  H. Trinkaus, Scripta Mat. 23 (1989) 1773.  L.J. Perryman and P.J. Goodhew, J. Nucl. Mater. 165 (19891 110.  W. Nixon and D.A. Macinnes, J. Nucl. Mater. 101 (1981) 192.  B.J. Buescher and R.O. Meyer, J. Nucl. Mater. 48 (1973) 143.  V.N. Chernikov, H. Trinkaus, P. Jung and H. Ullmaier, J. Nucl. Mater. 170 (1990) 31.  Hj. Matzke, J. Chem. Sot. Faraday Trans. 86 (19901 1243.  L.E. Thomas, C.E. Beyer and L.A. Charlot, J. Nucl. Mater. 188 (1992) 80.