Effects of Soluble Fission Products on Thermal Conductivities of Nuclear Fuel Pellets

Transcription

1 Journal of NUCLEAR SCIENCE and TECHNOLOGY, 31[8], pp.796~802 (August 1994). Effects of Soluble Fission Products on Thermal Conductivities of Nuclear Fuel Pellets Shinji ISHIMOTO, Mutsumi HIRAIt Kenichi ITOtt and Yoshiaki KOREI Nippon Nuclear Fuel Development Co., Ltd.* (Received November 5, 1993) Simulated high burnup UO2 and (U, Gd)O2 pellets, doped with soluble fission product elements (Sr, Zr, Y, La, Ce, Nd), were prepared. Pellet thermal diffusivities were measured by a laser flash method and their thermal conductivities were evaluated. Thermal conductivities decreased with an increase in the total amount of soluble elements at low temperatures, while they were almost independent of soluble element content at higher temperatures. In the heat transfer process, phonon-phonon scattering was dominant for UO2 and simulated low burnup fuel, while phonon-point defect scattering was more important for higher burnup fuel. By applying Klemens' model, thermal conductivities of UO2 with soluble fission products was expressed in the form of an empirical equation. Then with empirical parameters from simulated burnup UO2 and the previous (U, Gd)O2 results, thermal conductivity of (U, Gd)O2 with soluble fission products was expressed as a function of Gd and soluble fission products contents within a fitting error of +-6%. KEYWORDS: thermodynamic properties, thermal conductivity, thermal diffusivity, laser Rash method, fuel pellets, uranium dioxides, gadolinium oxides, soluble fission products, solid solutions, burnup, nuclear fuels, temperature dependence, thermal conductivity equation I. INTRODUCTION Uranium dioxide (UO2) and (U, Gd)O2 have been used as nuclear fuel pellets in light water reactors (LWRs). Gaseous and solid fission products (FPs) are accumulated in the pellets during irradiation. Some solid FPs dissolve into the UO2 matrix at high temperatures, thereby affecting thermal conductivity. Several reports have been concerned with the effects of irradiation and dissolution of solid FPs on thermal conductivities of UO2 pellets. Daniel & Cohen(1) reported that UO2 thermal conductivity decreased on irradiation. The decrease, however, may be attributable not only to the dissolution of solid FPs but also to microstructural changes such as an 0/M ratio change, precipitation of insoluble FPs, cracking, bubble formation and irradiation damage accumulation. Thermal diffusivities were measured for unirradiated binary systems of UO2 and soluble FPs to evaluate effects of individual FPs (Gd(2)~(9), Sr(10), Zr (10)(11) y(12), or rare earth elements(13)) on thermal conductivities. These studies showed a decrease in thermal conductivity of UO2 fuel with increasing amounts of soluble FPs. Lucuta et al.(14) also showed, by measurements of thermal diffusivity and heat capacity in simulated high-burnup UO2 fuel (SIMFUEL), that the thermal conductivity of the UO2 pellet was almost inversely proportional to burnup. However, for (U, Gd)O2 fuel, there have been few studies on the effects of irradiation or soluble FPs on the thermal conductivity. In a previous experiment(9), thermal diffusivities were measured for (U, Gd)O2 pellets * Oarai-machi, Ibaraki-ken Present address : Toshiba t Corp., Shinsugita-cho, Isogo-ku, Yokohama 235. Present address : Hitachi tt Ltd., Saiwai-cho, Hitachi-shi

2 Vol. 31, No. 8 (Aug. 1994) 797 with high Gd contents to establish an empirical equation on the thermal conductivity in the form of Klemens' model. In this study, (U, Gd)O2 and UO2 pellets, doped with soluble fission product elements to simulate high burnups, were prepared and their thermal diffusivities were measured. Thermal conductivities were calculated from thermal diffusivities and an empirical equation was proposed for thermal conductivity of simulated high burnup UO2 and (U, Gd)O2 with soluble FPs. II. EXPERIMENT 1. Samples Uranium dioxide powder, Gd2O3 powder, and oxide powders of selected elements as described below were weighed and mixed in an agate mortar. Compositions of samples were determined as follows : Some FPs (Sr, 2r, Nb, Y., La, Ce, Pr, Nd, Pm, Sm and Eu) interact with phonons as soluble ions in the fuel operating temperature ranges. The concentrations of soluble FPs in UO2 and U05-6 wt% Gd203 (UO2-8.7 mol% GdO1.5) pellets at burnups of 30, 60, 90 GWd/t U were calculated with the ORIGEN2 code(15). Some elements with low concentration (Nb, Pr, Pm, Sm and Eu) were represented by a single element as follows : The effect of a point defect i (substitutional impurity) on thermal conductivities related to the scattering cross section parameter, Gi, of the phonons by the point defect(16). The scattering cross section parameter Gi is approximated by the following equation(17) : Y'zr=Yzr(Gzr+GNb)GZr (2) Y'ce= Yce(GCe+GPr)/Gce (3) Y'Nd YNd(GNd+GPm+ GSm+ GEU)/GNd where y'i is dopant concentration and the reported values of gi(18)(19) are used in Eq. ( 1). Although the value of e is considered to differ between elements, e was assumed to be constant (e=30) in this study. Actinide elements (U, Pu, Am, Cm) were represented by U. Strontium forms zirconates and/or uranates with Zr and/or U and does not dissolve in the UO2 fuel"". However its behavior is unclarified under irradiation conditions. Thus amounts of Sr and Zr corresponding to the calculated concentrations were added to samples. Compositions of UO2 and (U, Gd)O2 fuels with simulated burnups are shown in Table 1. Table 1 Compositions of UO2 and (U,Gd)O2 fuels with simulated burnups as metal atom fraction (%) (4) (1) where Mi and gi are the atomic mass and the ion radius of the point defect i, respectively ; M and g are the average atomic mass and the average ion radius of the host lattice site ; yi is the atomic fraction of the point defect i; and e the parameter representing the magnitude of the strain generated in the lattice. Then low concentration elements were represented by a element with almost the same Mi and gi using Eq. (1). That is, The mixed oxide powders were pressed into pellets at about 300 MPa, and these were sintered at about 2,000 K for 4 h in a stream of H2-H20 (oxygen potential : about -330 kj/mol) for (U, FPs)O2 and in a stream of N2-H2-H2O (oxygen potential : about -310 kj/mol) for (U, Gd, FPs)O2 to get stoichiometric compositions(21)(22). 41

3 798 J. Nucl. Sci. Technol., The sintered pellets were about 10 mm in diameter. Disk samples of 1 mm thickness were sliced from pellets for thermal diffusivity measurements. No microcracks or precipitates were observed by scanning electric microscopy (SEM) and wavelength dispersed X-ray analysis (WDX) for any samples. Table 2 lists the sizes and densities of samples. The densities were measured by an immersion method. Table 2 Sizes and densities of samples for thermal diffusivity measurements calculated by,=ma/(a3na), rtd (5) where MA is average atomic mass of an unit cell for the O/M ratio=2.00, a a lattice parameter, and NA Avogadro's number. 3. Measurements and Analysis Method Thermal diffusivities were measured by a laser flash method for which the apparatus and procedure have been described in detail elsewhere(8). Thermal conductivity was calculated by KM=aMCprM, (6) where KM is the thermal conductivity of sample with density of rm, am the thermal diffusivity and C, the specific heat capacity. Thermal conductivity was normalized to 95% TD using the modified Loeb equation(23), that is, KM=Kth(1-eP j, (7) where If th is the thermal conductivity of sample with the density of 100% TD, P the Theoretical densities (TD) were calculated using the lattice parameter described below. 2. X-ray Diffraction Analyses The X-ray diffraction patterns were measured with a diffractometer using Ni-filtered Cu Ka1 radiation. For (U, FPs)O2, a full width at half maximum (FWHM) of a peak was almost the same as that of UO2 and the peak was split into Ka1 and Ka2. This indicated that these samples were almost completely homogeneous solid solutions. Although the diffraction pattern of (U, Gd, FPs)O2 had a small peak due to free UO2 at the lower angle of the solid solution peak, the ratio of free UO2 in (U, Gd, FPs)O2 solid solution was so small (less than 5% in intensity) that the effect of free UO2 on the thermal conductivity could be ignored in the thermal conductivity evaluation ; thermal conductivities difference between (U, Gd, FPs)O3-UO2 and (U, Gd, FPs)O2 is less than 4%, which is within the thermal diffusivity measurement error (±5%). The lattice parameters were calculated by the least square method using the six diffraction lines above 100ß in 2t. Theoretical densities, rtd were porosity and e the experimental parameter. Here the value reported by Brandt & Neuer (2 4) was used, that is, =2.6-5x10-4(T ) e, (8) where T is the temperature in K. From Eq. (7) thermal conductivity normalized to 95% TD, K95, could be expressed by K95=Km(1-0.05e)/(1-Pe). (9) III. RESULTS AND DISCUSSION 1. Lattice Parameters Figure 1(a) and (b) show the relationship between lattice parameters and simulated burnups in (U, FPs)O2 and (U, Gd, FPs)O2, respectively. The lattice parameters decrease with increasing simulated burnups, i. e. soluble FPs content, as reported by others(14)(31). The solid line shows the theoretical values calculated by Eq. (10), for the O/M ratio=2.00, (10) where gi and go are the ion radii of the metal (15)(19)(gs r2+_0.126 nm, gzr4=0.084 nm, gy3+=, 42

4 Vol. 31, No. 8 (Aug. 1994) 799 Fig. 1 Lattice parameters of (U, FPs)O2 and (U, Gd, FPs)O nm, gla3+=0.116 nm, gce4+=0.097 nm, gnd3+ = nm, and gu4+= nm, gu5+=0.088 nm) and oxygen(18) (go2-= nm) and xi the ionic fraction of cation. The measured values agree with the calculated line. Their good agreement indicates that the 0/M ratio of the samples is nearly equal to Thermal Diffusivities Considering the porosity correlation, am is normalized to 95% TD, that is, a 95 =am [( (1-P)]/[(1-Pe)/(1-0.05)]. (11) The normalized thermal diffusivities of (U, FPs)O2 and (U, Gd, FPs)O2 are shown in Fig. 2(a) and (b), respectively. The thermal diffusivities of (U, FPs)O2 decrease with increasing FPs content at low temperatures although at higher temperatures their data are almost independent of FPs content, which is consistent with results by Lucuta et al.(14) The thermal diffusivities of (U, Gd, FPs)O2 also decrease with increasing FPs content. However the reduction ratio of thermal diffusivities for (U, Gd, FPs)O2 is smaller than those for (U, FPs)O2. Fig. 2 Thermal diffusivities of (U, FPs)02 and (U, Gd, FPs)02 (normalized to 95%TD) 3. Thermal Conductivities By using Eq. (6), thermal conductivities were calculated for (U, FPs)O2 and (U, Gd, FPs)O2 from their thermal diffusivity data and specific heat capacities. Here, specific heat capacities of UO2(25) were used for those of 43

5 800 f. Nucl. Sci. Technol., (U, FPs)O2 and (U, Gd, FPs)O2. Specific heat capacities in (U, FPs)O2 and (U, Gd, FPs)O2, calculated from Kopp's law, agree with those of UO2(25) within +-2% error. The normalized thermal conductivities, K96 are shown in Fig. 3(a) and (b) for (U, FPs)O2 and (U, Gd, FPs)O2, respectively. Thermal conductivities decrease with increasing FPs content at low temperatures, while their values are almost independent of FPs content at higher temperatures. Fig. 3 Thermal conductivities of (U, FPs)O2 and (U, Gd, FPs)O2 (normalized to 95%TD) In the same way as for (U, Gd)O2(9), measured thermal conductivities of (U, FPs)O2 can be expressed by KM=Kp+CT3, (12) where Kp is the phonon contribution to the thermal conductivity and C the constant. Provided that C is independent of densities and FP contents, the normalized thermal conductivity can be written by where (13) (14) When phonon-point defect (substitutional impurity) scattering and phonon-phonon scattering (Umklapp process) occur simultaneously, the thermal conductivity contributed by phonons Kp can be expressed by following equations based on relaxation-time theory(16)(26) (Klemens' model) : (15) (16) where S is the constant and K0 the thermal conductivity for a defect-free sample. In the temperature range in which mainly phonon scattering contributes to thermal conductivity, i. e. when phonon-phonon scattering dominates, Eq. (15) can be approximated by(8)(27) Kp (A+BT)-1, (17) where A and B are coefficients. On the other hand, when phonon-point defect scattering dominates, Eq. (15) can be approximated by (8)(26) Kp=(A'T)-0.5, (18) where A' is the coefficient. The thermal conductivity Kp of UO2 may be approximated by Eq. (17), while Eq. (18) would give a fairly good approximation for Kp of fuels with high dopant amounts. In order to determine the dominating process in thermal conductivities of (U,FPs)O2, the logarithmic normalized thermal conductivies contributed by phonons log(k:p/w -1K-1) are plotted in Fig. 4 vs. m logarithmic temperature log(t/k). Here, assuming that C in Eq. (14) is independent of impurity species (FPs, Gd), the reported value(9) of C for (U, Gd)O2 was used in calculation of KZ. 44

6 Vol.31, No.8 (Aug. 1994) The gradients decrease with increasing FPs contents from for pure UO2 to for 90 GWd/t burnup UO2. This indicates that phonon-phonon scattering is dominant in low FPs content UO2, while phonon-point defect scattering is more important in high FPs content UO2. These results indicate that neither Eq. (17) nor (18) can express thermal conductivites of (U,FPs)O2 with a wide range of FPs contents. Therefore Eq. (15) should be applied to expression of thermal conductivities for (U,FPs)O2. values of coefficients for (U, Gd)O2(9) are listed in Table 3. A detailed discussion of Eqs. (19) (22) was given elsewhere(9). Table 3 Empirical parameters in thermal conductivity equation For (U,FPs)O2, the value of G in Eq. (16) is approximately proportional to the total FPs content, because composition of soluble FPs is almost constant. Then Eq. (16) can be approximated by ~ (23) Fig. 4 Logarithmic plot of phonon contribution to normalized thermal conductivities in (U,FPs)O2 vs. temperature For (U,Gd)O2 with a wide range of Gd content (up to 14.2 at %)(9), the normalized thermal conductivity is expressed by and x can be approximated by (19) (20) (21) where DGd is the coefficient, YGd the metallic fraction of Gd and A0 and B0 are coefficients. Although DGd is theoretically independent of temperature, the experimental value depends on temperature as follows : DGd=D0,Gdexp(D1,GdT) (22) where D0.Gd and D1,Gd are coefficients. The (24) Using a least square method at temperatures from 400 to 1,873 K, experimental coefficients Do,FP and D1,FP are obtained for (U, FPs)O2, which are listed in Table 3. Since the effect of point defects (substitutional impurities : Gd, FPs) on phonon scattering can be expressed by the parameter Diyi1/2 (i =Gd,FP) in Eqs. (20) and (23), the parameter x for (U,Gd, FPs)O2 can be expressed by summation of the contribution due to Gd and FPs, that is, (25) Using the coefficients for (U,Gd)O2 and (U, FPs)O2 listed in Table 3, thermal conductivities of (U, Gd, FPs)O2 are calculated from Eqs. (19) and (25). Figure 5 compares the measured thermal conductivities Kmeas and the calculated values Kcal. The calculated values agree with the measured values within a fitting error of +-6%. This indicates that the effect of soluble impurities, produced during irradiation, on thermal conductivity can be expressed by a unified equation for UO2 and (U, Gd)02 fuels. IV CONCLUSION (1) Thermal diffusivities were measured for (U,FPs)O2 and (U,Gd, FPs)O2 at temperatures from 300 to 1,873 K. Thermal conductivities for these samples were cal- 45

7 802 J. Nucl. Sci. Technol., for Gd content up to 14.2 at% and soluble FPs content up to 6.95 at% and temperatures from 400 to 1,873 K. ACKNOWLEDGMENT The authors would like to thank Mr. H. Masuda for preparing the samples. REFERENCES Fig. 5 Comparison between measured and calculated thermal conductivities in (U,Gd,FPs)O2 culated from the thermal diffusivity results. (2) The thermal conductivities of (U, FPs)O2 and (U,Gd, FPs)O2 decreased with increasing amounts of soluble FPs at low temperatures, while at high temperatures, they were almost independent of FPs amounts. (3) By applying Klemen's model to lattice thermal conductivities of (U,FPs)O2 and using empirical parameters, thermal conductivities were expressed as a function of the atomic fraction of soluble FPs and temperature. By using empirical parameters for (U,Gd)O2 and (U,FPs)O2, thermal conductivities of (U,Gd, FPs)O2 were expressed as a function of Gd(yGd) and FPs(yFp.) contents and temperature (T) within a fitting error of +-6%. The form of the equation, normalized to 95% TD was (1) DANIEL, R. C., COHEN, I.: WAPD-246, (1946). (2) FUKUSHIMA, S., et al.: J. Nucl. Mater., 105, 201 (1982). (3) PRESTON, S. D., et al.: High Temp.-High Pressures, 21, 287 (1989). (4) THORNTON, T. A., et al.: Trans. Am. Nucl. Soc., 43, 348 (1986). (5) CHOTARD, A., et al.: Out of pile physical properties, in pile thermal conductivity of (U, Gd)O2, IAEA Tech. Comm. on Properties of Materials for Water Reactor Fuel Elements, Methods of Measurement, Vienna, (1986). (6) PEEHS, M., et al.: J. Nucl. Mater., 106, 221 (1982). (7) LEE, H. J., KIM, C. W.: J. Korean Nucl. Soc., 8, 81 (1976). (8) HIRAI, M. : J. Nucl. Mater., 173, 247 (1990). (9) HIRAI, M., ISHIMOTO, S.: J. Nucl, Sci. Technol., 28[11] 995 (1991). (10) HIRAI, M., et al.: Preprint 1990 Annu. Meeting of AESJ, H31. (11) MURABAYASHI, K., et al.: Preprint 1974 Fall Meeting Nucl. Fuels & Mater., AESJ, A40. ) FUKUSHIMA, S., et al.: J. Nucl. Mater., (12 102, 30 (1981). (13) FUKUSHIMA, S., et al.: ibid., 114, 312 (1983). (14) LUCUTA, P. G., et al.: ibid., 188, 198 (1992). CROFF, A. G. : Nucl. Technol., 62, 335 (15) (1983). KLEMENS, P. G.: Proc. Phys. Soc., A68, (16) 1113 (1955). 7) ABELS, (1 B. : Phys. Rev., 131, 507 (1963). (18) OHMICHI, T., et al.: J. Nucl. Mater., 102, 40 (1981). SHANNON, (19) D. : Acta Cryst., A32, 751 (1976). (20) KOIZUMI, M., et al.: J. Nucl. Mater., 51, 90 (1974). (21) UNE, K., OGUMA, M. : ibid., 131, 88 (1985). (22) UNE, K. : ibid., 150, 93 (1987). LOEB, A. L.: J. Am. Ceram. (23) Soc., 37, 96 (1954). BRANDT, R., NEUER, G.: J. Non-Equilib. (24) Thermodyn., 1, 3 (1976). HAGRMAN, D. L., (25) REYMANN, G. A., (Eds.) : TREE-NUREG-CR-0497, (1979). ) KLEMENS, P. G.: Phys. Rev., (26 119, 507 (1960). (27) KLEMENS, P. G. : Proc. Phys. Soc., A208, 108 (1951). 46