An experimental study of the distribution of retained xenon in transient-tested UO2 fuel

.kmrnal of Nudear Materials 199 0993) &C-KU ~o~-H~~aud

An experimental study of the distribution of retained xenon in transient-tested UO, fuel

XRF and EPMA results for the d~str~but~~~of retained xenon in twenty fuef pins are surveyed. The aim is to show the progress #at has been achieved by ~rnbi~in~ these methods. One of the main concerns of the paper is the retiability of the XRF and EPMA me~u~me~ts aud the iden~~t~o~. of the principal sources of ~~~~a~~~. Another, is the wealth of new rne~ba~~st~ information that has been acquired by s~st~atj~a~~~ ~~~o~~~ XRF and EPMA w&h ~~afft~tat~~ image ana&% @IA) of the locat size distrib~tjo~ of the gas bubbles in the fuel. It is &own that by correlating the three data sets it is possible to establish the distrib~~u of retained gas on the grain ~~dari~ and to estimate the pressure of the gas contained in grain boundary bubbles. It is concluded that often gas release during a reactor power transient cannot be predicted on the basis of simple gas diffusion considerations and that it is not possible to derive a gas diffusion coefficent of general relevance from puncturing data.

In 1980 the Risa National Laboratory ia ~enrna~ began a series of fission gas release projects. The aim was to provide both the ken&g authorities and the fuel vendors with data on LWR performance in reactor

power tr~sien~ fl,23. Great importance was placed on the Iocal ana&sis of the fuel mie~s~~~ture and composition following a transient because this would provide clues to the mechanisms of gas release. From the inception of the First Project, electron probe microanalysis (EPMA) was used to determine the radiaf d~st~butio~ of xenon retained in the fuel. It soon became apparent, however, that the EMMA technique has one great drawback; it does not inchtde the concentrations of xenon retained on the grain boundaries or trapped in huge bubbles or pores within the grains. Consequently the focal Ievef of gas reiease may be overestimated. To overcome this problem Mogensen proposed the use of X-ray fhtorescence aualysis CCRF> in combination with EPMA. In XRF ~nfo~ation is Elsevier Science Publishers B.V.

gathered fr~~rn a much greater depth within the fuef than in EPMA and consequent& the gas omitted in EPMA is included in the XRF me~urements. The radial distribu~on of retained fission gas was first measured by XRF in 1984. It was found that not on& did XRF gke the true focal $eve$ of gas retease, but that if the radial d~s~~ution pro&s obtained by XRF and EPMA were compared then the coneentration of fission gas on the grain boundaries could be derived. XRF and EPMA results for the distribution of retained xenon in transient-tested UO, fuel have been included in several of the authors’ publications (see fur example refs.. [3-511. The data shows that the interlinkage of gas bubbles on the grain boundaries generaily controls the rate of gas release from high burnup fuel under transient conditions I&41 and that fuet temperature and internal mechanical restraint are of equal ~rn~~an~ in determining the extent of gas bubble interfinkage and hence the Ievel, of release during a power transient [S].

Up to now, a paper dealing specifically with the measurement by XRF and EPMA of retained xenon in transient-tested UO, fuel has not been presented in the open literature. Most of the XRF and EPMA results published to date have been incorporated in papers concerned with the mechanisms of fission gas release. In contrast, the XRF and EPMA techiques are central in the present work which aims to show the progress that has been made as a result of combining these methods. One of the main concerns of this paper is the reliability of the XRF and EPMA measurements and identi~cation of the sources of uncertainty. Another is the wealth of new mechanistic information that has been acquired by systematically combining XRF and EPMA with detailed quantitative image analysis (QIAI which provides data on the local size distribution of the gas bubbles in the fuel. By correlating the three data sets it is possible, for example, to establish the distribution of retained gas on the grain boundaries and within the UO, grains and to estimate the pressure of the gas contained in grain boundary bubbles.

2. Fuel types and their iffadiation histories The results reported in this paper were obtained on the HWR and BWR fuels that were transient-tested in the Second Rise Fission Gas Project [2]. The Rise National Laboratory supplied the HWR fuel and General Electric provided the BWR fuel. These carried the prefix codes “M” and “STR”, respectively. Both fuels consisted of sintered UO, pellets in a Zircaloy-2 metal sheath. The Rise and GE fuels differed from one another in two important ways. First, the GE pellets were chamfered, whereas the Rise pellets were dished. Second, the density of the GE fuel had been adjusted during fabrication using a proprietary pore former. A detailed account of the pellet and fuel pin design can be found in table 1 of ref. [2]. 2.1. Base irradiation The Rise fuel was irradiated in the OECD reactor at Halden (Norway). The pins were contained in the Danish fuel assembly IFA 161 and were irradiated to a burnup in the range 3.3 to 5.3 at%. The irradiation lasted 2025 days during which time the pin averge power decreased from 44 to 10 kW m-‘. Up to 10% of fission gas was released in the course of the irradiation. The GE fuel was irradiated in the Millstone-l Reactor (USA) to a burnup in the range 1.7 to 3.5 at%. The irradiation spanned 8 power cycles and lasted 2880

days. During this time the peak power fell from about 15 kW m-’ at the end of the third cycle to 8-10 kW m-’ in the eigth cycle. Fission gas release was very low; about 0.1%. The local burnup levels of the Rise and GE fuel sections investigated by XRF and EPMA are given in table 1. The burnup was derived from the ‘a’Cs axial gamma scan for the pin after calibration by radiochemical determinations. More information about the base irradiations can be found in ref. [Z]. 2.2. The transient tests The transient tests were carried out in the DR3 reactor at Rise. Altogether, seventeen tests were performed on the GE and Rise fuel types. Fifteen were carried out on refabricated fuel segments fitted with a pressure transducer to follow the evolution of fission gas release. For the purposes of comparison the remaining two tests were made on uninstrumented (not refabricated) full length GE fuel pins. In the tests on Rise fuel, power increases above 25 kW m-t were made in steps of 2 kW m- ’ followed by a break of 4 h or longer so that the average ramp rate did not exceed 0.5 kW m-’ hh’. In most of the GE tests, the fuel was first given a conditioning treatment of 30 kW mm ’ for 6 h before the power was raised to the terminal level over 15 to 30 min. Usually the transient tests lasted 3 days, but a few were of 6 days duration. In the 3 day tests on Rise fuel the hold time was 24 h whereas for the tests on GE fuel it was 62 h. Several of the tests on GE fuel featured abrupt power changes during the hold time (either dips or spikes). A more detailed description of the test programme is contained in ref. [2]. The transient terminal powers (‘ITLI seen by the Rise, and GE fuel sections examined by EPMA and XRF are given in table 1. The GE and Rise fuels behaved very differently under transient conditions. The pressure measurements showed that the Rise fuel released an important percentage of gas throughout the transient, but only a small amount of gas on termination of the test (about 5%). In contrast, the GE fuel released little gas during the test unless it incorporated power dips or spikes, but it released a large percentage of gas on termination of the test (about 25%). Fig. 1 shows the power schedules for the transient tests on the Riso pin M23-I-21R and the GE pin STR017-3R, and the cumulative percentage of gas released as measured by the pressure transducers. The difference in the release behaviour is clearly seen.

87

M. Mogensen et al. / Distribution of retained xenon in UO, fuel

Table 1 Fuel sections analysed in the XRF-EPMA Burnup (at%)

Pin section

investigation programme

TTL a) (kW m-l)

Fill gas

Analysis technique

Designation in fig. 3

EPMA XRF EPMA EPMA XRF EPMA XRF EPMA XRF EPMA XRF EPMA XRF XRF XRF XRF EPMA XRF EPMA

n k m

Rise fuel 3.5 5.5 5.3 4.1 4.6 4.6 4.7 4.8 3.2 3.5 5.5 5.5 3.3 4.4 3.2 4.8 4.8 5.2 5.2

M78-1-12 b, M78-1-18 b, M78-1-19 b, M78-1-32 b, M23-1-6-5 M23-1-6-6 M23-1-9-5 ‘) M23-1-9-6 ‘) M38-8R-2 M23-l-17R-3 M23-I-21R-2 M23-l-21R-3 M19-2-20 b, M38-10 b, M73-2-8R-2 M72-2-2R-14 M72-2-2R-12 M72-2-7R-13 M72-2-7R-15

39.7 39.3 41.7 41.7 42.8 39.9 39.0 39.7

0.1 Xe 0.1 Xe 0.5 He 0.5 He 0.1 Xe 0.1 Xe 0.1 Xe 0.1 Xe

39.7 40.2-41.4 41.0 41.0

0.1 Xe 0.1 Xe 0.5 He 0.5 He

43.2 43.2 42.2 42.2 37.2 37.0 13.7 15.1 41.8 41.8 30.8 36.4 41.0 43.0 43.0 46.6 46.4 43.0 43.0

0.5 He 0.5 He 0.5 He 0.5 He 0.1 Xe 0.1 Xe 1.7 He 1.7 He 1.7 He 1.7 He 1.7 He 1.7 He 1.7 He 1.6 He 1.6 He 0.5 He 0.5 He 0.5 He 0.5 He

41.9

0.5 He

General Electric fuel STR013-8R-4 STR013-8R-3 STR017-3R-9 STR017-3R-8 STR017-5R-5 STR017-5R-4 STR018-3 STR018-4 STR018-21 STR018-20 STR018-12 STR018-15 STR018-41 STR025-3R-10 STR025-3R-7 STR014-3R-8 STR014-3R-6 STR019-8R-3 STR019-8R-2 STR016-9 b, STR016-4R-5

d, d,

d, d, e, e,

1.7 1.7 3.4 3.4 3.4 3.4 2.8 2.9 3.3 3.3 3.2 3.2 3.2 3.1 3.1 1.6 1.6 2.3 2.3 2.9 3.1

XRF EPMA XRF EPMA XRF EPMA XRF EPMA XRF EPMA EPMA EPMA EPMA XRF EPMA XRF EPMA XRF EPMA EPMA EPMA

Pin STROl8 was uninstrumented, i.e., not refabricated. The number preceeding the chemical symbol of the fill gas is the pressure in MPa. a) Transient terminal level. b, Not transient-tested. ‘) Long hold time (85.5 h). d, With power dips. e, With power spikes to 50 kW m-l.

30

Risr Pin M23-l-21R

’

I

5 r

.

----i

GE Pin STROl7-3R 50.

Fig. 1. Power schedule for the transient tests on Rise fuel pin M23-l-21R and the GE fuel pin STROl?-3R and the cnmulative percentage of gas released as measured by the pressure transducers.

3. The experimental techniques Both EPMA and XRF were used to measure the radial distribution of retained xenon in the Rise and GE fuels. EPMA was carried out on 22 fuel sections and XRF on 18 fuel sections (table 1) most of them located adjacent to the sections used for EPMA. To facilitate comparison, the measured EPMA and XRF concentrations were converted to relative concentrations. For this purpose the average ~ncentration of xenon in the outer region of the fuel between r/r0 = 0.8 and 0.9 was taken as 1.0. Were, gas release, if it occurred was so small as to be undetectable by either XRF or EPMA, and hence camplete retention was assumed. For calculation of the percentage release the radial d~s~ibution of xenon generated was obtained by extrapolating to the pellet centre the concentrations measured in the outer region of the fuel where the profile

was flat. Where the measured retention profile lay systematically below the extrapolated line the difference was taken as release. When calculating the percentage of release from the XRF profile the steep increase in xenon concentration at the Fuel surface was ignored. QIA was used to determine the variation in the percentage of pores and large gas bubbles aIong the fuel radius. These are located predominantly on the grain boundaries. Where possible QIA was carried out on the fuel section next to the one used for either XRF or EPMA. The general aim was to identify local changes in the size and population of the pores and gas bubbles that could explain the difference in the local concentration of retained xenon measured by XRF and EPMA.

Microprobe analysis was carried out at an acceleration potential of 25 keV and a beam current of 250 nA using the procedure developed at the Institute for Transuranium Elements 161.Using the expressions proposed by Reed f7] it was calculated that at 25 keV the depth of electron penetration in uranium dioxide is about 0.5 pm and that the diameter of X-ray excitation is about 3.5 pm. The conventional microprobe correction procedure has been carried out using a new method IS], which is based on the Quadrilateral Model of Scott and L+ove191.All the EPMA data previously reported by the Institute for Transuranium Elements were corrected using a modified version of the CQRZAF program of Tong [lo]. In genera1 the xenon concentrations obtained with the new correction procedure are about 15% higher than those obtained using the earlier program. The radial distribution of xenon in the UQ, matrix was determined by point analysis at intervals of 50 to 150 pm. At each location six measurements were made. These were up to 10 pm apart and were placed away from grain boundaries thereby avoiding pores, large gas bubbles and cracks. The specimen current image (absorbed electron currentI was used to obtain information about the distribution and morphology of the pores and gas bubbles at the locations where point analysis was carried out. These features appear white in the electron microgtaphs (see fig. 9). In transient-tested fuel between about r/r0 = 0.6 and the fuel centre an appreciabIe fraction of the retained xenon may reside in bubbles. When this is so. the intensity of X-ray emission is strongly dependent on their size and distribution. Generally, the larger and

more dispersed the bubbles the lower is the emitted X-ray intensity. The effects may be corrected for using the model of Ronchi and Walker [ll]. This considers the probability of an electron-gas bubble interaction, the depth distribution of X-ray production and the effects of gas density on X-ray production. For the purposes of carrying out the correction the local size distribution of the gas bubbles must be established along the same fuel radius using replica electron microscopy. 3.2. X-ray ~~res~en~e analyst X-ray fluorescence analysis was carried out at the Risa National Laboratory. The fuel sample was contained in a lead block. A rotating anode, high intensity X-ray generator (trademark; RlGACU) was used to produce the 50 keV primary X-ray beam. This measured 4 X 10 mm and impinged on the surface of the sample at an angle of 45”. The intensity of the Xe K, characteristic line in the XRF spectrum was monitored using a solid state germanium detector. A collimator confined the analysed area to 0.35 x 4 mm. The smaller dimension being in the direction of traverse. To reduce the radiation background the fuel sample was thinned to 0.1-0.2 mm and the X-ray beam was deflected 3.5” by a graphite crystal inserted between the collimator and the detector. The XRF sample was a longitudinal slice of fuel which had been cut diametrically from the pellet. Intensity measurements were made along the fuel radius at intervals of 0.25 or 0.5 mm. The intensity of the U L, line was measured at the same time as the Xe K, line intensity and used to reveal the presence of wide cracks and the loss of fuel, as well as to pinpoint the position of the pellet surface. The depth of analysis is taken to be 18 pm. At this depth appro~mately 37% (e-r) of the X-rays generated are emitted from the specimen surface. A gas standard consisting of xenon at a pressure of 0.9 bar was used to convert the the measured X-ray intensity to an absolute concentration, Further information about the XRF technique, such as the experimental setup, can be found in ref. [12]. 3.3. Quantitative image analysis Detailed QIA was performed at the Rise National Laboratory. A computer based image analysis system developed on site and attached to a shielded optical microscope was used. The optical image to be analysed was acquired from the microscope with a television camera and converted to a digital bitmap image of

512 x 512 pixels which was displayed on a colour monitor. After interactive selection of the grey scale threshold to enhance the contrast of the porosity, features that were not wanted, such as holes resulting from grain loss during specimen preparation or small cracks, were erased and dividing lines were drawn between interconnected pores. Computer software was used to track the circumference of each pore and to calculate the pore area by planimetry. The pore area was then converted to an equivalent diameter and classified in 17 loga~thmically increasing pore size intervals from 0.7-1.4 Frn to 89-125 pm. Porosity measurements on transient-tested fuel were made at a magnification of 2520 X (at the monitor). At this magnification the area analysed was 100 X 100 urn and the limit of resolution was 0.3 pm*. Up to 120 porosity measurements were carried out across the fuel section. The images analysed were generally located adjacent to each other, but if cracks occupied more than 10% of the image area an analysis was not performed. Upon completion of the measurements the resulting 2D size distribution was converted to a 3D volume fraction dist~bution using the computer program LINES?’ 1131.The method of inversion is based on a mathematical description of the properties of a thinly distributed particulate phase developed by Nicolson 1141.The relative error on the individual porosity values is estimated to be 5% and the radial position at which the measurements were made (centre of the optical image) is accurate to 0.01 on the relative radius scale.

4. Reliabiiity of the EPMA and XRF data For EPMA, the confidence limit on the measured concentrations at a significance level of 99% is about 5% relative at 0.5 wt% and lo-20% relative at 0.05 wt%. The limit of detection for xenon is 200-250 ppm. These values were calculated using the expressions formulated by Ancey et al. 1151and are based solely on the statistics of X-ray counting. The accuracy of the measured EPMA concentrations is determined mainly by the statistics of X-ray counting and the effects of gas bubbles on the emitted X-ray intensity. Generally, the xenon X-ray intensity emitted from transient-tested fuel is no longer carrected for the effects of gas bubbles. The reason being that gas bubbles are often very inhomogeneously dispersed in the central region of the fuel and as a result the concentration of retained xenon varies widely fron

M. Mogensen et al. / Distribution of retained xenon in UO, fuel

90

point to point. Under these circumstances the correction is meaning~l only if replica electron microscopy can be carried out at exactly the same spot as EPMA. Despite this problem, the correction was applied in the cases of sections M23-1-6-6, STROlS-20 and STR017.5R-4. For all three specimens the corrected concentrations were only 4-10% higher than the measured values. The large point to point variation that may occur in the concentration of retained xenon in the central region of transient-tested fuel consititutes one of the principal sources of error in the EPMA measurements. Because it is difficult to get the right balance between areas of low and high concentration, the true level of retention in the central region of the fuel is seldom determined. In the majority of cases met so far, the level of xenon retention in the fuel grains was underestimated, which suggests that bubble free areas in the grains were preferentially selected for EPMA. Consequently, comparison of the EPMA and XRF profiles erroneously indicates that xenon is retained on the grain boundaries in the central region of the fuel. Determination of the amount of grain boundary gas at the pellet mid-radius, however, is unaffected by the aforementioned error because at this iocation bubble free areas within the grains are not generally present. The nature of the problem is illustrated in fig. 2 which shows the variation in the dist~bution of retained xenon in the GE fuel sample STR0253R-7 which was transient-tested to 43 kW m-‘. In addition to the radial concentration profiles measured by EPMA and XRF the figure shows the results from point

1

Xe Cow, +

wt%

Wltb b”bbl..

0.4 t

0 0

I

/

L7

,o

0.2

0

I

0.4

0

0.0

0.8

1

Relative Radius,r/PO Fig. 2. Concentrations of xenon measured in areas with and without gas bubbles in the central region of section STR0253R-7 and their correlation with the EPMA and XRF distribution profiles.

analyses in grain areas with and without gas bubbles. It is evident that the ~ncentration of retained xenon was much higher in areas where gas bubbles existed. Grain areas with bubbles contained 0.2-0.3 wt% xenon, whereas areas without bubbles contained fess than 0.05 wt% xenon. It is also seen that in the region between r/r,, = 0.5 and the pellet centre the EPMA concentrations measured in areas populated with bubbles lies on or just above the XRF profile. This indicates that the volume of fuel that is bubble free was relatively small. Clearly, the disparity between the XRF and EPMA profiles in this region is due to the fact that the volume of bubble free fuel that contributed to the analysis was different in the two cases. For XRF the Limit of detection for xenon is about 500 ppm and the uncertainty on an absolute coneentration of 0.5 wt% is estimated to be about 10% refative (1~). This uncertainty level has been established in part by comparing the measured xenon concentrations in the outer region of the fuel with the generated concentration calculated from the bumup, and in part by repeating the analysis of a reference fuel specimen. One source of this uncertainty is the poor reproducability of the count rate from the gaseous xenon standard. It is considered that the main cause of this was a variation in the thickness of the xenon gas layer seen by the detector through the thin beryllium window. This may have been caused by changes in the atmospheric pressure or the ambient temperature or both. The uncertainty on the relative X-ray intensity within the same XRF diametrical scan seems to be much better than 10%. If the reproducibility of the X-ray count rate is taken as a measure of the uncertainty then it is found to be approximately 3% (1~). The uncertainty on the relative X-ray intensity is much more important than the uncertainty on the absolute xenon concentration because the XRF-EPMA comparison and the release value for the cross section are both based on the relative X-ray intensity, i.e., on the shape of the radial ~ncentration profile, and do not involve the absolute xenon concentration. The reliability of the XRF profiles can be checked in two ways, First, the release figure obtained on integrating the relative XRF profile can be compared with the puncture result. This reveals whether the XRF profile has the correct form. Second, the absolute concentration of xenon measured in the outer region of the fuel between r/r0 = 0.8 and 0.9, where gas release is not generally detected can be correlated with the predicted concentration derived from the burnup. This provides an indication of the accuracy of the xenon concentrations measured by XRF.

91

M. Mogensen et al. / Distribution of retained xenon in UO, fuel

As XRF is purported to measure all the xenon retained in the fuel, the release value derived from the XRF profile should correspond to that obtained by puncturing. The XRF and puncturing results for 17 fuel sections are compared in table 2. Since the XRF data are the results of local measurements, whereas the puncturing result represents an integral measurement of the release from the whole pin, a true comparison is possible only in cases where the axial power profile is quite flat; that is to say, where the form factor is close to one. It can be seen from table 2 that when this is the case good agreement exists between the XRF and puncturing results. However, it is also evident from the table that in all but two flat-profile cases (M23-l-21R and STR017-SR) XRF gave a higher release value. This is attributed to the fact that when calculating the percentage of release from the XRF data the radial flux profile, which declines in direction of the pellet centre, was assumed to be flat. Calcula-

tion has shown that this discrepancy raised the XRF release values by two to five percentage points, which is generally the amount by which the XRF figures for release differ from the puncturing results. Comparison of the concentration of xenon measured in the outer region of the fuel with the predicted concentration derived from the burnup not only reveals how accurate the data is but also exposes any systematic errors in the measurements. The measured XRF concentrations are plotted against the predicted concentration in fig. 3. The EPMA concentrations are also included in the plot. It can be see that the xenon concentrations measured by XRF and EPMA are consistent and are generally in good agreement with the predicted concentrations. These findings support the view that the data are reliable. The predicted concentrations were calculated from the burnup using the irradiation yields obtained by the method of Mogensen [16]. For the Risa fuel the xenon yield was found to

Table 2 Percentage of fission gas released from the Rise and GE fuels as measured by XRF and puncturing 1

2

3

4

5

6

Fuel pin

Av. pin power (kW m-l)

Form factor a)

XRF b’

Puncturing

Difference (col. 4 - col. 5)

40.1

1.05

41.6 40.0

1.02 1.03

40.5 39.8

1.07 1.10

24 d’ 8.8 32 d’ 20 d’ 8.1 30 d, 21 d,

40.3 40.1

1.10 1.04

22 11 36 21 10 35 32 8 30 20

23-27 d’

42.2 42.4 38.7 42.7 ” 42.3 44.7 42.1

1.02 1.02 1.00 1.32 1.02 1.04 1.03

14 22 18 16 21 25 35

11.1 18.8 19.7 5.5 18.2 17.4 30.0

Rise fuel M23-l-21R M19-2 ‘) M23-l-9 M23-l-6 M38 ‘) M38-8R M73-2-8R e, M78-1 ” M72-2-2R e, M72-2-7R

,‘,.:r

-2 3.2 4 1 1.9 5 11 2.4 4 - (3-7)

General Electric fuel STR013-8R STR017-3R STR017-5R STR018 e, STR025-3R STR014-3R STR019-8R

The uncertainty on the puncturing results is 5%. a) Peak pin power/average pin power. b, Pin section numbers can be found in table 1. ‘) Not transient-tested. d, Base irradiation + transient test release. e, Steep axial power profile. n Peak pellet.

2.9 3.2 -1.7 10.5 2.3 7.6 5

92

M. Mogensen et al. / Distribution ojretaincd xenon in UO, fuel

Measured Concentration,

f

EPMA

wt%

Data

0.6 -

Fw details of pins a to z and A to I? see table 1.

i 0

0.1

0.2

0.3

0.4

0.5

0.6

Predicted Concentration,

0.7

OS8

wt%

Fig.3.Theaverage

~~~~nt~at~o~ of xenm measured in the radial interval r/r, = 0.8~0.9 by XRF and EPMA correlated with the predicted c~~~~tr~tjo~ derived from tile burnup. The broken tines mark the limits of the 3cr scatter band for the XRF data.

vary from 0.245 to 0.261 with increase in burnup from 3.2 to 5.2 at%. The xenon yield for the GE fuel was calculated to be 0.26 in the burnup range 2.9 to 3.4 at% and 0.257 at lower burnups.

5. Resuits

5.1. RadiaEd~st~~tio~

of retained

xenon

5.2. Radial distriblit~~~

ofxenonin

the trmsient-tested

fuels

In the case of the transient-tested fulels, XRF often measured more retained gas than EPMA, which is taken to indicate that there was fission gas trapped on the grain boundaries. Figs. 6 and 7 show the radial distribution of retained xenon in transient-tested fuel

in the base-

irradiated ,fuels

Rslstlve

Xe Cone.

lay---,

In the case of the base-irradiated fuels there was little difference between the radial distribution of retained xenon measured by XRF and EPMA. Figs. 4 and 5 show the XRF and EPMA profiles for the base-irradiated Risa fuel pin M78-1 and for part of the GE fuel pin STR018 that had seen such a low power in the transient test that it is assumed that no release had occurred. It can be seen that for both fuel types the normal&d EPMA and XRF profiles are in gmd agreement. As already stated, during the base irradiation the Riscb fuel released up ta 10% of its fission gas, whereas release from the GE fuel was around 0.1% only. The release values derived from the EPMLA and XRF profiles are given in table 3 and are in accord with these figures.

0

0.2

0.4 Relative

0.6

0.8

1

Radius, rlro

Fig. 4. Radial distribution of retained xenon in the baseirradiated Rise fuel pin M7&1. EPMA, section M78-I-19; XRF, section M78-l-18.

Relative Xe Cane. 1.4

I’ ’

XRP Data

+ 6PYADh

,,*_

* XRPfhlcl

+

EPYA Data

+

++ I

1.0

i

l0.8 9.6 -

f -b-b++*+

0

0 0

0.2

a4

0.6

0.6

I

Fig. 5. Radial distribution of retained xenon in thg part of the GE fuel pin STROll that had seen a low power in the transient test (15 kW m-l). EPMA, section STR018-4; XRF, section STR018-3.

from the Rise pin M23-l-21R and the GE pin STROl?-3R. It is seen from fig. 6 that in M23-I-21R the XRF and EPMA profiles start to diverge close to where gas release began at about T/T* = 0.78. The

Table 3 EPMA and XRF resuits for the percentage of xenon released from six Ris0 fuel pins and eight GE fuel pins

pin

l-l-La’

EPMA

XRF

5max. 30 43 38 34 36

8 21 36 30 22 20

9 7 8 12 16

24 35 18 0 30 25 35 23

14 22 18 0 16 25 35 21

10 13 0 a 14 0 0 2

(kW m-*1

EPMAXRF b’

Rise fuel M7&1 c’ M23-l-6 M23-l-9 M72-2-2R M23-l-21R M72-2-7R

39.3,39_7 41.7 39.7-41.4 39.7.39.0 41.0

a2

0.4

I a6

0.6

Fig. 6. Radial distribution of retained xenon in the transienttested Ris0 fuel pin M23-l-21R. EPMA, section M23-1-21 R-3; XRF, section M23-l-21R-2.

profiles remain separated until r/r,, = 0.4 where they converge once more before dividing again in the centrat region of the fuel. In STROl?-3R gas release began closer to the fuel centre at r/r* = 0.67 and as seen from fig. 7 the EPMA and XRF profiles begin to separate almost immediately after. ft is ais0 seen that the largest disparity in the two profiles occurs at about r/r0 = 0.6 and &hat at the fuel centre similar concentrations of gas are measured by EPMA and XRF. EPMA and XRF results for the percentage of xenan released from a number of transient-tested Ris(6 and GE fuel pins are given in table 3. It is evident that in most cases XRF gave a much Iower release value than

General Electric fuel STR013-8R STR017-3R STR017-.5R STROIS STROH STR014.3R STR019-8R STRO;IS-JR

43.2 42.2 37.0,37.2 15.1, 13.7 41.8 46.4,46.6 43.0 43.0

1

Fielative Radius. r/r,

Flektke R8diut3,r/r*

Fuel

0

Pin section numbers can be found in table 1. a> Transient terminal levef. b, Percentage of the xenon generated that is retained bubbles on the grain boundaries. cl Nat transient-tested.

in

Fig. 7. Radial dist~~ut~~ of retained xenon in the transienttested GE fuel pin STRUt7-3R. EPMA, section STRQ17-3R8; XRF, section STR017-3R-9.

M. Mogensenet al. / Distributionof retainedxenon in UO, fuel

94

5.3. Radial distribution of porosity in transient-tested .fuel

not caused by the transient test. In the outer part of the fuel nearly all such pores were artifacts resulting from grain fall-out during specimen preparation, whereas in the central region of the fuel much of the porosity had formed early in the base irradiation when the pin had seen a linear power in excess of 40 kW m -‘. In this region the volume percentage of pores in all four size classes increases as the pellet centre is approached. From the electron absorption micrographs in fig. 9 it is possible to identify the changes in the fuel microstructure that determine the form of the porosity profiles in fig. 8. For example, it can be seen that the maximum in the volume percentage of the smaller pores at r/r,, = 0.6 is related to the emergence of gas bubbles on the grain boundaries (micrograph c). Moreover, the maximum in the percentage of the larger pores at r/r0 = 0.4 is plainly associated with the growth and interlinkage of grain boundary bubbles and the development of a network of escape tunnels at the

Owing to the precipitation of gas bubbles, fuel that was transient-tested to powers above about 30 kW m-i became highly porous. Porosity data for M23-1-21 R is contained in fig. 8. This shows the radial variation in the volume percentage of pores in the four size classes 0.7-1.4, 1.4-2.8, 2.8-4.0 and 4.0-5.6 urn. It is seen that pores in the size classes 0.7-1.4 and 1.4-2.8 urn have a different radial distribution to those in the size classes 2.8-4.0 and 4.0-5.6 pm. In the first two size classes the volume percentage of pores peaks at r/r0 = 0.6 whereas in the other two size classes it peaks at r/r0 = 0.4. Moreover, the volume percentage of pores in the largest size class, 4.0-5.6 pm, falls to a miniumum in the radial interval r/r0 = 0.5 to 0.6, close to where the volume percentage of pores in the smallest two size classes, 0.7-1.4 and 1.4-2.8 km, is highest. These differences can be explained by the fact that most of the pores in the size range 2.8-5.6 pm were

POluoltY. WI.0 1s

I

0.6

0’

ch.4

0.7-14

lml)

I

0

0.4

0.2

Poromy.

I.4

. *

(8lm

0.2

0.8

1

vol.2

0.2

0

2.6

0.4

0.8

0.8

1

08

0.2

1

Porooity. ml.+

I 1.2.

81zaCl~2.8-4.OYm

(8lb

.

ClMm

4.0-m

*

um)

I-

I$-&@ 0.2 0

-

I

0 0

0.2

0.4 ftelative

Fig. 8. Radial

distribution

0.0 Ftadur,

profiles

0.8 r/r,

1

0

0.2

0.4 Ralathm

for pores (mainly gas bubbles) in the four size classes 0.7-1.4 4.0-5.6 km in section M23-l-21R-2.

Fladlu8,

pm, 1.4-2.8

r/r0 Frn, 2.8-4.0

pm and

M. Mogensen et al. / Distribution

of retained xenon in UO,

fuel

Fig. 9. Electron absorption micrographs showing the local fuel m~crostruc~re at six radial positions in section M23-l-ZlR-3.

95

and therefore their form is not so well established as in the case of the Rise fuel. Nevertheless, it is evident that the porosity profiles are similar to those found in the Risa fuel for pores of comparable size. The main features being maxima close to r/r0 = 0.6 and 0.4, and an increase in the volume percentage of pores in the central part of the fuel. Again, ceramography indicates that the maxima are due to the formation and development of grain boundary bubbles and that the increase in the volume percentage of pores in the size class 0.7-1.4 pm near the fuel centre is caused by the growth of gas bubbles within the grains.

0

0.2

0.4

0.8

0.6

1

o 8 Porosity, ~01%

6. Discussion

b. Si7.eClass 0.7-1.4 urn

6.1. Distribution and locatim of retained gas

4

0

0.2 t

01

0

1 0.2

0.4

0.8

0.8

I

Relative Ftadius, r/ru Fig. 10. Radial distribution profiles for pores (mainly gas bubbles) in the size classes 0.7-1.4 p,rn and 1.4-4.0 &rn in section STR017-3R-9.

grain edges (see micrographs d and e). Finally, it is seen from micrograph f that in the central region of the fuel the increase in the volume percentage of pores in the size range 1.4-4.0 urn is mainly due to the growth of intragranular gas bubbles. In contrast, the steep increase in the percentage of pores in the size range 4.0-5.6 pm is mainly caused by the appearence of large intergranular pores from the base irradiation. It seems that the formation of the latter may have been assisted by grain growth. In addition, many of the large intergranular pores seen in micro~aph f appear to have migrated as much as 20 pm leaving in their rear areas free of gas bubbles. The direction of travel is parallel to the radial temperature gradient, from lower to higher temperatures pointing to an evaporation condensation mechanism. Porosity data for the GE pin STR017-3R is shown in fig. 10. Radial distribution profiles for pores in the size classes 0.7-1.4 and 1.4-4.0 pm are presented. For each porosity profile only six data points are available

There is a basic difference in the way that retained fission gas is distributed in base-irradiated and transient-tested UO, fuel. As seen from figs. 4 and 5, for base irradiated fuel the EPMA and XRF profiles match almost perfectly indicating that most of the retained gas resides in the fuel lattice and in small intra~nular bubbles (< 0.1 pm in size). From fig. 4 it is evident that good agreement is obtained even when appreciable gas release is recorded, as in the case of the Rise, fuel. This agreement is significiant because it argues against the preferential accumulation of fission gas on the grain boundaries during the base irradiation. An assumption that appears to be widely embraced 117-191. In the case of transient-tested fuel, the XRF and EPMA profiles often show marked differences. This is clearly seen in figs. 6 and 7. Generally, differences in the profiles exist because part of the gas released from the fuel grains is retained on the grain boundaries. However, as indicated in section 4, care is required in interpreting the data. For example, in the case of M23-l-21R there is a marked disparity between the XRF and EPMA profiles in the central region of the fuel which suggests that an apprecible amount of gas has been retained on the grain boundaries. However, this appears not to be the case. The disparity in the region between r/r0 = 0.4 and the pellet centre probably results because the EPMA determinations were repeatedly made in bubble free regions of the grains where the concentration of retained xenon was less than 0.05 wt%. Had the proportion of bubble free areas anafysed

by EPMA

been

representative

of their

volume fraction in the fuel then the measured XRF and EPMA concentrations would undoubtly have been similar. Hence, the XRF profile can be taken as a true

97

M. Mogensenet al. / Distributionof retainedxenon in UO, fuel

measure of the local level of gas retention. As seen from micrograph f in fig. 9, the volume of fuel that was bubble free in the central region of M23-l-21R was in fact relatively small. There is apparently a variety of reasons for the occurrence of bubble-free regions within the fuel grains. In the case of M23-l-12R they appear to be the result of grain boundary sweeping up the temperature gradient in association with grain growth. This is insistent with a previous observation that the appearance of bubble free regions in a Siemens-KWU fuel preceded columnar grain growth [20]. On the other hand, investigations carried out on fuel samples from STRO18 have indicated that the formation of bubble-free zones in this fuel type was the result of the effects of internal restraint [S]. It is also pointed out that the absence of bubbles does not automatically signify that the concentration of retained xenon in the area in question is negligible. The reverse may be true. This is the case when bubble-free zones are found in the centre of the fuel at the beginning of the release process& In this case, it is the bubble-rich regions that contain a lower concentration of retained xenon. In the case of both M23-l-21R and STR017-3R the difference in the XRF and EPMA profiles that is found close to the mid-radial position is due to the retention of gas in grain boundary bubbles prior to their full interlinkage. This is evident from the fact that the extra concentrations of xenon detected by XRF peak at the position where the volume percentage of small pores in the size class 0.7-2.8 urn is highest. As already seen (subsection 5.3) these pores represent the gas bubbles on the grain boundaries. The radial variation in the ~n~ntration of grain boundary gas in M23-l-21R and STR017-3R is shown in figs. 21 and 12, respectively. The quantity plotted is the difference in the absolute concentrations of xenon measured by XRF and EPMA. It is seen that following an initial steep rise, the concentration of grain boundary gas in M23-l-21R reaches a rn~rn~ of about 0.16 wt% at about r/r0 = 0.55 before plunging to zero at r/r0 = 0.4. Differences between the XRF and EPMA profiles in the central region of the fuel are evidently the result of a fault in the EPMA measurements and have been ignored (see above). In total about 34% of the xenon inventory had been released from the grains and about one fifth of this was retained on the grain boundaries. Locally, at r/r0 = 0.55 the amount of gas retained on the grain boundaries amounted to about 45% of that release from the grains. In STR017-3R the concentration of grain boundary gas also reaches its highest value 10.17 wt%f close to r/r0 = 0.55, but in this case

o 2 Xe Conch. wt% .

0.2

0

0.4

0.6

0.8

1

Reiatlve Radius, r/r, Fig. 11. Radial variation in the concentration of xenon on the grain boundaries in pin M23-l-21R.

the distribution exhibits a tail which extends almost to the pellet centre. Once more, this tail presumably arises because bubble free areas were preferently selected for EPMA and hence the ~ncentration of xenon retained within the grains has been underestimated. As is the case in M23-l-21R, most probably there is little gas on the grain boundaries in the region between r/r0 = 0.4 and the fuel centre. Again, the peak in the gas distribution is located close to where the density of gas bubbles on the grain boundaries was highest (see fig. lob). 6.2. Gas pressure in grain boundary bubbles An important fact that comes to light when the EPhfA and XRF profiles are compared with the QIA

o 2Xe Cont., wt% I

(m)

1./\

0.16 -

0.1 -

0.06

-

0

\

0

02

0.4

0.6

Relative Radiur.

0.8

1

r/r,

Fig. 12. Radial variation in the concentration of xenon on the grain boundaries in STR01’7-3R.

M. Mogensen et al. / Distribution of retained xenon in UO, fuel

98 Table

4

Calculated average pressure bubbles

of the in the RisQ pin M23-l-21R

Radial position

n a)

T

(mol cm-“)

(“0

4.17x 1.03x 1.45x 1.49x 7.53 x

1240 1290 1320 1350 1410

gas

in grain

v b,

boundary

Pressure @IPa)

(r/r”) 0.7 0.65 0.6 0.55 0.45

10-s 1o-4 lo-” 1o-4 10-s

0.009 0.011 0.011 0.011 0.007

75 232 411 473 316

a) Xe+Kr. Weight fraction of Kr in the gas is assumed to be 0.097 (ref. [16]). “) Volume fraction of pores in the size range 0.7-2.8 pm.

results is that the gas bubbles on the grain boundaries are highly overpressurised. Calculations for the GE fuel section STR018-20 have shown that the gas pressure in the bubbles on the grain boundaries was a little over 100 MPa at temperatues above 1400°C [5]. This result, however, is based on the assumption that all the porosity measured by QIA was located on the grain boundaries and that the fission gas was evenly distributed throughout the pore volume. In the case of M23-l-21R, higher gas pressures of several hundreds of megapascals have been calculated for the grain boundary bubbles in the radial interval r/r,, = 0.4 to 0.6 (table 4). This pressure level should be more accurate than the 100 MPa cited above, because in the case of specimen M23-l-21R it has been possible to identify the size range of the pores (bubbles) in which the bulk of the gas was contained. Moreover, there is no uncertainty associated with a large release of gas on termination of the transient test as there is in the case of STROl8. Compared to the surface tension pressure of the grain boundary bubbles (2y/r) the calculated gas pressures of several hundreds of megapascals is extremely high. For gas bubbles in the size class 0.7-2.8 pm the surface tension pressure ranges from just 0.9 to 3.4 MPa (assuming y = 0.6 J me*>. As previously, the pressure of the gas in the grain boundary bubbles was calculated using the hard sphere equation of state of Brearly and Maclnnes 1211which is written: P=

(nkT/V)(l

where n the grain the local of pores reduced

+y +y2-y3)(1

-y>-‘,

is the number of moles of gas (Xe boundaries, y is the reduced density fuel temperature and I/ is the volume (bubbles) in the size range 0.7-2.8 density, y, is given by (rd3/6XN,/V>,

(1) + Kr) on and T is fraction pm. The where

d is the diameter of a xenon atom which was taken to be 0.37 nm and Ng is the number of gas atoms on the grain boundaries. The local temperature, T, was derived from a radial temperature profile constructed in accordance with measured centre-line temperatures 1221 and the proposal of Bagger and Mogensen [23] that the onset temperature for gas release is close to 1200°C and is unaffected by burnup. The values of the variables n, T and V used in the calculation of the pressure, P, are given in table 4. 6.3. The rate-determining step in fission gas release Fission gas release during a power transient is considered to occur in two steps [24]. First, gas diffuses out of the grains to the grain boundaries where part of it collects in bubbles. Then following a buildup in concentration, the trapped gas is released to the pin-free volume when the bubbles interlink or when microcracking occurs along the grain boundaries. The second step, which involves the venting of grain boundary bubbles has been shown to be the slowest and rate determining step [4,24]. This is concluded from the fact that the largest concentration of grain boundary gas is invariably found at the foot of the EPMA profile (cf., figs. 6 and 11). Its accumulation at this location indicates that at the start of the release process, i.e., between the shoulder and the foot of the EPMA profile, the rate of diffusion of gas out of the grains is faster than the rate at which the gas can escape from the grain boundaries. In the central region of the fuel there is little if any gas on the grain boundaries. In this region gas release from the grains to the grain boundaries stops long before the end of the test. Moreover, the high temperature promotes bubble interlinkage and the formation of escape tunnels so that any gas reaching the grain boundaries is quickly released to the pin-free volume. It would appear that the accumulation of gas on the grain boundaries is sustained until the pressure of the gas in the bubbles reaches several hundreds of megapascals depending on the clad restraint. At this point the internal pressure causes the bubbles to grow with the result that they interlink to form escape paths for the trapped gas. To be consistent with this scenario the onset position for gas release as measured by XRF should be at a radial position closer to the fuel centre (at a higher temperature) than the onset position as given by EPMA. That is to say, gas release from the fuel grainS should be detected in advance of release from the grain boundaries. However, this is not the case. Almost without exception, XRF and EPMA give, within the

limits of uncertainty, the same onset position for gas release. To explain this it has to be born in mind that the gas which reaches the grain boundaries at the start of the release process comes from a narrow band of fuel on each side of the boundary. If this is recognised, it will be realised that since EPMA is carried out in the fuel grain interior away from grain boundaries then this early release will not be detected. EPMA measurements across single grains in transient-tested UQ2 fuel has shown that close to grain boundaries there is often less retained xenon than in the centre of the grain [25]. This is ilIus~ated in fig. 13 which shows the distribution of xenon in a single grain at r/r,, = 0.69 in the fuel section STROIB-20, close to the onset position for gas release. The data indicates that a concentration gradient exists within the grain. It can be seen that the concentration of xenon falls from 0.51 wt% (complete retentions in the middle of the grain to as low as 0.43 wt% adjacent to the grain boundary. This constitutes a local release of about 15%.

It follows from the discussion in subsection 6.3 that if the interlinkage of grain boundary bubbles can be suppressed then gas release to the pin free volume during a power transient will be reduced. For the “STR” fuel supplied by GE this is clearly evident from

xe cono, WY

OS81 Compkb Wontion

0.6 .

~ 0.4 -

0.3 -

F = 0.03

F = 0.04

0.21

0.1

0: 0

6

10

16

19.6

Grain Diameter, urn Fig. 13. The distribution of xenon in a single grain of fuel at r/r,, = 0.69 in section STRGIS-20 close to the onset position for gas release. Gas has been released adjacent to the grain boundaries. F is the integral fractional release.

Table 5 Goncentration of grain boundary xenon and the change in pin diameter during the transient test Fuel pin

Diameter change (urn) Midpellet

Pellet interfaces

Xenon Cont. (wt%)

Ris@ fuel 56

0.053

M23-l-9

25

3 max.

50

0.043

M72-2-2R M23-1.21R

37 43

81 73

0.050 0.087

M72-2-7R

48

71

0,109

M23-1-6

General Electric fue1 -STRG13-3R =) STRG17-SR STR017-3R STRCW ‘) STRG14-3R =r STRGI9dR ar STRG25-3R

3 30 52 50 Ii: 59

0.007 0 0,058 0.060 0 0 0.008

Rise fuel pellets were dished whereas GE fuel pellets were chamfered. at Sharp power changes during the hold time. b, Pin sections 20 and 21,

the pressure transducer response records. These revealed that this fuel type released significant quantities of gas to the pin-free volume only on termination of the transient test or when there was a dramatic change in power during the test (fig. 11. We have cogently argued that the absence of release at constant power was due to a high mechanical restraint pressure which prevented bubble interlinkage on the grain boundaries [5]. When the power was decreased the mechanical restraint pressure was removed with the result that gas bubbles on the grain boundaries were able to interlink allowing the trapped gas to escape. In addition, thermal shock effects caused rni~r~ra~kin~ at the grain boundaries which also facihtated gas release. The basic indicator of the level of the mechanical restraint pressure is the pe~anent strain in the cladding which shows itself as a change in the pin diameter. For a number of Risa and GE fuel pins, table 5 gives the concentration of xenon retained on the grain boundaries and the diameter change during the transient test obtained by profilometry. it can be seen that for the Rise pins, with the exception of M23-f-6, the larger the change in pin diameter at the mid-pellet position the higher is the level of gas retention on the grain boundaries. In the case of the GE

loo

M. ~oge~e~

et al. / ~~tri~utio~

pins the picture is complicated by the different power histories employed [2]. Nevertheless, it is evident that where the test had included power peaks or dips the change in the pin diameter was small and little or no gas was contained on the fuel grain boundaries. In contrast, a high terminal power was maintained throughout the tests on STR018 and STR017-3R and both these pins showed a large change in diameter and high gas retention on the grain boundaries. The data for STR017-5R and STR025-3R, however, are inconsistent with the above trends. The gas concentration quoted in table 5 is the difference between the XRF and EPMA measurements given in column 5 of table 3 multiplied by the predicted xenon inventory derived from the burnup. A correction has not be made for errors in the EPMA concentrations caused by the preferential selection of bubble free areas in the central region of the fuel (see subsection 6.1). This means that for many of the pins in table 5 the concentration of grain boundary gas is slightly overestimated.

7. Conclusions X-ray fluorescence analysis can be used to measure retained xenon on grain boundaries not detected by electron probe microanalysis. This gas is usually found at intermediate radial positions in transient-tested fuel. The inte~retation of the data generated by XRF and EPh&$ is not as straightfo~ard as it may appear at first sight. Because the gas retained within the grains is often very unevenly distributed in the central region of transient tested fuel the amount of grain boundary gas cannot always be assessed from a straight comparison of the EPMA and XRF profiles. If, for example, EPMA is restricted to areas in the fuel where few or no bubbles exist then the concentration of grain boundary gas will be overestimated. To obtain a complete picture of the distribution and location of retained gas in a nuclear fuel, XRF and EPMA can be used in conjunction with high precision QIA. With QIA it is possible to identify within narrow limits the size class of the pores (gas bubbles) in which the bulk of the grain boundary gas is located. The results obtained with, these techniques in the three Rise Fission Gas Release Projects show that in many cases it is the interlinkage of gas bubbles on the grain boundaries that controls the rate of gas release from high burnup nuclear fuel during a power transient. The driving force for bubble growth is the internal gas pressure which can reach several hundred megapas-

of rerained xenon in iJO, fuel cals. Compared with the surface tension pressure, which is just a few megapascals, this pressure is considerable and is taken as proof that grain boundary bubbles are highly overpressurised. Further, Rise Project results reveal that the mechanical restraint pressure within the fuel is of importance in dete~ining the level of gas release under transient conditions since it slows down bubble interlinkage on the grain boundaries. It is also evident that in the central region of transient-tested fuel the level of gas release is not everywhere the same. Frequently, the release level varies greatly from grain to grain and even from point to point within a single grain. All this means that often gas release during a power transient cannot be predicted on the basis of simple gas diffusion considerations (using the Booth Model [26] for example). It also means that it is not possible to derive a gas diffusion coefficient of general relevance from release data obtained by puncturing. These conclusions indicate that in order to accurately describe fission gas release during a power transient, computer codes must be able to operate with other mechanisms besides thermal diffusion and must, above all, be able to incorporate the effects of mechanical restraint pressure. Another fact that emerges from the Riss data is the importance of fuel type. For instance, of the total amount of gas released from the GE fuel, about 80% was released at the end of the transient test on shutdown. In contrast, almost all the gas released from the Rise fuel was reieased during the transient hold time. The difference in behaviour is attributed to a high level of mechanical restraint pressure in the GE fuel [S]. But other factors such as the pore structure and the burnup level prior to a power transient will also be important in determining the release characteristics of a fuel. In addition, choice of design parameters, such as gap size, fill gas type and pressure, will also be crucial in determining how a particular fuel behaves with respect to gas release at a high power rating.

References RI P. Knudsen, C. Bagger, H. Carlsen, H. Misfeldt and M. Mogensen, Nucl. Technol. 72 (1986) 258. Dl P. Knudsen, C. Bagger, H. Carlsen, B.S. Johansen, M. Mogensen and I. Misfeldt, Proc. ANS Topical Mtg. on LWR Fuel Performance, Willj~sburg, USA, 1988, p. 189. [31 M. Mogensen, CT. Walker, I.L.F. Ray and M. Coquerelle, J. Nucl. Mater. 131 (198.5)162.

M. Mogensen et al. / Distribution of retained xenon in UO, fuel [4] C.T. Walker and M. Mogensen,

J. Nucl. Mater. 149 (19871 121. [5] C.T. Walker, P. Knappik and M. Mogensen, J. Nucl. Mater. 160 (1988) 10. [6] C.T. Walker, J. Nucl. Mater. 80 (1979) 190. [7] S.J.B. Reed, Proc. 4th Int. Congress on X-ray Optics and Microanalysis, eds. R. Castanig, P. Deschamp and J. Philibert (Hermann, Paris, 1966) p. 339. [8] I. Farthing, G. Love, V.D. Scott and C.T. Walker, in: Electron Beam Microanlysis, eds. A. Boekestein and M.K. Pavicevic, Mikrochim. Acta 1992 (supplement 12) pp. 117. [9] V.D. Scott and G. Love, X-ray Spectrom. 21 (1992) 27. [lo] M. Tong, J. Microsc. (Paris) 8 (1969) 276. [ll] R. Ronchi and C.T. Walker, J. Phys. D13 (1980) 2175. [12] M. Mogensen, J. Als-Nielsen and N.H. Andersen, Determination of Fission Products in Irradiated Fuel by X-ray Fluorescence, Report Rise M-2599 (1986). [13] H.A. Triebs, LlNEST; A FORTRAN-IV program for the Estimation of Linear Properties of Particale Size Distributions, Report Hanford Engineering Laboratories, HEDL-TME 71-181 (1971). 1141 W.L. Nicolson, Biometrika 57 (1970) 273. [15] M. Ancey, F. Bastenaire and R. Tiiier, J. Phys. DlO (1977) 817. [16] M. Mogensen, Int. J. Mass Spect. and Ion Phys. 48 (1983) 389.

101

[17] N. Zimmermann, Eur. Appl. Res. Rep. Nucl. Sci. Technol. 5 (1984) 1349. [18] E. Porrot, F. Lefebvre, M. Charles and C. Lemaignan, Proc. ANS Topical Mtg. on LWR Fuel Performance, Williamsburg, USA, 1988, p. 267. [19] K. Une and S. Kashibe, J. Nucl. Sci. Technol. 27 (1990) 1002. [20] C.T. Walker and M. Coquerelle, Proc. Int. Topical Mtg. on LWR Fuel Performance: Fuel for the 90’s, Avignon, France, 1991, vol. 2, p. 506. [21] I.R. Brearly and D.A. MacInnes, J. Nucl. Mater. 95 (1980) 239. [22] P. Knudsen, C. Bagger, M. Mogensen and H. Toftegaard, Proc. IAEA Tech. Mtg. on Fission Gas Release and Fuel Rod Chemistry Related to Extended Burnup, Pembroke, Canada, 7 April-l May, 1992, to be published. [23] C. Bagger, and M. Mogensen, ibid. ref. [22]. [24] M. Mogensen, P. Knudsen and C.T. Walker, Proc. IAEA Symp. on Improvements in Water Reactor Fuel Technology and Utilisation, Stockholm, 15-19 September 1986 (IAEA, Vienna, 1987) pp. 291. [251 C.T. Walker and K. Lassmann, J. Nucl. Mater. 138 (1986) 155. [26] A.H. Booth, Atomic Energy of Canada Ltd, Chalk River, Ontario, Canada, Report ACEL-496 (1957).