Thermal conductivity of SIMFUEL

Journal of Nuclear Materials 188 (1992) 198-204 North-Holland

Thermal conductivity of SIMFUEL P.G. Lucuta a, Hj. Matzke b, R.A. Verrall a and H.A. Tasman b aAECL Research, Chalk River Laboratories, Chalk River, Ontario, Canada KOJ IJO * ’ Commission of the European Karlsruhe, Germany

Communities, Joint Research Centre, European Institute for Transuranium Elements, W-7500

Thermal diffusivity and specific heat of SIMFUEL - simulated high-burnup UO, fuel with an equivalent burnup of 3 and 8 at% - were measured between 300 and 1800 K, and the data were combined to obtain the thermal conductivities. The thermal conductivity of SIMFUEL provides a model for the intrinsic conductivity of high-burnup fuels (i.e. without gas bubbles). The results on conductivity of 3 and 8 at% burnup SIMFUEL were lower than those measured for UO, by 29 and 45% at 300 K and by 6 and 15% at 1773 K. The reduction in thermal conductivity was approximately linear with burnup. The change in thermal conductivity is a possible explanation for the enhanced gas release observed from high-burnup fuel.

1. introduction

The importance of thermal conductivity of UO, in determining fuel operating temperatures has led to numerous experimental and theoretical studies (e.g. refs. [l-6]). The dependence on temperature and porosity has been well studied, and is incorporated in computer codes on fuel behaviour. Very little work, however, has been done on the effect of burnup on thermal conductivity, partly because of the difficulty in dealing with heavily irradiated material, and partly because of the difficulty in obtaining well-characterized samples of a sufficient size to work on. In this paper we report thermal properties of well-characterized simulated high-burnup UO, fuel - SIMFUEL. The only reported study on irradiated high-burnup fuels by Daniel and Cohen [7] showed a marked decrease in thermal conductivity at high burnup compared to the fresh fuel. Their data for 4 at% ** burnup, analyzed by Marchandise [8], showed a difference of 27% at 773 K compared to unirradiated fuel, decreasing to 10% at 1773 K. These are measurements that include all changes in the fuel induced by irradiation: dissolved and precipitated fission products,

* The work was jointly funded by CANDU Owners Group and AECL Research. * * 1 at% burnup = 225 MW h/kg U = 9375 MWd/t U. Elsevier Science Publishers B.V.

changes in stoichiometry, displacement of the atoms in the lattice, and gas bubbles and cracks. Kleykamp [9] and Ondracek and Schulz [lo] have calculated the effect of the fission products, not including gas bubbles or crack formation. Kleykamp predicted that solid solutions of fission products in UO, would reduce the thermal conductivity, and that the precipitated fission products would increase it. Ondracek and Schultz calculated that the conductivity reduction would be 7% at 1073 K at a very high burnup (18 at%,). An alternative method of determining the effect of irradiation on the conductivity is to simulate the burnup by doping UO, with appropriate additives. Because gases and volatiles are not added, the microstructure does not contain the bubbles observed in irradiated fuel, but their effects can be calculated by computer codes. Several experiments have measured the effect of a single additive on thermal conductivity - gadolinia [ll-131, yttria [14], different rare earths [15] and titania [16]. Except for titania, which is not a fission product, all additives decreased the conductivity and the reduction was proportional to the amount of the additive [ll-151. Fukushima et al. 113-151 concluded that for each additive D in solid solution (U,_,D,)O,, the thermal resistivity R = l/A, at temperatures below 1700 K could be expressed by a linear relation,

R=A(x)+B(x)T,

(1)

where the coefficients A and B depend on the compo-

P.G. Lucuta et al. / Thermal conductivityof SIMFVEL

sition x. Schmitz et al. [17] fabricated simulated (U,Pu)G, fuel with eight additives at an equivalent burnup of 16 at%, and showed that between 773 and 1073 K, the conductivity of the high-burnup simulated fuel was comparable to pure (U,Pu)O, when the O/M ratio was 1.97, but was 30% lower when the ratio was 2.00. A similar experiment by Runfors [18] with UO, doped with oxides of zirconium, rare earths, and alkaline earths (forerunners of SIMFUEL) indicated a decrease in conductivity by 18% compared to pure UO, between 773 and 1273 K. We have previously reported the fabrication procedure of UO,-based SIMFUEL (SIMulated high burnup nuclear FUEL) with an equivalent burnup of 3, 6 and 8 at% [19,20]. Extensive characterization [19,20] demonstrated the equivalence of the microstructure and phase structure of SIMFUEL to irradiated fuel that is largely free of gas bubbles. Thermal diffusivity, specific heat and thermal conductivity of these SIMFUEL compositions are reported here. The use of SIMFUEL for thermal conductivity measurements has a number of advantages: The intrinsic thermal conductivity of the material is measured. This is useful for modelers; effects of porosity and gas bubbles are accounted for in the codes. The microstructure is well characterized. It is difficult to obtain sufficiently large samples of irradiated high-burnup fuel to make accurate thermal diffusivity or conductivity measurements. Also, the microstructure may vary throughout the fuel pellet selected for measurements and may not be known exactly for the samples used. The absence of radioactivity permits easy and reliable measurements on SIMFUEL.

I.

Experimental

2.1. Sample preparation and characterization SIMFUEL pellets with equivalent burnup of 3 and 8 at% were prepared by adding 11 stable oxides to UO,. Complete descriptions of the fabrication methods and characterization results have been provided earlier [19-211. The additives represent all classes of fission products except the fission gases and volatiles. The compositions, calculated with the aid of the ORIGEN code, were corrected so that the total composition of each of the solid fission-product classes was correct. The fabrication route ensured intimate mixing

199

Fig. 1. Typical microstructure of 8 at% SIMFUEL showing equiaxed matrix grains and spherical metallic precipitates. Scanning electron micrograph of thermally-etched sample.

and a representative phase structure; the key processes were attrition milling, spray drying and sintering at 1973 K [19]. A typical SEM microstructure of SIMFUEL (fig. 1) displays equiaxed matrix grains and spherical metallic precipitates containing Ru, MO, Pd and Rh. It was shown earlier [19,20] that the UO, matrix contains dissolved fission products distributed uniformly throughout the grains and ceramic phases finely precipitated at the grain boundaries. Pure UO, pellets, representing 0 at% burnup, were prepared in the same way and the thermal properties measured for comparison. Disks about 12 mm and 6 mm in diameter and 1 mm thick, with a thickness uniform to f0.002 mm, were prepared from the sintered pellets for thermal diffusivity measurements. Optical microscopy was used to select disks free of cracks. Smaller samples, about 4 mm in diameter and 1.5 mm thick, were used for specific heat measurements. The density, measured by immersion in distilled water, was found to be 10.55 g/cm3 (98% of theoretical density (TD)) for 3 at% burnup and 10.43 g/cm3 (98.6% of TD) for’ 8 at% burnup SIMFUEL . The theoretical densities were calculated for the two SIMFUEL compositions from the accurately measured lattice parameter of the matrix, which provides the volume of the unit cell, and the actual composition of the SIMFUEL, which provides the average atomic weight. These densities were 10.81 and 10.57 g/cm3 for the 3 and 8 at% burnup SIMFUEL, respectively.

200

P.G. Lucuta et al. / Thermal conductivity

2.2. Thermal conductivity Thermal diffusivities were measured in high-vacuum by two methods: (1) laser-flash method (300-1800 K, 1.3 X lOA Pa), and (2) modulated electron-beam method (1000-1900 K, 1.36 X 10e4 Pa). The laser-flash method is a standard method that measures the time lag for heatup of the back surface of the specimen. Analyses accounted for the finite width of the laser pulse and radial heat flow using the methods of Clark and Taylor [221. The experimental uncertainties are less than 3% between 300 and 800 K and less than 5% above 800 K. In the second method, a sinusoidally modulated electron beam heats the sample 1231. The phase lag of the front and back surface temperature is measured and used to calculate the thermal diffusivity. One-dimensional heat flow is assumed. Scatter in the data was about 15%. The specific heat of the two compositions of SIMFUEL has also been measured. Standard differential scanning calorimeter (DSC) with sapphire as a reference was used between 300 and 900 K. For higher temperatures, between 700 and 1600 K, the enthalpy

was measured and the specific heat deduced. The thermal conductivity A was calculated by combining the thermal diffusivity (Y with the specific heat cp and density p: A = cYc,p.

(2)

Density variation with temperature of the SIMFUEL was accounted for using the thermal expansion coefficient of UO, (10 X 10m6 K-’ [6]). All thermal conductivity values were normalized to 95% dense by using the Loeb equation A =&-,(I

-PP),

(3)

where P is the pore volume fraction, the subscript TD means fully dense and P(T) = 2.58 - 0.58 x 10m3T (12411. Similar results were obtained using the Eucken-Maxwell porosity correction equation.

3. Results and discussion The specific heat of SIMFUEL, for temperatures between 300 and 1700 K, is plotted in fig. 2, and the measured values are given in table 1. Data measured by DSC, between 300 and 900 K, are accurate to within 1%. The scatter of high temperature results was larger (+ 10%). Nevertheless, they confirmed the trend and permitted, reliable extrapolation of the DSC data. In fig. 2, all cp values are shown together

with the mean

Gi *

of SIMFVEL

0.36

s

0.34

g

0.30

8k

0.29

3

0.27

g

0.25

0.32

0.23 300

600

900

1200

1500

Temperature ( K 1 Fig. 2. Specific heat of 0, 3 and 8 at% SIMFUEL measured by DSC method between 300 and 900 K and derived from the enthalpy values between 800 and 1700 K. The drawn line refers to Kopp-Neumann calculations for 8 at% burnup SIM FUEL.

values for the high temperatures above 900 K. The specific heat of SIMFUEL was also computed using the Kopp-Neumann rule [25], and the results are shown in fig. 3. The calculated and measured values were in very good agreement (within + 1%) in the lower temperature range. The mean values of the experimental data at high temperature are also fitted well by the computed values (fig. 2). The specific heat of SIMFUEL is systematically higher than that for the pure UO, (fig. 2). Nevertheless, the difference in the cp of 8 at% burnup SIMFUEL and UO, amounts only to 1.5%, in good agreement with the 0.8 to 2.3% difference predicted by calculation. Thermal diffusivity of UO, and 3 and 8 at% burnup SIMFUEL is shown in fig. 4 and table 1 as a function of temperature. Average values are shown for the modulated electron-beam data. Using these data, the measurements from the two methods agree within about 5%. Thermal conductivities of UO,, 3 and 8 at% burnup SIMFUEL, normalized to 95% TD, are given also in table 1 for various temperatures between 300 and 1800 K. They are plotted against temperature in fig. 5. The effect of burnup is obvious, as the results show a significant degradation of the thermal conductivity of SIMFUEL compared to that of UO,. At 300 K, the thermal conductivities of 3 and 8 at% bumup SIMFUEL are 71 and 53% of that of pure UO,. At 1773 K, the differences are smaller: 94 and 85% for 3 and 8 at% SIMFUEL, compared to UO,. Each 1 at% burnup corresponds to a decrease in thermal conductivity of about 6-9% at low temperatures (300 K) and

P.G. Lucuta et al. / Thermal conductivity of SIMFUEL

l-2% at high temperatures (1770 K). Most of the difference in thermal conductivity of SIMFUEL compared to fresh UO, is due to the difference in thermal diffusivity; specific heat had only a small effect and it is in the opposite direction. Because the metallic precipitates intuitively should increase thermal conductivity of SIMFUEL, the reduction is caused primarily by the dissolved fission products and possibly by the ceramic phase precipitates. Since the volume fraction of these precipitates is very small, it will have only a small effect. This is in qualitative agreement with the single additive tests [ll-151. Compared to thermal conductivities reported for 4 at% burnup irradiated fuel 181,these results for SIMFUEL, interpolated to 4 at% burnup, are systematically higher. We obtained a reduction by 16%, 10% and 8% at 773,

201

1273 and 1773 K, compared to 27%, 16% and 10% reported for irradiated fuel [8] at the same temperatures. Nevertheless, this is reasonable agreement, considering the earlier measurements were made in-reactor in 1964 on irradiated fuel that may have included gas bubbles. The thermal resistivities (R = l/h) of UO, and SIMFUEL are shown in fig. 6. As obtained by Fukushima et al. [13-151 for the single additive tests, the resistivity varies linearly with temperature for each SIMFUEL burnup R=A+BT.

W

The parameters

A and B for each bumup were determined by fitting straight lines to the data. Van Vliet and Haas [26] predicted that the parameter A would

Table 1 Thermal properties of UO, and 3 and 8 at% burnup SIMFUEL Temp.

Density

Specific heat

Diffusivity

Thermal conductivity (W/mK)

(K)

(g/cm3)

(J/&J

(cm*/s)

Measured

Normalized to 95% TD

0.237 0.281 0.301 0.312 0.318 0.326 0.331 0.336 0.338

0.0324 0.0232 0.0172 0.0141 0.0112 0.0094 0.0084 0.0072 0.0067

8.281 6.994 5.511 4.670 3.750 3.211 2.889 2.520 2.353

7.576 6.424 5.086 4.329 3.492 3.003 2.715 2.378 2.225

0.242 0.282 0.301 0.313 0.320 0.328 0.333 0.336 0.338

0.0226 0.0175 0.0138 0.0118 0.0098 0.0086 0.0075 0.0067 0.0064

5.773 5.182 4.336 3.832 3.232 2.877 2.560 2.275 2.190

5.395 4.858 4.079 3.618 3.062 2.735 2.442 2.178 2.100

0.0172 0.0138 0.0117 0.0100 0.0088 0.0078 0.0069 0.0062 0.0059

4.413 4.081 3.656 3.209 2.866 2.564 2.318 2.076 1.984

4.010 3.724 3.353 2.958 2.654 2.386 2.168 1.951 1.869

0 at% burnup UO, 300 473 673 873 1073 1273 1473 1673 1773

10.785 10.728 10.664 10.601 10.539 10.478 10.417 10.357 10.328

3 at% burnup SIMFUEL 300 473 673 873 1073 1273 1473 1673 1773

10.556 10.500 10.438 10.376 10.315 10.255 10.196 10.137 10.108

8 at% burnup SIMFUEL 300 473 673 873 1073 1273 1473 1673 1773

10.430 10.375 10.314 10.253 10.193 10.133 10.075 10.017 9.988

0.246 0.285 0.303 0.313 0.321 0.326 0.332 0.337 0.339

/

202

P.G. Lucuta et al. / Thermal conductivity of SIMFUEL

SIM-3% 0.20 300

I

I

1

500

700

900

I 1100

-

1 1300

I 1500

0.5% 1700

Temperature (Kl Fig. 3. Specific heat of UO, from ref. [27] and of 3 and 8 at% burnup SIMFUEL calculated using the Kopp-Neumann the difference of the latter two from the UO, data. dependent on burnup, while B would be largely independent of burnup. Analysis of our results

be linearly yields R=

[0.053+(0.016kO.O015)b] +[2.2-(0.005 f O.O02)b]x 10-4T,

(4b)

is expressed in Km/W and b is the burnup in at%. This is good agreement with Van Vliet and Haas, indicating that most of the burnup dependence is in the temperature-independent parameter, phonon-defeet interaction term. Fig. 7 is a plot of the thermal resistivity versus burnup for three selected temperatures, showing linear variation.

where

rule, as well

From the thermal conductivity, the central temperature T, of the fuel can be calculated for a given linear rating x and a given surface temperature T, from the conductivity integral x=4r

R

Tch dT. / r,

(5)

For a typical CANDU * reactor linear power of 45 kW/m, the central temperatures obtained from eq. (5) using our data are about 1500 K for UO, and 1700 K

* CANada _Deuterium Uranium.

. 7.20

g

;f;

6.40

3 at% SIMFUEL %

g !5

5.60

8 at% SIMFUEL

0.020 0.015

!

0.010

g

0.005 300

600

900

1200

1500

1800

Temperature (K) Fig. 4. Thermal diffusivities as a function of the temperature for UO, and 3 and 8 at% burnup SIMFUEL, measured by laser-flash and modulated electron-beam methods.

300

600

900

1200

1500

1800

Temperature (K) Fig. 5. Thermal conductivities, normalized to 95% of theoretical density, plotted versus temperature for UO, and SIMFUEL with an equivalent burnup of 3 and 8 at%.

P. G. Lucuta et al. / Thermal conductivity of SIMFUEL

i

The conductivity in SIMFUEL is lower than in pure UO, and this difference is largest ‘at’ low_,temperatures. The changes in thermal conductivity are approximately linear in burnup up to 8 at% burnup-equivalent SIMFUEL, the highest tested. This decrease in thermal conductivity is a possible explanation for observed increased gas release at high burnup.

0.40

$

0.40

:g

0.32

sf $

0.24

&

0.16

$

0.08 300

600

900

1200

Temperature

1500

1600

0.56 s

0.46

-

p ‘5

0.40

-

:Z I M

0.32

-

0.24

-

0.16

c

0.06

-

1773K, --

--+-

1073J

0

*

-

-

h-

-

-

2

/

-

r

-

-

*-

4

6

Bumup

(at%)

8

10

Fig. 7. Thermal resistivity as a function of the burnup for 300, 1073 and 1773 K.

for 3 at% burnup

SIMFUEL. Similar results are obtained for LWR fuel at lower power ratings. This predicted increase in fuel operating temperatures due to the changes in the intrinsic thermal conductivity is a possible reason for enhanced gas release observed at high bumup, especially in those fuels that have not undergone high-temperature transients.

4. Conclusions l

The authors are grateful to I.J. Hastings for helpful discussions. The contributions of R.E. Taylor and H. Groot from Purdue University (West Lafayette, Indiana), D. Pellottiero from European Institute for Transuranium Elements and P. Hayward from AECL Research (Whiteshell Laboratories, Manitoba), for thermal diffusivity and specific heat capacity measurements are acknowledged.

References 3OOJ

/

_

-

&-

--

Acknowledgements

(K)

Fig. 6. Thermal resistivity of UO, and SIMFUEL (3 and 8 at% burnup) as a function of the temperature.

i

203

The thermal conductivity of simulated high-burnup UO, fuel has been measured. These data provide the changes in intrinsic thermal conductivity in irradiated fuel at high burnup.

[II A.B.G. Washington, UKAEA Report TRG Report 2236 (D) (1973). Dl R. Brandt, G. Haufler and G. Neuer, J. Non-Equilibrium Thermodyn. 1 (1967) 3. [31 G.J. Hyland, J. Nucl. Mater. 113 (1985) 125. 141 J.H. Harding and D.G. Martin, J. Nucl. Mater. 166 (1989) 223. [51 D.G. Martin, J. Nucl. Mater. 110 (1982) 73. I61MATPRO - A Handbook of Materials Properties for Use in the Analysis of Light Water Reactor Fuel Rod Behaviour, TREE-NUREG-1005, EG&G Idaho, Inc. [71 R.C. Daniel and I. Cohen, Bettis Atomic Power Report WAPD-246 (1964). 181 H. Marchandise, Commission of the European Communities Report EUR-4568 f (1970). [91 H. Kleykamp, Report KfK-1245 (1970). ml G. Ondracek and B. Schulz, Report KfK-1999 (1974) 43. 1111 SD. Preston, C. Barrett, P. Fassina, KC. Mills and N. Zaghini, High Temp.-High Press. 21 (1989) 287. D21 M. Hirai, J. Nucl. Mater. 173 (1990) 247. u31 S. Fukushima, T. Ohmichi, A. Maeda and H. Watanabe, J. Nucl. Mater. 102 (1981) 30. 1141S. Fukushima, T. Ohmichi, A. Maeda and H. Watanabe, J. Nucl. Mater. 105 (1982) 201. WI S. Fukushima, T. Ohmichi, A. Maeda and M. Handa, J. Nucl. Mater. 114 (1983) 312. [16] A.K. Sengupta, K.S. Arora, A. Kumar and C. Ganguly, High Temp.-High Press. 19 (1987) 509.

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P.G. Lucuta et al. / Thermal conductivity of SIMFUEL

[17] F. Schmitz, G. Dean, M. Housseau, F. Keroulas and J.C.

van Craeynest, Proc. Int. Meeting on Fast Reactor Fuel and Fuel Elements, Karlsruhe, 1970, eds. M. Dalle Donne, K. Kummerer and K. Schroeder, p. 396. [RX]U. Runfors, ENEA Fuels and Material Specialist Meeting on Fast Gas-Cooled Breeders, Stockholm, 1969, quoted by G. Fayl and K. Hansen, Rise Report No. 269 (1972). [19] P.G. Lucuta, B.J. Palmer, Bj. Matzke and D.S. Hartwig, Proc. 2nd Int. Conf. on CANDU Fuel, ed. I.J. Hastings, CNS, Toronto (1989) 132; also Atomic Energy of Canada Report AECL-10117 (1989). [20] P.G. Lucuta, R.A. Verrall, Hj. Matzke and B.J. Palmer, J. Nucl. Mater. 178 (1991) 48.

[21] Hj. Matzke, P.G. Lucuta and R.A. Verrall, J. Nucl. Mater. 185 (1991) 292. [22] L.M. Clark and R.E. Taylor, J. Appl. Phys. 46 (197.5) 714. 1231 H.E. Schmidt, M. van den Berg and L. van der Hoek, High Temp.-High Press. 1 (1969) 309. [24] M.J.F. Notley and J.R. McEwan, Nucl. Appl. Technol. 2 (1966) 117. [25] H.A. Tasman, ITU Technical Note KO290137 (1990). [26] J. van Wet and D. Haas, 6th Post-SMIRT Seminar on Mathematical/Mechanical Modelling of Reactor Fuel elements, Kippel, Switzerland, August 1987. [27] G.E. Moore and K.K. Kelly, J. Am. Chem. Sot. 69 (1947) 2105.