Fission iodine and xenon release from the UO2-U3O8 system with emphasis on radiation damage

Fission iodine and xenon release from the UO2-U3O8 system with emphasis on radiation damage

Journal of Nuclear Materials 57 (1975) 271-279 0 North-Holland Publishing Company FISSION IODINE AND XENON RELEASE FROM THE UO,-U,O, RADIATION DAMAGE...

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Journal of Nuclear Materials 57 (1975) 271-279 0 North-Holland Publishing Company

FISSION IODINE AND XENON RELEASE FROM THE UO,-U,O, RADIATION DAMAGE Koreyuki

SYSTEM WITH EMPHASIS ON

SHIBA

Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-Ken, Japan

Received 1 April 1975

Post-irradiation techniques were used to measure releases of fission iodine and xenon from uranium oxides with different O/U ratios ranging from 2.00 to 2.62. Heating curves for the releases revealed several peaks changing with the O/U ratios. The peaks coincided with each other between iodine and xenon and corresponded to the annealing processes of fission-fragment induced defects. The total release of iodine up to 1000°C was higher than that of xenon for the entire range of compositions studied. The total releases increased with O/U ratios, reached the maximum at U02.20 and dropped to the minimum at UOa.as. These observations lead to the following conclusions: (1) fission iodine and xenon are trapped at fission-fragment induced defects and released when they are annealed; (2) the more susceptible to radiation damage, the more fission gas is released; (3) the susceptibility to radiation damage seems to be related to isotropy (symmetry) of the crystal structure; (4) xenon tends to enter rather larger defects such as dislocation loops, pores, etc. due to the difference in trapping ability of the defects between iodine and xenon. Des techniques poste’rieures a l’irradiation ont et& utilides pour mesurer le degagement des gaz de fission, iode et xenon, provenant des oxydes d’uranium de rapport O/U different, s’6tendant de 2,00 a 2,62. Sur les courbes de degagement des gaz par chauffage apparaissaient plusieurs pits variables suivant la valeur du rapport O/U. Les pits coincidaient chaque fois au degagement de l’iode et du xenon et correspondaient aux processus de recuit des defauts induits par les fragments de fission. Le degagement total d’iode jusqu’a 1000°C Btait plus kleve que celui observe’ pour le xenon pour tout l’intervalle de composition dtudi6. Les ddgagements totaux de gaz augmentaient avec le rapport O/U, atteignaient un maximum pour U02.20, puis diminuaient jusqu’a un minimum pour UO 2.2s. Ces observations conduisent aux conclusions suivantes: (1) l’iode et le xenon de fission sont pig& par les defauts induits par les fragments de fission et digages de ces pibges quand ils sont recuits; (2) plus le matdriau est susceptible vis&vis des dommages par irradiation et plus le gaz de fission est dkgage; (3) la susceptibilitd au dommages par irradiation semble &tre relide B l’isotropie (sym6trie) de la structure cristalline; (4) le xenon tend a penetrer dans des defauts plus grands tels que boucles de dislocations, pores, etc. en raison de la diffdrence dans l’aptitude au pidgeage des d6fauts entre l’iode et le x&on. Die Jod- und Xenon-Spaltgasfreisetzung aus Uranoxid mit verschiedenen O/U-Verhaltnissen zwischen 2,00 und 2,62 wurde mit Hilfe von Nachbestrahlungsmethoden untersucht. Aus Aufheizkurven zur Freisetzung ergeben sich mehrere, vom O/U-Verhiltnis abhangige Peaks, deren Jod- und Xenon-Anteile sich iiberlagern und die Ausheilprozessen der durch Spaltfragmente induzierten Defekte entsprechen. Die gesamte Jod-Freisetzung liegt bis 1000°C hiiher als die des Xenons im ganzen untersuchten O/U-Bereich. Die gesamte Freisetzung steigt mit dem O/U-Verhaltnis, erreicht bei UO, 2. ihr Maximum und fallt auf ein Minimum bei UO 2 ss ab. Aus den Beobachtungen ergibt sich: (1) Jod und Xenon w&den an den durch Spaltfragmente induzierten Defektdn eingefangen und bei einer Wlrmebehandlung freigesetzt; (2) je empfindlither das Oxid gegeniiber einer Strahlenschiidigung ist, desto mehr Spaltgas wird freigesetzt; (3) die Empfindlichkeit gegeniiber einer Strahlenschlidigung scheint mit der Isotropie (Symmetric) der Kristallstruktur in Beziehung zu stehen; (4) Xenon neigt dazu, von grosseren Defekten, wie Versetzungsringen, Poren usw. aufgenommen zu werden, weil deren Flhigkeit, Jod und Xenon einzufangen, verschieden ist.

1. Introduction Fission gas release from UO2 has been extensively

studied using post-irradiation techniques [l- 121 and now seems to be explained by a model assuming that the fission gas is trapped by pre-existing porosity at

212

K. Shiba /Fission

low fission density and by radiation-induced defects at high fission density [6,9,11,12]. However, more recent work [ 131 suggests a,possibility that even at low fission density the fission gas has some interaction with the radiation-induced defects. This is one of the motives leading to the present study. As for the influence of O/U ratios on the fission gas release, there is a pioneer work by Lindner and Matzke [ 141, which indicates that the diffusion coefficient increases linearly with the O/U ratios. Miekeley and Felix [ 151 claim that the diffusion coefficients are independent of composition for 2.02 < O/U ratio < 2.24, bringing some conflict. It is important to know the release behavior of iodine in nuclear fuels. Few studies [3,16- 181 have been carried out on the release of iodine from UO2, probably because of the difficulty of such type of experiment. These studies show that the release of iodine is generally higher than that of xenon. No explanation has been given for this discrepancy and for the mechanisms of the iodine release. The objective of the present research is to study the release of iodine and xenon from uranium oxides as a function of O/U ratios with the experimental conditions other than the ratios kept as fixed as possible and to elucidate the above points of interest.

2. Experimental 2.1. Samples The starting material was depleted U02.04 powder (235U: 0.22%) whose purity was of nuclear grade. Stoichiometric U02 was prepared by reducing the starting material in a purified hydrogen stream at 1OOO’C. Other uranium oxides were obtained by oxidizing the U02.u4 p owders in a BET apparatus at a controlled temperature and pressure of oxygen. The amounts of oxygen consumed and weight gains after the oxidation were used to determine the O/U ratios of the products except for UO2.60 and UO2.62. The O/U ratios of the two oxides were determined using the reduction method. For homogeneity, both oxides were sealed in quartz ampoules in vacuum and annealed at 105O’C for 4h. They were slowly cooled in the furnace used for the annealing. The Debye-Scherrer method of X-ray analysis was

iodine and xenon release

Table 1 Description of specimens. No.

o/u ratio

Crystal structurea)

Surface area Cm*/g)

21 33 29 21 40 39 28 31 5 32 6 23 41

2.00 2.04 2.10 2.14 2.18 2.20 2.23 2.25 2.29 2.33 2.40 2.60 2.62

c c c c c c c c c+o c+o c+o o o

0.59 0.32 0.19 0.20 -b) 0.21 0.19 0.17 -b) 0.22 -b) 0.32 -b)

a) c = cubic, o = orthorhombic. b) - = not determined.

applied to characterizing the samples thus obtained. Their specific surface areas were determined by the BET method using nitrogen as an adsorbate. These data are given in table 1. The X-ray analysis confirms that the samples for the U02-U40g compositions are of the CaF, type structure and those for U409-U308 are mixtures of cubic and orthorhombic materials. These results are compatible with the phase diagram compiled [ 191. The specific surface areas are seen to remain much the same over the wide range of O/U ratios except for U02.00. 2.2. Irradiation About 300 mg of each sample were sealed in quartz breakables in vacuum (less than lop4 torr). The samples in breakables were irradiated at a thermal neutron flux of 5 X 10” n/cm2.sec, unless otherwise indicated, to a total dose of about 1 X 1016 n/cm2 and cooled for several days before use. The sample temperature under irradiation was estimated to be less than 80°C. 2.3. Release experiment The irradiated quartz breakable was set in the apparatus shown in fig. 1. After lifting the movable furnace (A), the breakable was fractured in a purified

K. Shiba /Fission iodine and xenon release purlfbd

iodide-iodate mixture as a carrier of 1311. The iodine and xenon were purged by helium gas and collected by a potassium-hydroxide solution trap and an activated charcoal trap, respectively. Gamma-assaying was done as described above. The column was renewed every run to avoid iodine contamination.

He inlet

1 I I

213

SIQ column

3. Results

ball joint

KOH gmnule polyethylene activated

bottle charcoal

Fig. 1. Apparatus for measuring the fission-gas release in an inert-gas atmosphere. helium stream with a breaker (iron bar sealed in quartz) moved by means of a magnet outside the column. The furnace was lowered down to the sample position and then switched on. The sample was heated at a programmed rate of 5 deg/min from 200” for iodine (from 50°C for xenon) to 1000°C. The iodine and xenon released from the sample were carried down through the column by the helium stream. The furnaces (B) and (C) functioned to keep these portions of the column at temperatures of 200-700°C. The heating conditions as well as the introduction of oxygen through the nozzle prevented the iodine from depositing on the inside wall of the column [20]. The iodine and xenon in the carrier gas were collected by a potassium-hydroxide granule trap and an activated charcoal trap cooled with dry ice-alcohol, respectively. The traps were exchanged generally every 10 min. The potassium-hydroxide granules in a trap were dissolved into water. The resulting solutions and charcoal traps were assayed for 131I (365 keV peak) and 133Xe (80 keV peak) respectively, using a 400 channel gamma-ray spectrometer. To measure the residual amounts of iodine and xenon in the sample, they were dissolved in an 8 M nitric-acid solution with addition of a potassium

The ratio of the counts (131 I or 133Xe) of each trap to the aggregate counts of all traps for a run was divided by the time for the trap (mostly 10 min); the quotient was plotted against the elapsed time. The histograms thus obtained were redrawn in the form of a smooth curve equivalent in area (called a heating curve), as shown in figs. 2-10. These heating curves for iodine and xenon are included in the same figure for a sample. However, this does not mean that both releases were measured at the same time. In some runs, only iodine or xenon was collected. The release experiment was at least duplicated for iodine but not always for xenon. Total amounts of iodine and xenon released during the period of a run are shown in terms of % in those figures and also plotted as a function of O/U ratios in fig. 11. These values include the amounts of xenon released by knock-out and pseudo-recoil during irradiation [ 131. The release from UO2.,0 during irradiation, for example, amounts to about 0.5% of the total xenon; the figure is the largest among the samples examined in the present study. Iodine also must have been released by these mechanisms. However, it was impossible to determine its amount at room temperature because the iodine was adsorbed on the sample. For presentation, it will be appropriate to divide the results into two groups: the UO,-U409 and the U409-U308 compositions. 3.1. UOz- UdO, compositions With UOZ.OOthere occurred a peak at 430°C and a plateau at about 600°C (even a plateau will be referred to as a peak from later on) for both iodine and xenon. Both curves are very similar in shape except for the low-temperature portion (lower than 3OO’C). However, the release of iodine tends to surpass that of xenon with increasing temperature and gives the max-

K. Shiba /Fission

214

iodine and

release

xenon

Time I mln I

The (mlnl

Fig. 2. Heating curves for iodine and xenon release from

Fig. 5. Heating curves for iodine and xenon release from

uo2 .oo-

uo2.14.

( Wmin)

uoeso -

---

Iodine,

Xenon,

released 8.7 % released

21.6 %

Time (mini

Fig. 3, Heating curves for iodine and xenon release from

Fig. 6. Heating curves for iodine and xenon release from

uo2.04-

U02.20.

Tinmet min) Fig. 4. Heating curms for iodine and xenon release from U%lO+

Fig. 7. Heating curves for iodine and xenon release from

imum value at 1000°C. Such a trend is general for the whole system studied. It is very probable that the iodine peak at 250°C arises from desorption of the iodine which has been released from the sample during irradiation and deposited on it, An additional peak for xenon is found at 180°C in

UO2.w. This peak as well as the 600°C peak are characteristic of the U02_04-U02.23 compositions. The peak at 430°C diminishes in relative intensity with O/U ratios from 2.00 to 2.18. This suggests that it is related to the UOZ+~ phase present for these compositions.

uo2.25

4

215

K. Shiba /Fission iodine and xenon release

4

m/m 5 g 0.50

uo2.33 -

---

iodine, 21.9 % released Xenon, 11.5% released

I rc

I

1

A: UOm, 1UO262,

0

329%

rhxed.

Sxld’nv

4Q7%

Mased.

3xlO’Sv

cc) 000 -

.

n B p 91 8. z

. . *’ 0

Fig. 8. Heating curves for iodine and xenon release from uo2.33.

The UO2.25 sample revealed the simplest pattern of release: only a small peak at 600°C. In addition, it is a unique sample that gives the minimum value of the total releases as shown in fig. 11. This figure also shows that the total releases of iodine and xenon increase with O/U ratios to reach the maximum value at 2.20 in this region. 3.2. r/,0,--U,O,

compositions

The curves of UO2.3, (fig. 8) are regarded as representative of the region of composition, where two distinct peaks are observed at 500 and 800°C with a small peak at 2OO’C. Again, there is no essential difference in release between iodine and xenon except that a shoulder is found at 350°C for xenon (figs. 8 and 10) and that the release of iodine is stronger than that of xenon. The total release of iodine and xenon increases monotonically with the O/U ratio to reach the maximum value at UO2.62 (fig. 11). 3.3. Effect of irradiation temperature For comparison, a sample of UO2.62 was irradiated at a flux of 3 X 1013 n/cm2*sec, which was about two orders of magnitude higher than usual, with the total exposure fixed. The iodine release from the sample is shown with that from the control sample in fig. 9. The higher neutron flux, hence, higher fission rate lowered the 500°C peak and instead increased the higher-temperature portion of release. The tendency that the higher fission rate decreases or eliminates lower-temperature peaks of release also prevails for the other samples studied.

0

60

Time

I.90

I20

(min 1

0

Fig. 9. Heating curves for iodine release from UO2.60 and U02.62 irrddiated at different neutron fluxes with the total dose kept constant.

The dependence on the fission rate implies a contribution of radiation-induced defects to the release. This change is considered to result from the increase in irradiation temperature rather than from the direct consequences of the increased fission rate because of the higher irradiation temperature estimated (200 versus 80”) and of the fiied fission density. Similar release behavior has been observed in ion-bombarded MgO [21]. 3.4. Repeating the release experiment In order to know the nature of the release peaks, some samples were again heated after the ordinary experiments (the first run) were completed. The results for UO2.62 are shown in fig. 10. No peak was observed in the second run and the releases were significantly decreased. This indicates that the elementary

u&62 lst N”

t%/min I

0

40

- Iodine 43.3 % released --. Xsnon 27.1 % rslsassd

60

I20 Tlmd t min

1

160

200

Fig. 10. Heating curves for iodine and xenon release from ‘fresh’ and once-heated UOz62.

216

K. Shiba /Fission

processes for these peaks are destroyed by the heat treatment of the first run and are of thermally irreversible nature. This behavior of the peaks is consistent with the phenomena of annealing of radiationinduced defects.

4. Discussion 4.1. Fission-product release and annealing of fissionfragment damage It seems pertinent here to rapidly review some typical studies on the annealing of fission-fragment damage in uranium dioxide. Lattice-parameter studies of the annealing behavior of radiation-induced defects have been described by Bloch [22] and Wait [23]. The first-named author observes that the lattice parameter of uranium dioxide decreases in two stages: one in the temperature range of IOO-400°C and the other in the range 500-900°C. The last-named author finds that the recovery behavior of the lattice parameter depends on the fission density, and at a low fission-fragment density of 1.8 X 1016 ff/cm3 there exist three annealing stages at 300,450 and 650°C. The polycrystalline material retains a small dilatation to 1000°C as contrasted with complete recovery of the unirradiated lattice parameter for single crystals. The recovery of the electrical conductivity of quenched and neutron-irradiated uranium dioxide has been studied by Nagels et al. [24] and Vollath [25]. Three recovery processes exist at 200,400 and 680°C. The 200°C process is characteristic for hyperstoichiometric uranium dioxide and is assigned to precipitation of the excess oxygen as U40,. The 400°C process is generally preceded by the reverse recovery and is independent of stoichiometry as well as of the presence of grain boundaries for irradiated and quenched materials. These facts support the assumption that this step corresponds to the annealing of Frenkel-type defects of the oxygen sub-lattice [25]. The last process can be explained by the migration of uranium point defects whereas the actual process is more complex

1241. These annealing experiments reveal the existence of three important recovery processes in irradiated UO2. Bearing in mind some differences in experi-

iodine and xenon release

mental conditions between these annealing experiments and the present release experiment, the three recovery processes correspond reasonably to the release peaks for xenon observed with the specimens for the composition UO,-U409. In addition, the variation of relative heights of the peaks with O/U ratios is in agreement with that of the electrical conductivity: the 400°C peak is predominant for UO2,o and the two peaks at 200 and 600°C become relatively large with O/U ratios. Consequently the release of xenon (and iodine) is controlled by the same mechanisms as the annealing processes for radiation-induced defects. As is expected from the lattice-parameter studies of irradiated UO2, almost all the point defects are annealed at temperatures smaller than 900°C. Therefore, the release at temperatures from 900- 1000°C constituting the substantial amounts of the total release, seems to be associated with the annealing of small clusters of vacancies and interstitials. The portion of the release could be attributed to the annealing of pre-existing defects. However, the contribution should be small if one takes into consideration the facts that all the samples were annealed at 105O’C prior to irradiation and that the release in the second run was much smaller than that in the first as shown in fig. 10. The presence and annealing of large clusters such as dislocation loops in irradiated UO2 have been demonstrated by Whapham and Sheldon [26] and by Golyanov and Pravdyuk [27] using transmission electron microscopes. The relation of the release to the annealing of the defects is considered to be applicable to the composition U409-U30a. For this composition, it is apparent that the peaks observed originate from the U3Oa phase which is present with the U409 phase. There seems to be no explanation for the origin of these annealing processes in the literature. The small release peak at about 2OO’C may be associated with separation of the disordered (homogenized) matrix into the U40, and the U3Oa phase in analogy with the precipitation of U40, for the composition UOZ-U409. In actuality, the X-ray diffraction peaks weakened by irradiation were intensified after annealing at 2OO’C with the samples for the composition. The peak temperature of 500°C observed in the present experiment is in good agreement with that in annealing experiments for irradiated (IIUO3, where the amorphous phase caused by irradiation recrystallizes to the original (YUO3 structure at this

K. Shiba /Fission iodine and xenon release

temperature [28]. Since there is a close similarity in structure between Us08 and cr UO,, this process may be associated with recrystallization of the U,Og phase present. It is difficult to find an explanation for the peak at the highest temperature. 4.2. Fission-product release and susceptibility to radiation damage Next let us examine the radiation damage to uranium oxides in connection with O/U ratios, Childs [29] has measured the stored-energy release from uranium oxides, with a wide range of O/U ratios, irradiated at 30--5O’C. The stored energy release increases in order of U02.00, U02.25, UO,,a, U02.~~. In particular, the last material is distinguished by a relatively large release of stored energy. This behavior of II308 seems to be parallel with the complete loss (metamiczation) of X-ray diffraction peaks observed after irradiation at low temperatures. Also in the region of UO,-UdO,, the UOz,, phase (diphase) is more susceptible to fission-fragment damage than UO2 and II409 are, as evidenced by the broadening and lowering of the X-ray diffraction peaks after a scion-fragment dose of 1015 ff/cm3 [28]. The dependence of the susceptibility to fissionfragment damage on the O/U ratio coincides with the variation of the total release with them as shown in fig. Il. The more susceptible to the damage, the more fission gas is released. Thus, the release curves in the figure can be said to represent the relative stability of

2.0212223242526 OAJ Ratio Fig. 11. Total amounts of iodine and xenon released to 1000°C from uranium oxides with various O/U ratios.

277

uranium oxides to fission-fragment damage, if a proper correction for the surface area is applied. As for the irradiation stability of ceramic materiah, it is well known that a cubic crystal structure exhibits the more excellent stability [30,3 I]. The present experiment yields the additional information that the stoichiometric material (UO2 or U409) is more stable than the non-stoichiometric one among cubic-structure materials. Primak [32] has explained that the susceptibility to irradiation damage is not determined by the initial state of the material, but by the difficulty of recrystallization of disordered regions formed by the traverse of fission fragments and by the difficulty with which dispersed atoms can again form bonds. On the other hand, Berman et al. [30] pointed out the importance of the initial state on the basis of the experimental observations. However, their hypothesis that the fission fragments act indirectly through anisotropic effects which distort the lattice and render it unstable seems not to be well defined for the image of irradiation instab~ity. This author considers that both ideas should be combined with slight modification. It is apparent that the region irradiated by fission fragments is heated to high temperatures and ‘quenched in’ within an extremely short period of time ( lop9 s) to the ambient temperature [33]. Then, the susceptibility to fissionfragment damage should be attributed to the difference in arrangement of atoms between the ‘quenched in’ and the initial state. A large difference will hamper the reversion of the ‘quenched in’ region to the original structure at the ambient temperature. The high-temperature state can be regarded as rather isotropic in arrangement of the matrix atoms, as expected from the fact that the crystal structure of the highest-temperature form is cubic in allotropic metals. Therefore, the cubic substances will give rise to a small difference in the arrangement and show an excellent resistance to irradiation. The stoichiometry will facilitate this tendency owing to the increased crystal symmetry. In addition, the increased symmetry will be effective in giving more channeling paths to the energetic particles and thus in reducing the damage. The surmise is supported by the fact that the maximum stability to irradiation is observed with stoichiometric U409, which has been confirmed to form the superlattice structure [38]. This fact cannot be explained in terms of physical properties such as

218

K. Shiba /Fission

thermal conductivity, bond strength [3 I], etc. that are a monotonic function of the O/U ratio. Conversely, U,Og will receive heavy irradiation damage because the original structure is anisotropic (orthorhombic) on the one hand and the ‘quenched in’ state is isotropic on the other. This is observed in the present experiment. This model explains the present experimental results though it is qualitative. A quantitative discussion may require additional experiments on single crystals of uranium oxides. 4.3. Interaction of fission gas with defects induced by fission fragments Two approaches have been made to locate inertgas atoms in UO2 crystals. Long et al. [34] and Matzke [35] showed that the release of xenon from UO2 crystals doped with suitable impurities for increasing the concentration of vacancies does not depend on either the cation or the anion vacancy concentration. It follows that the inert-gas atom does not migrate by a simple vacancy mechanism and hence is not located on either a cation or an anion site. This conclusion has further been confirmed by channeling experiments [36] using s22Rn which is one of the heaviest elements of the inert gases. It is concluded that xenon (and probably iodine) is located at defects in U02 crystals. Matzke [35] proposed a cluster consisting of a vacancy in the cation and two vacancies in the anion sub-lattice as such a defect that is annealed at temperatures of about 1300°C. On the above background, taking into consideration the good correspondence between the gas-release process and the annealing process of defects, it seems that iodine and xenon are trapped at fission fragment-induced defects and released when these defects are annealed. Then, the observation that there is no essential difference in the release between iodine and xenon permits us to conclude that the apparent interaction of iodine or xenon with the defects is weak. It appears necessary to make comments on the two release peaks (400 and 6OO’C) observed for the U02-U409 region. As has been discussed in subsect. 4.1, these peaks are associated with the migration of point defects in the anion and the cation sublattice. This might lead to the erroneous conclusion that the fission gas is located at a vacant site of the lattice. However, the fission gas must be located at

iodine and xenon release

defects other than point defects. The annealing process can be regarded as a restructuring process of the matrix during which the point defects are annihilated or converted into new defects by encountering surface or other defects. Some of the new defects may be movable and ready for being annealed at the temperature, while the remaining ones may be stable and remain to be annealed at a higher temperature. The former case seems to apply to the release at these temperatures. In other words, iodine and xenon are forced to migrate and to be released through cooperative movements of the matrix atoms which take place during the restructuring process initiated by the point-defect migration. Now we come to the point to discuss the difference in release between iodine and xenon. There are two possible reasons to expect that the release of iodine is larger than that of xenon. One reason arises from the initial distribution of iodine and xenon into the defects. A probability of a fission fragment being trapped at a defect, just after the fission event, should be determined by the product of the concentration and the trapping ability of the defect. The defect is, in practice, equally available for iodine and xenon. However, the trapping ability may vary from element to element, causing iodine to distribute more abundantly into the defects annealed at the present experimental conditions (
K. Shiba /Fission iodine and xenon release

temperatures and low fission densities whereas small defects instead of dislocation loops play an important role here. Thus, the fission-gas release cannot be free from the connection with fission fragment-induced defects over the wide range of temperature and fission density. In this sense, there exists no true diffusion for the fission gas in UO2 at temperatures smaller than 1000°C (this may be extended to 1300*C), although the diffusion coefficients obtained at the lowest fission density have been assumed to give the true values for the volume diffusion of fission gas Pll-

Acknowledgments The author wishes to express his thanks to Dr. M. Handa, Dr. S. Yamagishi and Mr. T. Fukuda for their discussions and Dr. S. Kitani for his encouragement .

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