- Email: [email protected]
A measurement of the irradiation-induced creep of mixed carbide nuclear fuel
Journal of Nuclear Mate&h 90 (1980) 232-239 0 Norm-bond ~b~s~~ Company
A ~EASU~~ENT NUCLEAR FUEL
OF THE I~DIATION-EDUCED
CREEP OF MIXED CARBIDE
I. MijLLER-LYDA and W. DIENST Kemforschungszentrum Karlsruke, Institut fiXrMat&z!Fedemi Republic of Germany
und Festktirperforschung, Postfach 3640, D- 7500 Karlsruhe,
Received 1 November 1979
In the BR 2 reactor at Mol, Belgium, a measurement of the irradiation induced creep of mixed carbide nuclear fuel up to high burnup was carried out. The dependence upon applied stress and burnup of 95% dense (U, Pu) C was measured within a temperature range between 500 and 720°C and at fllion rates between LO-l.5 X 1d4 f/cm3 * s. The used irradiation device was a Confluent-type capsule that allowed a variation of stress as well as temperature during irradiation. The length changes of the fuel specimen were determined by means of the microwave cavity resonance method. The obtained creep rates are proportional to stress and burnup-independent. The irradiation creep rates are about one order of magnitude below those of mixed oxide fuel. The fission product swelling rate increased with burnup form initially 1.2 to 3.0 ~01%per % burnup. At stress changes the fuel showed a transient swelling up to 0.2 ~01%. The theoretical background of carbide irradiation creep is briefly di-mssed.
creep deformations at compressive stresses of about some 10 MPa are of similar size as the fuel swelling, and the net deformations to be obtained at creep measurements on carbide fuel will be very small. For that reason a comparatively delicate me~urement device will be necessary to measure the irradiation creep rates with sufficient precision. This measurement device must allow an in-pile stress variation to distinguish between creep and swelling in principle. All these requirements can be accomplished by the Confluent capsule which was used in the Mol 12B3 experiment and which turned out to be an approved system. This report gives a detailed description and thorough analysis of irradiation creep measurements on gr,Pu)C*
1. Introduction In the last ten years considerable effort was spent on experimental investigation on irradiation-induced creep of oxide fuel [l j . The following main conclusion can be drawn from the results: for oxide fuel pins no considerable plastic strain of the cladding will have to be expected under steady-state operating conditions if sufficient void volume is provided. The irradiation plasticity of oxide fuel was found to be suffkient to make the internal void volume completely accessible to the fuel swelling. On the contrary cladding distensions measured at irradiated carbide pins indicated a much more rigid behaviour of carbide fuel. Rather accurate irradiation creep rate measurements were also needed for a reliable carbide fuel pin design that is not too conservative. The first experiments were made on UC samples. [2]. They were followed by the same on (U, Pu) C samples whose preliminary results were already mentioned [ 11. While theoretical estimations pointed at carbide irradiation creep rates two orders of magnitude below those of oxide creep rates, first measurements only revealed a difference of one order of magnitude. The
2. Theoretical considerations In order to find out efficient experimental conditions for irradiation creep tests on ceramic fuel samples, rough theoretical estimations were first made of the irradiation-induced diffusion f3 1. The results showed that there is an outstanding influence of 232
I. Mirller-Lyda, W. Dienst /Measurement of creep of mixed carbide nuclear fuel
ionization processes along the fission fragment tracks in nuclear fuels which is of major technical importance, at least for oxide fuel. The results were adopted to describe also irradiation-induced creep with regard to the Nabarro-Herring creep correlation, but bearing in mind that the physical arguments are disputable. Fig. 1 taken from [4] shows the main results of the estimations mentioned above. The lattice disturbance operative in oxide fuel was attributed to thermal diffusion in the zones which were highly overheated by very dense ionization along the fission fragment tracks (“thermal rods”). This type of disturbance, however, was largely excluded for carbide or nitride fuel because of the wide conduction electron-electron energy dispersion from the ionized zones and the better heat conduction to the surrounding material. For these fuels only a limited amount of irradiation-induced diffusion is certain to occur by atom site exchange processes during the formation and collapse of displacement spikes. This led to the conclusion that irradiation-induced diffusion and also irradiation creep of carbide fuel can be expected to be possibly two orders of magnitude below that of oxide fuel. Some information about irradiationinduced diffusion in metallic U-fuel, however, indicated that this expectation could be too low [3].
Ll*
leoo
I400
1200
233
Meanwhile it turned out - as can also be seen by the results in this report - that irradiation induced diffusion rates and creep rates of oxide and carbide fuel only differ by factors of 7-l 5 [ 1,2,5]. That cannot be due to a higher production rate of point defects in the lattice under irradiation than formerly estimated, for the used production rate of about 10’ points defects per fission could not be exceeded by a factor as large as 10. Therefore one has to conclude that the thermal effects ln the highly ionized zone along the fission fragment tracks must not be neglected for carbide fuel. Nevertheless, the situation in carbide fuel would not change decisively if the previous disturbance model of a quasi-molten zone along the fission fragment track was retained because the melting temperature of carbide fuel, in contrast to oxide fuel, will never be exceeded in any case. That model, however, is disputable anyway because the small overheated zone is strongly restrained by the surrounding material. It seems to be more appropriate to adopt a model that characterizes the overheated zone by very high compressive stresses and stress gradients caused by thermal expansion [6]. These stresses can reduce the probability of short-circuit recombination of vacancies and interstitials [7]. The interstitials will have to migrate much further until they can recombine with vacancies. By
800 T.K
1000
m Vs
10 -19
0;s
0;8
Fig. 1. Effective uranium self-diffusion coefficient in UO2 f/cm3 * s.
i
I]2
114 *10-v
n
l/T
(partly also UN,UC) under irradiation at a fusion rate of 2.5 x 10’4
234
I. Miller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
doing so, they will carry out much more atom site exchanges than only by r~rr~gement within a displacement spike. This leads to an increased rate of irradiation-induced diffusion due to atom-site exchange, compared with the situation without any interaction between overheated zones and point defect arrangements. As far as caution-induced creep is ~oncemed one must not consider atom site exchange, but stress-orientated annealing of temporarily stable point defects. In this respect the separation of vacancies and interstitials will increase the probability of formation and growth of dislocation loops or of dislocation climb by point defect annealing, both of which will be orientated relative to the external stress. The separation of vacancies and interstitials will be more effective in oxide fuel than in carbide fuel because of the stronger overheating along the fission fragment tracks. This expectation is supported by reference to correspon~g numbers of uranium Frenkel pairs remaining [7] which are about 5000 and 750 per fission in oxide and carbide fuel, respectively. This ratio is within the range for that of creep rates measured which will be demonstrated for irradiation induced creep rates of oxide and carbide fuel in the following. The general conclusion can be drawn that irradiation induced creep seems to be attributable to a combination of ionization heating and atom collision effects.
Fig. 2. Fuel specimen in the NaK chamber of the Confluent capsule.
ated by an intermediate molybdenum ring - threaded on a small steel tube (fig. 2). The essential fuel pellet characteristics are given in table 1.
3. The fuel specimen
4. Measurement device and irradiation
The fuel specimen consisted of a batch of four (U, Pu) C armular pellets which were - each separ-
The irradiation experiment was carried out with a creep me~u~ment capsule of type Confluent constructed by the CEN Grenoble and which had the following experiment and measurement possibilities: - In-pile length change measurements with a precision in the pm-range my means of the microwave cavity resonance method. - In-pile stress variation in the range between 2 and 50 MPa. - Temperature variation by gas exchange in a thermal barrier. A detailed description of the Confluent capsule is given in ref. [ 81. The fuel temperature can be varied by the exchange of gases of different thermal conduc-
Table 1 Fuel pellet main characteristics Material C content 0 + N content M2C3 content Geometry Outer diam. Inner diam. Pelletheight Number of pellets Sintering density
UO.85~0.15C 4.75%
I. Miiller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
I-L-
235
Motor
lnrulotor
1 I
II
Piston]
Fig. 3. Principle of the microwave resonator cavity measurement system.
tivity within a thermal barrier. The capsule was designed for a fuel temperature of 800 and 950°C with helium and nitrogen in the thermal barrier and a rating of 4500 W/cm3 = 1.4 X 1014 f/cm3 * s. At lower ratings, the temperature will be correspondingly lower. The fuel temperature was measured by means of two ther-
Mel 1283
mocouples in the central metal tube and in the medium molybdenum ring (fig. 2). The specimen is surrounded by stagnant NaK. Its temperature is measured by two additional thermocouples. The pressure upon the specimen is pneumatically produced from outside by gas loading in a two stage-pressure
irradiation
History
Fig. 4. Irradiation history of the Mol12B3 experiment (applied stress, fuel temperature, and thermal neutron flux.
I. Miiller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
236
chamber system. Compressive stresses up to 50 MPa can be attained with gas pressures up to 80 bar in the pressure chambers. The fuel stack length changes are measured by means of the microwave cavity resonance method. Here the dependence of the resonance frequency of microwaves in the GHz range upon the volume of a metallic cavity is used (fig. 3). This method is explicitly described in ref. [9]. The irradiation was carried out from 1977 to 1978 up to about more than 9000 h. The thermal neutron
Table 2 Moll2B3 operation conditions and deformations measured in 31 irradiation intervals of duration At; fission rate R in 1014 f/cm3 * s, compressive stress u, fuel temperature T, medium burnup in the interval B, AL measured deformation, & normalized deformation rate X lo6 No.
1 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
B
At
o
(%I
(h)
@iPa)
0.4 0.6 0.7 1.1 1.7 1.9 2.2 2.5 2.8 3.1 3.3 3.6 4.1 4.5 4.9 5.3 5.4 5.1 6.0 6.3 6.4 6.9 7.3 7.5 7.9 8.3 8.7 9.0 9.4 9.8 10.2
178 46 100 257 172 90 68 243 193 86 186 215 180 338 149 91 185 381 143 214 84 312 237 71 214 479 237 116 312 162 197
10 20 30 30 40 40 2 2 20 20 30 40 40 2 20 40 40 40 20 2 2 40 20 20 20 2 20 10 2 2 2
R
570 580 590 590 520 670 540 580 580 605 605 605 595 600 660 675 700 690 700 600 520 580 600 640 650 620 600 580 560 520 630
1.55 1.55 1.55 1.46 1.37 1.37 1.33 1.43 1.43 1.42 1.42 1.37 1.29 1.23 1.16 1.16 1.09 1.13 1.07 0.99 0.99 1.24 1.15 1.30 1.30 1.17 1.27 1.27 1.17 1.06 0.95
flux was raised by means of irradiation position changes from initially 1.4X 1014 n/cm2 * s to 3.5 X 1Or4 n/cm2 - s in order to compensate the decrease of the fission rate conditional on burnup. The aimed maximum fuel temperatures of 850-950°C could not be achieved as the gas gap was obviously too narrow. The fission rate and the bumup were calculated from the thermal neutron flux at the irradiation position and the irradiation time by using an empirical value for the flux depression both of fuel and capsule (table 2, fig. 4). The uncertainty of the neutron flux measurement was about 5%, and that of the capsule and fuel flux depression parameter about 10%. So the fission rates and the fission density are only exact within 15%. This uncertainty can be considerably reduced by means of a radiochemical bumup determination which will be carried out with the fuel post irradiation examination.
AL
C,,
Olm)
(h-l)
5. Evaluation of the deformation measurements
10.5 1.1 0 0.7 2.1, 6.6 9.1 25.6 7.4 7.4 1.4 9.4 10.9 39.6 8.3 1.0 11.2 23.9 28.2 39.5 10.5 14.3 .38.5 5.9 14.8 113.9 20.3 21.6 71.1 13.8 38.9
2.39 0.92 0 0.11 0.56 3.37 6.76 4.62 1.68 3.82 1.77 1.99 2.95 5.96 3.02 0.65 3.49 3.49 11.57 11.66 1.89 2.33 8.90 3.98 3.34 12.71 4.22 11.72 12.22 5.05 13.01
For the evaluation, time intervals of sufficiently stationary neutron flux and fuel temperature and a minimum duration of 40 h were selected from the irradiation history. The data of the 31 intervals suitable to the evaluation are given in table 2. The strain measurements were corrected with respect to power fluctuations by means of a relation between the specimen length and the specimen temperature. This correction relation could be obtained from measurements during a reactor start-up period. The length changes of the specimen measured in these intervals Ae, = M/L consisted of the fuel swelling AeS and of the irradiation creep deformation Ae,. Both deformations are countercurrent and of comparable size. Thus, Aem =
APE,+ Ae, .
A4 and Ae, both depend upon the fission rate and the interval duration At and could furthermore depend upon the bumup B and the fule temperature T. The variations of the applied stress in the experiment make possible a separation of the stress-dependent component of the strain (e,) and the stress-independent component (es). es can be interpreted as a stress-independent swelling rate which will be com-
I. Miiller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
231
parable to the usual low temperature swelling rate under cladding restraint.
be
de,/do = de,/do
with a constant swelling rate and a constant creep modulus. The calculation gives Cr = 9.83 X 10m6 and C, = -2.09 X lo-‘. The correlation coefficient between normalized measured values and those obtained from the fitting formula is 0.57 which is still not very satisfactory. Regarding the measured values one can suppose that the swelling rates increase with higher burnups, which leads to an approach of the form:
,
e, = e, - o(de,/do)
.
In the following it will be looked for a relation for I?, and &.,.,depending upon R, B, T, and u, and
furthermore it will be detected if there are still other parameters of fluence (e.g. transient effects). To simplify the evaluation it will be assumed for the present that 6, = AeJAt and &,= Ae,lAt depend linearly upon the fission rate R. These assumptions are usually made and were proved experimentally for the creep rate of oxide fuel in the range of the fission rates attained in this experiment [ 11.Strictly speaking such a proportionality wilI not apply to the swelling rate, but as the changes of the fission rate were not too large (1.0-1.5 X1014 f/cm3 *s), a linear dependence will be justificable within this region. The normalized deformation rates e,, are obtained from the AL values of table 2 by division by At and R/1014. For the determination of a swell and creep relation, the measured en will be described by approximative values 15,which can be represented as a linear function of the parameters B, T. u, or combinations between them &r,i= Ci + Czoi + C3Bi + .a. 7 where the index i refers to every single measurement. The coefficients C are obtained by the method of least square approximation, that is the value of Q,
has to be minimized. At its minimum 8Q/aCi will be 0 for all j. The resulting equation systems for the C’i are solved by the assistance of a computer. The measured values should be approximated by the least possible number of coefficients, that means it is looked for a formulation which on one hand is as simple as possible, but which on the other hand regards all the decisive influencing parameters. The quality of the approximation can be measured by the correlation coefficient between the &n,iand the &r,,. 6. Determination of the approximation function The simplest reasonable approach function would
er= cr + c,u
The result is: Ct = 4.35 X 10B6, C, = -1.37 X10-‘,
C3 = 6.83 X lo-’ and the correlation coefficient raises up to 0.81. A more precise analysis with regard to the burnup dependence of the swelhng rate with an additional C4Bz term gave a correlation coefficient of only 0.82, so a linear bumup dependence will be sufficient to describe the observed fuel swelling. Further analyses, with respect to a proportionality of the type T, p, BT or Bu, resulted in fitting values whose correlation coefficient was never above 0.83 and so these second-order terms can be neglected. Consider the plot of the values of the fitting formula &r= Cr t Cau + C3B versus the measured vahres of fig. 5 and regarding table 2, one can observe a correlation between the measured values and the stress changes. If the applied stress in one interval was increased compared to the preceding interval, the calculated value is too small, and vice versa. Let A&i= EJ - &,i, AUK= Ui- Ui_1,ATi = Ti - Ti-1 and look for a correlation between A&iand the changes of the operation conditions. The calculation gives a correlation coefficient of -0.47 between the A& and the Au and only 0.004 between the AE and ATvalues. That is, there is a transient swelling behavior of the fuel caused by stress and temperature changes, while the latter is negligible in the considered temperature range. A much better correlation exists between the Act and the products BiAq (0.56), which shows a strong coupling between the burnup and the transient swelling. Furthermore, it can be supposed that there is a saturation of the transient swelling effect with respect to stress changes and
238
I. M~~er-~~da, W. Dienst / Me~~~e~e~~
of creepof
mixed carbide nuclear jkeI
(2) Stationary linear swelling rate & = (4.35 + 0.68B[%])X10-26R
cm3 - s/fission - h ,
which is equivalent to the relation: SV,,(VAB)=(1.17 tO.lgE[%])vol%per%
burnup,
assuming isotropic swelling. (3) Transient deformation et = -1.92X1O-26 A&[1 - exp(-t/l30
h)
X m3 - @Pa * fission,
3 5 Measured
7 9 11 13 Deformation Rate, 10e6 h-l
Fig. 5. Formula values, plotted against the measured values: (*) including, (0) neglecting transient effects.
duration. This can be described by Ae N Aui [I - exp(-A&,&)]
,
Act = A&Ati , U, = min(l AUK I, Q) sign(Ao,) and to, u. are constants which have to be determined by trial and error to find the maximum correlation coefficient. This is achieved by the correlation: Ae = -6.30XIO-6Bjl
- exp[-(t/l30
h)])
Xmin(]Aol, 14MPa). Combining the stationary and the transient approach values, the measured and the formula values are correlated by a coefficient of 0.91. This is a satisfactory result considering the difficulties of the measurement. As can be seen from fig. 5, where the fitted values are plotted against the experimental values, the correspondence is raised for many values where the data points move towards the ef = $ line if the transient swelling is taken into the consideration. The following relations for the deformation of carbide fuel under irradiation can be derived from the results of the analysis: (1) Irradiation Induced creep rate e*1E.f = -1.37 X10-*’ u& cm3 * s/MPa +fission - h .
where the absolute value of Au is limited to 14 MPa. As an example, the total transient swelling of the fuel after a stress release of 20 MPa will be in the order of 0.2 ~01%at 5% burnup.
7. Conclusions The main results of the experiment were burnup and tem~rat~e-~dependent creep rates of the highly dense mixed carbide fuel as well as the proof of a considerable transient swelling at stress changes. Furthermore, a swelling rate increasing linearly with the burnup was observed. This swelling behaviour does not fully agree with expectations relevant to this [ 101, but up to now no other measurements were made in this temperature range. At 10% bumup, the swelling rate will be about 3 ~01%per percent bumup. Some later measurements not considered in this report showed no further increase, so this value will be the m~mum in this temperature range. Comparing the measured creep rate to other measurements in fv. 6, one can see a rather good agreement with other results. It is about one decimal order of magnitude below those of oxide fuel and are consistent with the theoretical considerations about the effective mechanisms mentioned before. The transient swelling and shrinkage of the fuel may be of technical importance with respect to mechanical interaction between fuel and cladding during power changes, because it could change the fuel contact pressure against the cladding caused by the differential thermal expansion. Finally, it should be remarked that the calculated swelling rates are i~~t~eous values rather than the lifetime average swelling rates which are used to estimate necessary void volume for accom-
I. MiiIler-Lyda, W.Dienst /.Measurement of creep of mixed carbide nuclear fuel
10%
1500 .
1300 no0 1000 * * . .
600
239
SPO 1.K
-7 c
L
.z 10-S.
10-6.
1o-7a
10-61 0.6
-
r 0.6
-
’ 1.0
’
. 1.2
’
’ 1.4
*
’ 1.6
l/T,
1O-3 K-’
Fig. 6. Mel 12B3 creep rate versus fuel temperature in comparison with previous results.
modation
of integral fuel swelling in uranium carbide
fuel pins.
References
[l] W. Dienst, J. NucL Mater. 65 (1977) 1. [ 21 D.J. Clough, J. Nucl. Mater. 56 (1975) 279. [ 31 W. Dienst, AECL-4375,1973 (German original, 1970).
[ 41 D. Brucklacher and W. Dienst, J. Nucl. Mater. 42 (1972) 285. [5] A. Hah and Hj. Matzke, J. Nucl. Mater. 48 (1973) 157. [6] H. Blank, Phys. Status Solidi 10 (1972) 465. [7] H. Blank, EUR 6600 EN (1979), Proc. Workshop on Fission Gas Behavior in Nuclear Fuels, Karlsruhe, 1978, p.307. [ 81 H.E. HKfner, Atomwirtschaft (Feb. 1974) 79. 191 M. Masson, J. Nucl. Mater. 65 (1977) 307. [lo] H. Blank, J. Nucl. Mater. 58 (1975) 123.
A ~EASU~~ENT NUCLEAR FUEL
OF THE I~DIATION-EDUCED
CREEP OF MIXED CARBIDE
I. MijLLER-LYDA and W. DIENST Kemforschungszentrum Karlsruke, Institut fiXrMat&z!Fedemi Republic of Germany
und Festktirperforschung, Postfach 3640, D- 7500 Karlsruhe,
Received 1 November 1979
In the BR 2 reactor at Mol, Belgium, a measurement of the irradiation induced creep of mixed carbide nuclear fuel up to high burnup was carried out. The dependence upon applied stress and burnup of 95% dense (U, Pu) C was measured within a temperature range between 500 and 720°C and at fllion rates between LO-l.5 X 1d4 f/cm3 * s. The used irradiation device was a Confluent-type capsule that allowed a variation of stress as well as temperature during irradiation. The length changes of the fuel specimen were determined by means of the microwave cavity resonance method. The obtained creep rates are proportional to stress and burnup-independent. The irradiation creep rates are about one order of magnitude below those of mixed oxide fuel. The fission product swelling rate increased with burnup form initially 1.2 to 3.0 ~01%per % burnup. At stress changes the fuel showed a transient swelling up to 0.2 ~01%. The theoretical background of carbide irradiation creep is briefly di-mssed.
creep deformations at compressive stresses of about some 10 MPa are of similar size as the fuel swelling, and the net deformations to be obtained at creep measurements on carbide fuel will be very small. For that reason a comparatively delicate me~urement device will be necessary to measure the irradiation creep rates with sufficient precision. This measurement device must allow an in-pile stress variation to distinguish between creep and swelling in principle. All these requirements can be accomplished by the Confluent capsule which was used in the Mol 12B3 experiment and which turned out to be an approved system. This report gives a detailed description and thorough analysis of irradiation creep measurements on gr,Pu)C*
1. Introduction In the last ten years considerable effort was spent on experimental investigation on irradiation-induced creep of oxide fuel [l j . The following main conclusion can be drawn from the results: for oxide fuel pins no considerable plastic strain of the cladding will have to be expected under steady-state operating conditions if sufficient void volume is provided. The irradiation plasticity of oxide fuel was found to be suffkient to make the internal void volume completely accessible to the fuel swelling. On the contrary cladding distensions measured at irradiated carbide pins indicated a much more rigid behaviour of carbide fuel. Rather accurate irradiation creep rate measurements were also needed for a reliable carbide fuel pin design that is not too conservative. The first experiments were made on UC samples. [2]. They were followed by the same on (U, Pu) C samples whose preliminary results were already mentioned [ 11. While theoretical estimations pointed at carbide irradiation creep rates two orders of magnitude below those of oxide creep rates, first measurements only revealed a difference of one order of magnitude. The
2. Theoretical considerations In order to find out efficient experimental conditions for irradiation creep tests on ceramic fuel samples, rough theoretical estimations were first made of the irradiation-induced diffusion f3 1. The results showed that there is an outstanding influence of 232
I. Mirller-Lyda, W. Dienst /Measurement of creep of mixed carbide nuclear fuel
ionization processes along the fission fragment tracks in nuclear fuels which is of major technical importance, at least for oxide fuel. The results were adopted to describe also irradiation-induced creep with regard to the Nabarro-Herring creep correlation, but bearing in mind that the physical arguments are disputable. Fig. 1 taken from [4] shows the main results of the estimations mentioned above. The lattice disturbance operative in oxide fuel was attributed to thermal diffusion in the zones which were highly overheated by very dense ionization along the fission fragment tracks (“thermal rods”). This type of disturbance, however, was largely excluded for carbide or nitride fuel because of the wide conduction electron-electron energy dispersion from the ionized zones and the better heat conduction to the surrounding material. For these fuels only a limited amount of irradiation-induced diffusion is certain to occur by atom site exchange processes during the formation and collapse of displacement spikes. This led to the conclusion that irradiation-induced diffusion and also irradiation creep of carbide fuel can be expected to be possibly two orders of magnitude below that of oxide fuel. Some information about irradiationinduced diffusion in metallic U-fuel, however, indicated that this expectation could be too low [3].
Ll*
leoo
I400
1200
233
Meanwhile it turned out - as can also be seen by the results in this report - that irradiation induced diffusion rates and creep rates of oxide and carbide fuel only differ by factors of 7-l 5 [ 1,2,5]. That cannot be due to a higher production rate of point defects in the lattice under irradiation than formerly estimated, for the used production rate of about 10’ points defects per fission could not be exceeded by a factor as large as 10. Therefore one has to conclude that the thermal effects ln the highly ionized zone along the fission fragment tracks must not be neglected for carbide fuel. Nevertheless, the situation in carbide fuel would not change decisively if the previous disturbance model of a quasi-molten zone along the fission fragment track was retained because the melting temperature of carbide fuel, in contrast to oxide fuel, will never be exceeded in any case. That model, however, is disputable anyway because the small overheated zone is strongly restrained by the surrounding material. It seems to be more appropriate to adopt a model that characterizes the overheated zone by very high compressive stresses and stress gradients caused by thermal expansion [6]. These stresses can reduce the probability of short-circuit recombination of vacancies and interstitials [7]. The interstitials will have to migrate much further until they can recombine with vacancies. By
800 T.K
1000
m Vs
10 -19
0;s
0;8
Fig. 1. Effective uranium self-diffusion coefficient in UO2 f/cm3 * s.
i
I]2
114 *10-v
n
l/T
(partly also UN,UC) under irradiation at a fusion rate of 2.5 x 10’4
234
I. Miller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
doing so, they will carry out much more atom site exchanges than only by r~rr~gement within a displacement spike. This leads to an increased rate of irradiation-induced diffusion due to atom-site exchange, compared with the situation without any interaction between overheated zones and point defect arrangements. As far as caution-induced creep is ~oncemed one must not consider atom site exchange, but stress-orientated annealing of temporarily stable point defects. In this respect the separation of vacancies and interstitials will increase the probability of formation and growth of dislocation loops or of dislocation climb by point defect annealing, both of which will be orientated relative to the external stress. The separation of vacancies and interstitials will be more effective in oxide fuel than in carbide fuel because of the stronger overheating along the fission fragment tracks. This expectation is supported by reference to correspon~g numbers of uranium Frenkel pairs remaining [7] which are about 5000 and 750 per fission in oxide and carbide fuel, respectively. This ratio is within the range for that of creep rates measured which will be demonstrated for irradiation induced creep rates of oxide and carbide fuel in the following. The general conclusion can be drawn that irradiation induced creep seems to be attributable to a combination of ionization heating and atom collision effects.
Fig. 2. Fuel specimen in the NaK chamber of the Confluent capsule.
ated by an intermediate molybdenum ring - threaded on a small steel tube (fig. 2). The essential fuel pellet characteristics are given in table 1.
3. The fuel specimen
4. Measurement device and irradiation
The fuel specimen consisted of a batch of four (U, Pu) C armular pellets which were - each separ-
The irradiation experiment was carried out with a creep me~u~ment capsule of type Confluent constructed by the CEN Grenoble and which had the following experiment and measurement possibilities: - In-pile length change measurements with a precision in the pm-range my means of the microwave cavity resonance method. - In-pile stress variation in the range between 2 and 50 MPa. - Temperature variation by gas exchange in a thermal barrier. A detailed description of the Confluent capsule is given in ref. [ 81. The fuel temperature can be varied by the exchange of gases of different thermal conduc-
Table 1 Fuel pellet main characteristics Material C content 0 + N content M2C3 content Geometry Outer diam. Inner diam. Pelletheight Number of pellets Sintering density
UO.85~0.15C 4.75%
I. Miiller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
I-L-
235
Motor
lnrulotor
1 I
II
Piston]
Fig. 3. Principle of the microwave resonator cavity measurement system.
tivity within a thermal barrier. The capsule was designed for a fuel temperature of 800 and 950°C with helium and nitrogen in the thermal barrier and a rating of 4500 W/cm3 = 1.4 X 1014 f/cm3 * s. At lower ratings, the temperature will be correspondingly lower. The fuel temperature was measured by means of two ther-
Mel 1283
mocouples in the central metal tube and in the medium molybdenum ring (fig. 2). The specimen is surrounded by stagnant NaK. Its temperature is measured by two additional thermocouples. The pressure upon the specimen is pneumatically produced from outside by gas loading in a two stage-pressure
irradiation
History
Fig. 4. Irradiation history of the Mol12B3 experiment (applied stress, fuel temperature, and thermal neutron flux.
I. Miiller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
236
chamber system. Compressive stresses up to 50 MPa can be attained with gas pressures up to 80 bar in the pressure chambers. The fuel stack length changes are measured by means of the microwave cavity resonance method. Here the dependence of the resonance frequency of microwaves in the GHz range upon the volume of a metallic cavity is used (fig. 3). This method is explicitly described in ref. [9]. The irradiation was carried out from 1977 to 1978 up to about more than 9000 h. The thermal neutron
Table 2 Moll2B3 operation conditions and deformations measured in 31 irradiation intervals of duration At; fission rate R in 1014 f/cm3 * s, compressive stress u, fuel temperature T, medium burnup in the interval B, AL measured deformation, & normalized deformation rate X lo6 No.
1 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
B
At
o
(%I
(h)
@iPa)
0.4 0.6 0.7 1.1 1.7 1.9 2.2 2.5 2.8 3.1 3.3 3.6 4.1 4.5 4.9 5.3 5.4 5.1 6.0 6.3 6.4 6.9 7.3 7.5 7.9 8.3 8.7 9.0 9.4 9.8 10.2
178 46 100 257 172 90 68 243 193 86 186 215 180 338 149 91 185 381 143 214 84 312 237 71 214 479 237 116 312 162 197
10 20 30 30 40 40 2 2 20 20 30 40 40 2 20 40 40 40 20 2 2 40 20 20 20 2 20 10 2 2 2
R
570 580 590 590 520 670 540 580 580 605 605 605 595 600 660 675 700 690 700 600 520 580 600 640 650 620 600 580 560 520 630
1.55 1.55 1.55 1.46 1.37 1.37 1.33 1.43 1.43 1.42 1.42 1.37 1.29 1.23 1.16 1.16 1.09 1.13 1.07 0.99 0.99 1.24 1.15 1.30 1.30 1.17 1.27 1.27 1.17 1.06 0.95
flux was raised by means of irradiation position changes from initially 1.4X 1014 n/cm2 * s to 3.5 X 1Or4 n/cm2 - s in order to compensate the decrease of the fission rate conditional on burnup. The aimed maximum fuel temperatures of 850-950°C could not be achieved as the gas gap was obviously too narrow. The fission rate and the bumup were calculated from the thermal neutron flux at the irradiation position and the irradiation time by using an empirical value for the flux depression both of fuel and capsule (table 2, fig. 4). The uncertainty of the neutron flux measurement was about 5%, and that of the capsule and fuel flux depression parameter about 10%. So the fission rates and the fission density are only exact within 15%. This uncertainty can be considerably reduced by means of a radiochemical bumup determination which will be carried out with the fuel post irradiation examination.
AL
C,,
Olm)
(h-l)
5. Evaluation of the deformation measurements
10.5 1.1 0 0.7 2.1, 6.6 9.1 25.6 7.4 7.4 1.4 9.4 10.9 39.6 8.3 1.0 11.2 23.9 28.2 39.5 10.5 14.3 .38.5 5.9 14.8 113.9 20.3 21.6 71.1 13.8 38.9
2.39 0.92 0 0.11 0.56 3.37 6.76 4.62 1.68 3.82 1.77 1.99 2.95 5.96 3.02 0.65 3.49 3.49 11.57 11.66 1.89 2.33 8.90 3.98 3.34 12.71 4.22 11.72 12.22 5.05 13.01
For the evaluation, time intervals of sufficiently stationary neutron flux and fuel temperature and a minimum duration of 40 h were selected from the irradiation history. The data of the 31 intervals suitable to the evaluation are given in table 2. The strain measurements were corrected with respect to power fluctuations by means of a relation between the specimen length and the specimen temperature. This correction relation could be obtained from measurements during a reactor start-up period. The length changes of the specimen measured in these intervals Ae, = M/L consisted of the fuel swelling AeS and of the irradiation creep deformation Ae,. Both deformations are countercurrent and of comparable size. Thus, Aem =
APE,+ Ae, .
A4 and Ae, both depend upon the fission rate and the interval duration At and could furthermore depend upon the bumup B and the fule temperature T. The variations of the applied stress in the experiment make possible a separation of the stress-dependent component of the strain (e,) and the stress-independent component (es). es can be interpreted as a stress-independent swelling rate which will be com-
I. Miiller-Lyda, W.Dienst /Measurement of creep of mixed carbide nuclear fuel
231
parable to the usual low temperature swelling rate under cladding restraint.
be
de,/do = de,/do
with a constant swelling rate and a constant creep modulus. The calculation gives Cr = 9.83 X 10m6 and C, = -2.09 X lo-‘. The correlation coefficient between normalized measured values and those obtained from the fitting formula is 0.57 which is still not very satisfactory. Regarding the measured values one can suppose that the swelling rates increase with higher burnups, which leads to an approach of the form:
,
e, = e, - o(de,/do)
.
In the following it will be looked for a relation for I?, and &.,.,depending upon R, B, T, and u, and
furthermore it will be detected if there are still other parameters of fluence (e.g. transient effects). To simplify the evaluation it will be assumed for the present that 6, = AeJAt and &,= Ae,lAt depend linearly upon the fission rate R. These assumptions are usually made and were proved experimentally for the creep rate of oxide fuel in the range of the fission rates attained in this experiment [ 11.Strictly speaking such a proportionality wilI not apply to the swelling rate, but as the changes of the fission rate were not too large (1.0-1.5 X1014 f/cm3 *s), a linear dependence will be justificable within this region. The normalized deformation rates e,, are obtained from the AL values of table 2 by division by At and R/1014. For the determination of a swell and creep relation, the measured en will be described by approximative values 15,which can be represented as a linear function of the parameters B, T. u, or combinations between them &r,i= Ci + Czoi + C3Bi + .a. 7 where the index i refers to every single measurement. The coefficients C are obtained by the method of least square approximation, that is the value of Q,
has to be minimized. At its minimum 8Q/aCi will be 0 for all j. The resulting equation systems for the C’i are solved by the assistance of a computer. The measured values should be approximated by the least possible number of coefficients, that means it is looked for a formulation which on one hand is as simple as possible, but which on the other hand regards all the decisive influencing parameters. The quality of the approximation can be measured by the correlation coefficient between the &n,iand the &r,,. 6. Determination of the approximation function The simplest reasonable approach function would
er= cr + c,u
The result is: Ct = 4.35 X 10B6, C, = -1.37 X10-‘,
C3 = 6.83 X lo-’ and the correlation coefficient raises up to 0.81. A more precise analysis with regard to the burnup dependence of the swelhng rate with an additional C4Bz term gave a correlation coefficient of only 0.82, so a linear bumup dependence will be sufficient to describe the observed fuel swelling. Further analyses, with respect to a proportionality of the type T, p, BT or Bu, resulted in fitting values whose correlation coefficient was never above 0.83 and so these second-order terms can be neglected. Consider the plot of the values of the fitting formula &r= Cr t Cau + C3B versus the measured vahres of fig. 5 and regarding table 2, one can observe a correlation between the measured values and the stress changes. If the applied stress in one interval was increased compared to the preceding interval, the calculated value is too small, and vice versa. Let A&i= EJ - &,i, AUK= Ui- Ui_1,ATi = Ti - Ti-1 and look for a correlation between A&iand the changes of the operation conditions. The calculation gives a correlation coefficient of -0.47 between the A& and the Au and only 0.004 between the AE and ATvalues. That is, there is a transient swelling behavior of the fuel caused by stress and temperature changes, while the latter is negligible in the considered temperature range. A much better correlation exists between the Act and the products BiAq (0.56), which shows a strong coupling between the burnup and the transient swelling. Furthermore, it can be supposed that there is a saturation of the transient swelling effect with respect to stress changes and
238
I. M~~er-~~da, W. Dienst / Me~~~e~e~~
of creepof
mixed carbide nuclear jkeI
(2) Stationary linear swelling rate & = (4.35 + 0.68B[%])X10-26R
cm3 - s/fission - h ,
which is equivalent to the relation: SV,,(VAB)=(1.17 tO.lgE[%])vol%per%
burnup,
assuming isotropic swelling. (3) Transient deformation et = -1.92X1O-26 A&[1 - exp(-t/l30
h)
X m3 - @Pa * fission,
3 5 Measured
7 9 11 13 Deformation Rate, 10e6 h-l
Fig. 5. Formula values, plotted against the measured values: (*) including, (0) neglecting transient effects.
duration. This can be described by Ae N Aui [I - exp(-A&,&)]
,
Act = A&Ati , U, = min(l AUK I, Q) sign(Ao,) and to, u. are constants which have to be determined by trial and error to find the maximum correlation coefficient. This is achieved by the correlation: Ae = -6.30XIO-6Bjl
- exp[-(t/l30
h)])
Xmin(]Aol, 14MPa). Combining the stationary and the transient approach values, the measured and the formula values are correlated by a coefficient of 0.91. This is a satisfactory result considering the difficulties of the measurement. As can be seen from fig. 5, where the fitted values are plotted against the experimental values, the correspondence is raised for many values where the data points move towards the ef = $ line if the transient swelling is taken into the consideration. The following relations for the deformation of carbide fuel under irradiation can be derived from the results of the analysis: (1) Irradiation Induced creep rate e*1E.f = -1.37 X10-*’ u& cm3 * s/MPa +fission - h .
where the absolute value of Au is limited to 14 MPa. As an example, the total transient swelling of the fuel after a stress release of 20 MPa will be in the order of 0.2 ~01%at 5% burnup.
7. Conclusions The main results of the experiment were burnup and tem~rat~e-~dependent creep rates of the highly dense mixed carbide fuel as well as the proof of a considerable transient swelling at stress changes. Furthermore, a swelling rate increasing linearly with the burnup was observed. This swelling behaviour does not fully agree with expectations relevant to this [ 101, but up to now no other measurements were made in this temperature range. At 10% bumup, the swelling rate will be about 3 ~01%per percent bumup. Some later measurements not considered in this report showed no further increase, so this value will be the m~mum in this temperature range. Comparing the measured creep rate to other measurements in fv. 6, one can see a rather good agreement with other results. It is about one decimal order of magnitude below those of oxide fuel and are consistent with the theoretical considerations about the effective mechanisms mentioned before. The transient swelling and shrinkage of the fuel may be of technical importance with respect to mechanical interaction between fuel and cladding during power changes, because it could change the fuel contact pressure against the cladding caused by the differential thermal expansion. Finally, it should be remarked that the calculated swelling rates are i~~t~eous values rather than the lifetime average swelling rates which are used to estimate necessary void volume for accom-
I. MiiIler-Lyda, W.Dienst /.Measurement of creep of mixed carbide nuclear fuel
10%
1500 .
1300 no0 1000 * * . .
600
239
SPO 1.K
-7 c
L
.z 10-S.
10-6.
1o-7a
10-61 0.6
-
r 0.6
-
’ 1.0
’
. 1.2
’
’ 1.4
*
’ 1.6
l/T,
1O-3 K-’
Fig. 6. Mel 12B3 creep rate versus fuel temperature in comparison with previous results.
modation
of integral fuel swelling in uranium carbide
fuel pins.
References
[l] W. Dienst, J. NucL Mater. 65 (1977) 1. [ 21 D.J. Clough, J. Nucl. Mater. 56 (1975) 279. [ 31 W. Dienst, AECL-4375,1973 (German original, 1970).
[ 41 D. Brucklacher and W. Dienst, J. Nucl. Mater. 42 (1972) 285. [5] A. Hah and Hj. Matzke, J. Nucl. Mater. 48 (1973) 157. [6] H. Blank, Phys. Status Solidi 10 (1972) 465. [7] H. Blank, EUR 6600 EN (1979), Proc. Workshop on Fission Gas Behavior in Nuclear Fuels, Karlsruhe, 1978, p.307. [ 81 H.E. HKfner, Atomwirtschaft (Feb. 1974) 79. 191 M. Masson, J. Nucl. Mater. 65 (1977) 307. [lo] H. Blank, J. Nucl. Mater. 58 (1975) 123.