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Thermal diffusivity measurement of (U, Pu)O2−x at high temperatures up to 2190 K
Journal of Nuclear Materials 443 (2013) 286–290
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Thermal diffusivity measurement of (U, Pu)O2x at high temperatures up to 2190 K Kyoichi Morimoto a,⇑, Masato Kato a, Masahiro Ogasawara b a b
Nuclear Fuel Cycle Engineering Laboratories, Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan Inspection Development Company, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan
a r t i c l e
i n f o
Article history: Received 26 March 2013 Accepted 19 July 2013 Available online 27 July 2013
a b s t r a c t The thermal diffusivities of uranium and plutonium mixed oxide (MOX) fuels with 30% Pu-content were measured at temperatures from 990 to 2190 K by the laser flash method. In high-temperature measurements of the stoichiometric specimen, a difference was observed between measurements during heating up and cooling down which seemed to be caused by a change of the oxygen to metal (O/M) ratio. Estimation of the O/M ratio decline by the Knudsen–Langmuir equation, which can be used to discuss evaporation behavior, suggested that the O/M ratio of the stoichiometric specimen had started to decrease at 1800 K. For the O/M ratio of 1.95, that estimation showed that the O/M ratio did not change up to 2200 K. It was also found from the experimental results that no significant changes of O/M ratios of specimens with O/M ratio less than 1.95 were observed. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
Thermal conductivity of nuclear fuel is one of the most important physical properties for fuel design and performance analysis of fuel rods. Thermal conductivity is normally calculated as the product of thermal diffusivity, heat capacity and density. Thermal conductivities of MOX fuels have also been derived from thermal diffusivities in the many studies [1–11]. During fast reactor operation, a large thermal gradient is generated in oxide fuel pellets with high linear heat rate. Consequently, centerline temperature of fuel pellets is very high, beyond 1800 K [12–14]. In the case of a reactor accident, this temperature becomes even higher. As shown in Fig. 1, there are a few measurements related to the temperature dependence of thermal conductivity to the high-temperature region [1,3,5,15], showing significant differences in the temperature dependence. Besides, the Pu-contents of the specimens used in the previously reported measurements were mainly under 20%. In this study, we prepared MOX fuels with 30% Pu and measured their thermal diffusivities up to 2190 K as a function of the O/M ratio. In some measurements in the high-temperature region, we observed a difference in the temperature dependence during heating up and cooling down. This behavior was discussed from the viewpoint of evaporation of species. In addition, we discussed the dependences of thermal diffusivities on the temperature and the O/M ratio.
2.1. Preparation of specimens
⇑ Corresponding author. Tel.: +81 29 282 1111; fax: +81 29 282 9473. E-mail address: [email protected] (K. Morimoto). 0022-3115/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnucmat.2013.07.048
The specimens used in this study were (U0.68, Pu0.30, Am0.02)O2x pellets fabricated by these conventional powder metallurgy process. The raw powders were cold-pressed at 4.5 t/cm2 and the compacts were sintered at 1973 K for 3 h under an atmosphere of Ar–5%H2 mixed gas containing moisture. Americium is a decay product of Pu-241. The pellets were sliced into disks for thermal diffusivity measurement. The O/M ratios of all specimens were adjusted to 2.00. Details of stoichiometry adjustment have been mentioned in the previous work [16]. The impurities and the main characteristics of the specimens are shown in Tables 1 and 2 respectively. The densities were measured by a water immersion method at room temperature. One specimen was crushed into powder and its lattice parameter was measured with an X-ray diffractometer (RINT-1100, Rigaku Co. Ltd.). The lattice parameter agreed with that calculated by Vegard’s law from those (0.54702 nm and 0.53954 nm) of stoichiometric UO2 and PuO2. Metallographic cross section was examined with an optical microscope (Union Optical Co. Ltd.) and an electron probe microanalyzer (EPMA; JXA-8800, JEOL Ltd.). It was confirmed that the pore were dispersed uniformly (Fig. 2). The EPMA mapping in Fig. 3 shows that the specimen had a good homogeneity with little noticeable segregations. The specimens with O/M ratio from 1.92 to 1.95 were prepared by reducing the stoichiometric specimens. The reduction done by heating in a humidified Ar–5%H2 mixed gas. Details of O/M ratio adjustment for specimens have been described elsewhere [17].
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Fig. 2. Microstructure image obtained for 30%Pu-MOX. The pores are dispersed uniformly.
Fig. 1. Comparison of temperature dependence on thermal conductivities. Van Craeynest and Weilbacher [1] and Weilbacher [3] had measured the thermal conductivities of MOX with 20% Pu-content. Bonnerot [5] had measured those of MOX with 24% and 30% Pu-contents. Carbajo et al. [15] had evaluated those of MOX in Pu-content range from 3% to 15%.
Table 1 Metallic impurity specimens.
contents
of
the
prepared
Element
Concentration (ppm)
Ag Al B Cd Cr Cu Fe Mg Mn Ni Si V Zn Ca Pb Sn Mo Na
<5 <100 <5 <5 <50 <10 <100 <15 <20 <50 <100 <50 <100 <30 <30 <30 <50 80
laser flash apparatus (TC-7000UVH, ULVAC-RIKO Co. Ltd.). All measurements were carried out under a vacuum of less than 1 103 Pa. Details of the thermal diffusivity measurements have been described elsewhere [16]. The recorded data were converted to thermal diffusivities by the curve-fitting method [18]. Three measurements were carried out at each temperature and these values were averaged. In order to correct porosity effects on thermal diffusivities, the data were normalized to 100% theoretical density (TD) using the modified Maxwell–Eucken relation:
k¼
ð1 pÞ k0 ; ð1 þ b pÞ
ð1Þ
where p is the porosity, k is the thermal conductivity of a real specimen of porosity p, k0 is the thermal conductivity of a 100%TD specimen, and b = 0.5 is the constant obtained from previous studies [16,19]. As the thermal conductivity (k) is described from the thermal diffusivity (a), the heat capacity (C), and the density (q) by k ¼ a C q, Eq. (1) is rewritten as follows:
aCq¼
ð1 pÞ a0 C q: ð1 þ b pÞ
ð2Þ
The normalized thermal diffusivity can be obtained by substituting the relation between the real density of q and the theoretical density q0, q = q0 (1 p), into Eq. (2) as follows:
The O/M ratios of hypostoichiometric specimens were gravimetrically determined from the weight change between the stoichiometric state and the hypostoichiometric state at room temperature. 2.2. Thermal diffusivity measurements The prepared specimens were used in thermal diffusivity measurements in the temperature range from 990 to 2190 K with a
a0 ¼ a ð1 þ b pÞ:
ð3Þ
After the thermal diffusivity measurements, O/M ratios of the specimens were measured again with a thermogravimetric-differential thermal analyzer (TG8120 of Rigaku Co. Ltd.). The O/M ratios of the specimens before and after the thermal diffusivity measurement are listed in Table 3.
Table 2 Main characteristics of the specimens. Specimen no.
Pu/(U + Pu + Am) (mol%)
Am/(U + Pu + Am) (mol%)
Theoretical density (%TD)
Specimen weight (g)
Diameter (mm)
Thickness (mm)
HT-1 HT-2 HT-3 HT-4 HT-5
29.52
2.19
93.7 93.1 93.0 93.4 92.8
0.286 0.266 0.275 0.328 0.327
5.52 5.50 5.51 5.75 5.73
1.12 1.09 1.12 1.21 1.23
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Fig. 3. EPMA mapping results. The specimen had a high degree of homogeneity and no segregation among the constituent elements.
1.6E-02
Table 3 Maximum measurement temperature of each specimen and variation of O/M ratios before and after thermal diffusivity measurements.
HT-1 HT-2 HT-3 HT-4 HT-5
Maximum temperature (K)
2170 2195 2194 2194 2077
O/M ratio Before
After
Average
2.000 1.945 1.935 1.923 1.913
1.950 1.946 1.928 1.928 1.918
– 1.946 1.932 1.926 1.916
O/M=2.000 high-temp. Cooling [this work]
Thermal diffusivity (cm2/s)
Specimen no.
O/M=2.000 high-temp. Heating [this work]
1.4E-02
O/M=2.000 low-temp. Heating [17] O/M=2.000 low-temp. Cooling [17] O/M=1.946 low-temp. Heating [17]
1.2E-02
1.0E-02
O/M=2.000
8.0E-03
6.0E-03
O/M=1.946
3. Results 4.0E-03 600
800
1000 1200 1400 1600 1800 2000 2200
Temperature (K) Fig. 4. Comparison of thermal diffusivities measured in the high-temperature region in the present study (circular marks) with those measured in the lowtemperature region in a previous study [17] (square and triangular marks). The dashed line shows the temperature dependencies of thermal diffusivities of specimens measured at low-temperature region.
1.4E-02 HT-2 O/M=1.946 Heating
Thermal diffusivity (cm2/s)
Fig. 4 shows the thermal diffusivities of the stoichiometric specimen measured at temperatures exceeding 1800 K (high-temperature region) in present study. Thermal diffusivities of (U0.68, Pu0.30, Am0.02)O2.00x (x = 0.00–0.08) measured at temperatures below 1770 K (low-temperature region) from our previous study [17] are also shown. Thermal diffusivities of the stoichiometric specimen measured during the cooling process in the high-temperature region were significantly lower than those measured during the heating process; this was unlike measurements in the low-temperature region. Thermal diffusivities measured during the cooling process in the high-temperature region were almost identical to those for the specimen of O/M = 1.946 in the low-temperature region. Fig. 5 shows the thermal diffusivities of the hypostoichiometric specimens measured in the high-temperature region in the present study as functions of temperature and O/M ratio. For each O/M ratio, the thermal diffusivities measured during the cooling process were almost identical to those measured during the heating process. It was also shown that the thermal diffusivities decreased with increasing temperature and with the decrease of O/M ratio in the hypostoichiometric region. As shown in Table 3, the specimen with initial O/M ratio of 2.00 decreased to O/M ratio of 1.95 after the thermal diffusivity measurements. On the other hand, there was practically no difference in O/M ratios before and after the thermal diffusivity measurement when O/M ratios of the specimens were less than 1.95.
1.2E-02
HT-2 O/M=1.946 Cooling HT-3 O/M=1.932 Heating HT-3 O/M=1.932 Cooling
1.0E-02
HT-4 O/M=1.926 Heating HT-4 O/M=1.926 Cooling
8.0E-03
HT-5 O/M=1.916 Heating HT-5 O/M=1.916 Cooling
6.0E-03
4.0E-03
2.0E-03 800
1000 1200 1400 1600 1800 2000 2200 2400
Temperature (K) Fig. 5. Thermal diffusivities of the hypostoichiometric specimens measured in the high-temperature region.
4. Discussion 4.1. Change of thermal diffusivities during heating up and cooling down From the findings in Fig. 4 that the thermal diffusivities of the stoichiometric specimen obtained in the cooling process were much lower than those in the heating process and that the O/M ratio of the stoichiometric specimen decreased to 1.95 after the
thermal diffusivity measurements, we inferred that these phenomena were caused by the evaporation of vapor species from this specimen at high temperature. In addition, our previous study showed that there were no practical changes in the thermal diffusivities and the O/M ratios during the thermal diffusivity measurements in the low-temperature region [16]. From these facts, it is considered that the evaporation occur in high-temperature condition exceeding 1800 K.
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n
O=M ðtþDtÞ
h m io mUO ðtÞ mPuO ðtÞ W ðtÞ m m UO ðtÞ O=M ðtÞ MðtÞ 3 MUO3 þ 2 MUO2 þ MUOðtÞ þ 2 MPuO2 þ MPuOðtÞ UO PuO 3 2 2 ( " #) ¼ ; Xm W ðtÞ iðtÞ M ðtÞ Mi
1.0E-02
(a)
1.0E-04
Vapor Pressure (atm)
In order to infer the relation between the O/M ratio changes of the specimens and the evaporation of vapor species at high temperature, the estimation of these changes based on Knudsen–Langmuir equation [20] was carried out. In this estimation, the main vapor species were assumed to be UO3, UO2, UO, U, PuO2, PuO and Pu. The O/M ratio of specimen in heating and cooling was calculated as a function of time by the following equations:
1.0E-06
1.0E-08 Calculation results
1.0E-10
i
ð4Þ
1.96
UO3 UO2 PuO2 PuO 1.98
at 2241 K
2.00
2.02
2.00
2.05
O/M
ð5Þ
1 pðOÞ ; O2 ðgÞ ¼ OðgÞ; K O2 =O ¼ 2 pðO2 Þ1=2
ð6Þ
1 pðUOÞ UðgÞ þ O2 ðgÞ ¼ UOðgÞ; K U=UO ¼ ; 2 pðUÞ pðO2 Þ1=2
ð7Þ
1 pðUO2 Þ UOðgÞ þ O2 ðgÞ ¼ UO2 ðgÞ; K UO=UO2 ¼ ; 2 pðUOÞ pðO2 Þ1=2
ð8Þ
1 pðUO3 Þ UO2 ðgÞ þ O2 ðgÞ ¼ UO3 ðgÞ; K UO2 =UO3 ¼ ; 2 pðUO2 Þ pðO2 Þ1=2
ð9Þ
1.0E+00
(b) 1.0E-05
VaporPressure (atm)
where W(t), M(t), T(t) and A are, respectively, weight, molecular weight, temperature and surface area of the specimen at time t; Mi, mi(t), and pi(t) are, respectively, molecular weight, evaporation amount and vapor pressure of vapor species i at t; R is the gas constant and Dt is a short interval enough to neglect temperature change in heating and cooling. The vapor pressures of vapor species, pi, were calculated using Rand–Markin model [21] based on thermodynamic equilibrium theory. In hypostoichiometric MOX, the (U1y, Puy)O2x was assumed to be an ideal solid solution of UO2 and PuO2m (m = x/y). The vapor pressures were calculated from the relations (R T lnðK i Þ ¼ Df G0i ) between the Gibbs free energies of formation (Df G0i ) for these species and the equilibrium constants (Ki) for following reactions (6)–(13). The detailed information of the calculation and the Df G0i were given in Ref. [22].
1.0E-10
1.0E-15 p(UO 2) p(UO) p(PuO 2) p(Pu)
1.0E-20
1.0E-25 1.85
p(UO 3) p(U) p(PuO) Total
1.90
1.95
O/M Fig. 6. (a) Comparison between the experimental and calculated vapor pressures of main vapor species of MOX with 20% Pu-content at 2241 K. Marks are the values measured by Battles et al. [23]. Lines are the values calculated theoretically. (b) Vapor pressures of vapor species at 2000 K calculated using Rand–Markin model [21]. Vapor pressure of UO3 is highest in all species when O/M ratio is 2.00.
2.02
2.00
1 pðPuOÞ PuðgÞ þ O2 ðgÞ ¼ PuOðgÞ; K Pu=PuO ¼ ; 2 pðPuÞ pðO2 Þ1=2
ð10Þ
1 pðPuO2 Þ PuOðgÞ þ O2 ðgÞ ¼ PuO2 ðgÞ; K PuO=PuO2 ¼ ; 2 pðPuOÞ pðO2 Þ1=2
ð11Þ
PuO2m ðsÞ þ
1.0E-12 1.94
1.98
O/M ratio
miðtÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Mi ; ¼ piðtÞ Dt A 2 p R T ðtÞ
Experimental results[23]
UO3 UO2 PuO2 PuO
1.96
1.94
1.92
O/M=2.00 O/M=1.95
1.90
m pðPuO2 Þ O2 ðgÞ ¼ PuO2 ðgÞ; K PuO2m ðsÞ=PuO3 ðgÞ ¼ ; 2 y pðO2 Þm=2
0
500
1000
1500
2000
2500
Temperature (K)
ð12Þ ð13Þ
Fig. 7. Calculation results of the O/M ratio changes during the measurements for initial O/M ratios of 2.00 and 1.95. For O/M ratio of 2.00, the calculation was carried out from room temperature to 2220 K. For O/M ratio of 1.95, the calculation was carried out from room temperature to 2270 K.
In this calculation, the influence of Am in the specimen was neglected because the content of it was very small. Fig. 6(a) shows the comparison between the experimental values of main vapor species of MOX measured by Battles et al. [23] and the calculation values of those derived from the above mentioned calculation. In this comparison, the vapor pressures of the vapor species of MOX with 20% Pu-content at 2241 K were adopted because the number of the experimental values was limited.
Although the experimental values at O/M ratio of 2.00 were not shown in the report of Battles et al., they estimated that the vapor pressure of UO3 was highest in this condition. Fig. 6(b) shows the vapor pressures at 2000 K for the vapor species of the specimen in this study calculated using the Rand-Markin model. The main vapor species are UO3, UO2, PuO2, and PuO. When O/M ratio was greater than 1.95, the vapor pressure of
UO2 ðsÞ ¼ UO2 ðgÞ; K UO2 ðsÞ=UO2 ðgÞ ¼
pðUO2 Þ : ð1 yÞ
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K. Morimoto et al. / Journal of Nuclear Materials 443 (2013) 286–290
Thermal diffusivity (cm2/s)
1.4E-02
1.2E-02
HT-1 O/M=2.000
HT-2 O/M=1.946
HT-3 O/M=1.932
HT-4 O/M=1.926
HT-5 O/M=1.916 1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03 800
1000 1200 1400 1600 1800 2000 2200 2400
Temperature (K) Fig. 8. Thermal diffusivities measured during the heating of MOX with 30% Pucontent on various O/M ratios.
(2) For specimens with O/M ratio less than 1.946, thermal diffusivities obtained during both the heating and the cooling processes of the high-temperature measurements were almost the same because the O/M ratio did not change during the high-temperature measurements. (3) The O/M ratio changes of specimens during the high-temperature measurements were discussed using the Knudsen–Langmuir equation. Evaluations by the Rand-Markin model showed that the main vapor species were UO3, UO2, PuO2 and PuO. From the calculation results at 2000 K, the vapor pressure of UO3 was the highest among all species in the range of the O/M ratio of about 1.96 or more. Therefore, the O/M ratio decreased because a large amount of oxygen in the specimen was evaporated together with UO3. When the O/M ratios of specimens were less than 1.95, the O/M ratio did not change up to 2200 K because the vapor pressures of the main vapor species were the same order and a little evaporation was expected under these conditions. (4) The measurements of thermal diffusivities of the stoichiometric specimen below 1800 K had high reliability because no significant change of O/M ratio was observed. When the O/M ratio of specimens was less than 1.95, the measurements could be done at temperatures up to 2200 K because the change of O/M ratio was slight.
UO3 was the highest among all species. On the other hand, when O/ M ratio was about 1.95, the vapor pressures of the main vapor species were almost the same order. Fig. 7 shows the calculation results of the O/M ratio changes during the measurements for initial O/M ratios of 2.00 and 1.95. In the former, the O/M ratio started to decrease at about 1800 K and it was about 1.95 after completing the measurement. In the latter, the O/M ratio started to decrease at about 2200 K, but it did not decrease significantly. These calculation results about the O/M ratio change were in good agreement with the experimental results above mentioned.
We are pleased to acknowledge Mr. H. Uno, Mr. T. Tamura, Mr. H. Sugata, Mr. T. Sunaoshi and Mr. K. Shibata for their assistance in the sample preparation, and in carrying out the EPMA, XRD, and other analysis.
4.2. Temperature dependence of thermal diffusivity
References
The thermal diffusivities during the heating process of MOX with 30% Pu-content on various O/M ratios are shown in Fig. 8. In the stoichiometric specimen, the measurements obtained below 1800 K had high reliability because only a little evaporation was expected at such a low temperature region. When the O/M ratios of specimens were less than 1.95, the measurements obtained below 2200 K also had high reliability because a little evaporation was expected under these conditions as shown in Fig. 7. The thermal diffusivities decreased with increasing temperature and with larger deviation of O/M ratios from stoichiometry. In the high-temperature region, the difference in thermal diffusivities of each O/M ratio decreased. At temperatures above 1800 K, the thermal conductivities shown in Fig. 1 increased with increasing temperature, unlike the behavior seen for thermal diffusivities. This high-temperature behavior of thermal conductivity was due to the heat capacity behavior.
[1] J.C. Van Craeynest, J.C. Weilbacher, Study of the thermal conductivity of mixed uranium–plutonium oxides, Tech. Rep. CEA-R-3488, 1968. [2] R.L. Gibby, J. Nucl. Mater. 38 (1971) 163–177. [3] J.C.Weilbacher, Measurement of thermal diffusivity of mixed uranium plutonium oxides, Tech. Rep. CEA-R-4572, 1974. [4] S. Fukushima, T. Ohmichi, A. Maeda, M. Handa, J. Nucl. Mater. 116 (1983) 287– 296. [5] J.M. Bonnerot, Thermal properties of mixed uranium and plutonium oxides, Tech. Rep. CEA-R-5450, 1988. [6] A.B.G. Washington, UK atomic energy authority, Tech. Rep. TRG R-2236, 1973. [7] J.H. Harding, D.G. Martin, J. Nucl. Mater. 166 (1989) 223–226. [8] Y. Philipponneau, J. Nucl. Mater. 188 (1992) 194–197. [9] P.G. Lucuta, H.I. Matzke, I.J. Hastings, J. Nucl. Mater. 232 (1996) 166–180. [10] C.R. Ronchi, J. Appl. Phys. 85 (1999) 776–789. [11] C. Duriez, J.P. Alessandri, T. Gervais, Y. Philipponneau, J. Nucl. Mater. 277 (2000) 143–158. [12] M. Bober, G. Schumacher, D. Geithoff, J. Nucl. Mater. 47 (1973) 187–197. [13] M. Inoue, J. Nucl. Mater. 282 (2000) 186–195. [14] R.J.M. Konings, T.R. Allen, R.E. Stoller, S. Yamanaka, Comprehensive Nuclear Materials, Elsevier Science, Amsterdam, 2012. [15] J.J. Carbajo, G.L. Yoder, S.G. Popov, V.K. Ivanov, J. Nucl. Mater. 299 (2001) 181– 198. [16] K. Morimoto, M. Kato, M. Ogasawara, M. Kashimura, T. Abe, J. Alloys Compd. 452 (2008) 54–60. [17] K. Morimoto, M. Kato, M. Ogasawara, M. Kashimura, J. Nucl. Mater. 374 (2008) 378–385. [18] T. Baba, A. Cezairliyan, Int. J. Thermophys. 15 (1994) 343–364. [19] A. Biancheria, Trans. Am. Nucl. Soc. 9 (1966) 15. [20] O. Kubaschewski, C.B. Alcock, Metallurgical Thermochemistry, International Series on Materials Science and Technology, 5th, vol. 24. [21] M.H. Rand, T.L. Markin, Thermodynamics of nuclear materials 1967, in: Proceedings of the IAEA Symposium, Vienna, 1968. [22] D.R. Olander, Fundamental aspects of nuclear reactor fuel elements, TID26711-P1, Energy Research and Development Administration, US, 1976, pp. 155–160. [23] J.E. Battles, W.A. Shinn, P.E. Blackburn, R.K. Edwards, in: W.N. Miner (Ed.), Plutonium 1970 and Other Actinides, Nuclear Metallurgy, Part II, American Institute of Mining, vol. 17, Metallurgical and Petroleum Engineers, New York, 1970, p. 733.
5. Conclusions The thermal diffusivities of (U, Pu)O2.00x solid solutions (x = 0.00–0.08) were measured by the laser flash method in the temperature range from 990 to 2190 K. The measured values were normalized to 100%TD by using the modified Maxwell-Eucken relationship to evaluate the influences of temperature and O/M ratio on thermal diffusivity. These results are summarized as follows: (1) The thermal diffusivities of the stoichiometric specimen obtained during the cooling process of the high-temperature measurements were greatly lower than those in the heating process because the O/M ratio decreased during the hightemperature measurements.
Acknowledgements
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Thermal diffusivity measurement of (U, Pu)O2x at high temperatures up to 2190 K Kyoichi Morimoto a,⇑, Masato Kato a, Masahiro Ogasawara b a b
Nuclear Fuel Cycle Engineering Laboratories, Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan Inspection Development Company, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan
a r t i c l e
i n f o
Article history: Received 26 March 2013 Accepted 19 July 2013 Available online 27 July 2013
a b s t r a c t The thermal diffusivities of uranium and plutonium mixed oxide (MOX) fuels with 30% Pu-content were measured at temperatures from 990 to 2190 K by the laser flash method. In high-temperature measurements of the stoichiometric specimen, a difference was observed between measurements during heating up and cooling down which seemed to be caused by a change of the oxygen to metal (O/M) ratio. Estimation of the O/M ratio decline by the Knudsen–Langmuir equation, which can be used to discuss evaporation behavior, suggested that the O/M ratio of the stoichiometric specimen had started to decrease at 1800 K. For the O/M ratio of 1.95, that estimation showed that the O/M ratio did not change up to 2200 K. It was also found from the experimental results that no significant changes of O/M ratios of specimens with O/M ratio less than 1.95 were observed. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental
Thermal conductivity of nuclear fuel is one of the most important physical properties for fuel design and performance analysis of fuel rods. Thermal conductivity is normally calculated as the product of thermal diffusivity, heat capacity and density. Thermal conductivities of MOX fuels have also been derived from thermal diffusivities in the many studies [1–11]. During fast reactor operation, a large thermal gradient is generated in oxide fuel pellets with high linear heat rate. Consequently, centerline temperature of fuel pellets is very high, beyond 1800 K [12–14]. In the case of a reactor accident, this temperature becomes even higher. As shown in Fig. 1, there are a few measurements related to the temperature dependence of thermal conductivity to the high-temperature region [1,3,5,15], showing significant differences in the temperature dependence. Besides, the Pu-contents of the specimens used in the previously reported measurements were mainly under 20%. In this study, we prepared MOX fuels with 30% Pu and measured their thermal diffusivities up to 2190 K as a function of the O/M ratio. In some measurements in the high-temperature region, we observed a difference in the temperature dependence during heating up and cooling down. This behavior was discussed from the viewpoint of evaporation of species. In addition, we discussed the dependences of thermal diffusivities on the temperature and the O/M ratio.
2.1. Preparation of specimens
⇑ Corresponding author. Tel.: +81 29 282 1111; fax: +81 29 282 9473. E-mail address: [email protected] (K. Morimoto). 0022-3115/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jnucmat.2013.07.048
The specimens used in this study were (U0.68, Pu0.30, Am0.02)O2x pellets fabricated by these conventional powder metallurgy process. The raw powders were cold-pressed at 4.5 t/cm2 and the compacts were sintered at 1973 K for 3 h under an atmosphere of Ar–5%H2 mixed gas containing moisture. Americium is a decay product of Pu-241. The pellets were sliced into disks for thermal diffusivity measurement. The O/M ratios of all specimens were adjusted to 2.00. Details of stoichiometry adjustment have been mentioned in the previous work [16]. The impurities and the main characteristics of the specimens are shown in Tables 1 and 2 respectively. The densities were measured by a water immersion method at room temperature. One specimen was crushed into powder and its lattice parameter was measured with an X-ray diffractometer (RINT-1100, Rigaku Co. Ltd.). The lattice parameter agreed with that calculated by Vegard’s law from those (0.54702 nm and 0.53954 nm) of stoichiometric UO2 and PuO2. Metallographic cross section was examined with an optical microscope (Union Optical Co. Ltd.) and an electron probe microanalyzer (EPMA; JXA-8800, JEOL Ltd.). It was confirmed that the pore were dispersed uniformly (Fig. 2). The EPMA mapping in Fig. 3 shows that the specimen had a good homogeneity with little noticeable segregations. The specimens with O/M ratio from 1.92 to 1.95 were prepared by reducing the stoichiometric specimens. The reduction done by heating in a humidified Ar–5%H2 mixed gas. Details of O/M ratio adjustment for specimens have been described elsewhere [17].
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Fig. 2. Microstructure image obtained for 30%Pu-MOX. The pores are dispersed uniformly.
Fig. 1. Comparison of temperature dependence on thermal conductivities. Van Craeynest and Weilbacher [1] and Weilbacher [3] had measured the thermal conductivities of MOX with 20% Pu-content. Bonnerot [5] had measured those of MOX with 24% and 30% Pu-contents. Carbajo et al. [15] had evaluated those of MOX in Pu-content range from 3% to 15%.
Table 1 Metallic impurity specimens.
contents
of
the
prepared
Element
Concentration (ppm)
Ag Al B Cd Cr Cu Fe Mg Mn Ni Si V Zn Ca Pb Sn Mo Na
<5 <100 <5 <5 <50 <10 <100 <15 <20 <50 <100 <50 <100 <30 <30 <30 <50 80
laser flash apparatus (TC-7000UVH, ULVAC-RIKO Co. Ltd.). All measurements were carried out under a vacuum of less than 1 103 Pa. Details of the thermal diffusivity measurements have been described elsewhere [16]. The recorded data were converted to thermal diffusivities by the curve-fitting method [18]. Three measurements were carried out at each temperature and these values were averaged. In order to correct porosity effects on thermal diffusivities, the data were normalized to 100% theoretical density (TD) using the modified Maxwell–Eucken relation:
k¼
ð1 pÞ k0 ; ð1 þ b pÞ
ð1Þ
where p is the porosity, k is the thermal conductivity of a real specimen of porosity p, k0 is the thermal conductivity of a 100%TD specimen, and b = 0.5 is the constant obtained from previous studies [16,19]. As the thermal conductivity (k) is described from the thermal diffusivity (a), the heat capacity (C), and the density (q) by k ¼ a C q, Eq. (1) is rewritten as follows:
aCq¼
ð1 pÞ a0 C q: ð1 þ b pÞ
ð2Þ
The normalized thermal diffusivity can be obtained by substituting the relation between the real density of q and the theoretical density q0, q = q0 (1 p), into Eq. (2) as follows:
The O/M ratios of hypostoichiometric specimens were gravimetrically determined from the weight change between the stoichiometric state and the hypostoichiometric state at room temperature. 2.2. Thermal diffusivity measurements The prepared specimens were used in thermal diffusivity measurements in the temperature range from 990 to 2190 K with a
a0 ¼ a ð1 þ b pÞ:
ð3Þ
After the thermal diffusivity measurements, O/M ratios of the specimens were measured again with a thermogravimetric-differential thermal analyzer (TG8120 of Rigaku Co. Ltd.). The O/M ratios of the specimens before and after the thermal diffusivity measurement are listed in Table 3.
Table 2 Main characteristics of the specimens. Specimen no.
Pu/(U + Pu + Am) (mol%)
Am/(U + Pu + Am) (mol%)
Theoretical density (%TD)
Specimen weight (g)
Diameter (mm)
Thickness (mm)
HT-1 HT-2 HT-3 HT-4 HT-5
29.52
2.19
93.7 93.1 93.0 93.4 92.8
0.286 0.266 0.275 0.328 0.327
5.52 5.50 5.51 5.75 5.73
1.12 1.09 1.12 1.21 1.23
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Fig. 3. EPMA mapping results. The specimen had a high degree of homogeneity and no segregation among the constituent elements.
1.6E-02
Table 3 Maximum measurement temperature of each specimen and variation of O/M ratios before and after thermal diffusivity measurements.
HT-1 HT-2 HT-3 HT-4 HT-5
Maximum temperature (K)
2170 2195 2194 2194 2077
O/M ratio Before
After
Average
2.000 1.945 1.935 1.923 1.913
1.950 1.946 1.928 1.928 1.918
– 1.946 1.932 1.926 1.916
O/M=2.000 high-temp. Cooling [this work]
Thermal diffusivity (cm2/s)
Specimen no.
O/M=2.000 high-temp. Heating [this work]
1.4E-02
O/M=2.000 low-temp. Heating [17] O/M=2.000 low-temp. Cooling [17] O/M=1.946 low-temp. Heating [17]
1.2E-02
1.0E-02
O/M=2.000
8.0E-03
6.0E-03
O/M=1.946
3. Results 4.0E-03 600
800
1000 1200 1400 1600 1800 2000 2200
Temperature (K) Fig. 4. Comparison of thermal diffusivities measured in the high-temperature region in the present study (circular marks) with those measured in the lowtemperature region in a previous study [17] (square and triangular marks). The dashed line shows the temperature dependencies of thermal diffusivities of specimens measured at low-temperature region.
1.4E-02 HT-2 O/M=1.946 Heating
Thermal diffusivity (cm2/s)
Fig. 4 shows the thermal diffusivities of the stoichiometric specimen measured at temperatures exceeding 1800 K (high-temperature region) in present study. Thermal diffusivities of (U0.68, Pu0.30, Am0.02)O2.00x (x = 0.00–0.08) measured at temperatures below 1770 K (low-temperature region) from our previous study [17] are also shown. Thermal diffusivities of the stoichiometric specimen measured during the cooling process in the high-temperature region were significantly lower than those measured during the heating process; this was unlike measurements in the low-temperature region. Thermal diffusivities measured during the cooling process in the high-temperature region were almost identical to those for the specimen of O/M = 1.946 in the low-temperature region. Fig. 5 shows the thermal diffusivities of the hypostoichiometric specimens measured in the high-temperature region in the present study as functions of temperature and O/M ratio. For each O/M ratio, the thermal diffusivities measured during the cooling process were almost identical to those measured during the heating process. It was also shown that the thermal diffusivities decreased with increasing temperature and with the decrease of O/M ratio in the hypostoichiometric region. As shown in Table 3, the specimen with initial O/M ratio of 2.00 decreased to O/M ratio of 1.95 after the thermal diffusivity measurements. On the other hand, there was practically no difference in O/M ratios before and after the thermal diffusivity measurement when O/M ratios of the specimens were less than 1.95.
1.2E-02
HT-2 O/M=1.946 Cooling HT-3 O/M=1.932 Heating HT-3 O/M=1.932 Cooling
1.0E-02
HT-4 O/M=1.926 Heating HT-4 O/M=1.926 Cooling
8.0E-03
HT-5 O/M=1.916 Heating HT-5 O/M=1.916 Cooling
6.0E-03
4.0E-03
2.0E-03 800
1000 1200 1400 1600 1800 2000 2200 2400
Temperature (K) Fig. 5. Thermal diffusivities of the hypostoichiometric specimens measured in the high-temperature region.
4. Discussion 4.1. Change of thermal diffusivities during heating up and cooling down From the findings in Fig. 4 that the thermal diffusivities of the stoichiometric specimen obtained in the cooling process were much lower than those in the heating process and that the O/M ratio of the stoichiometric specimen decreased to 1.95 after the
thermal diffusivity measurements, we inferred that these phenomena were caused by the evaporation of vapor species from this specimen at high temperature. In addition, our previous study showed that there were no practical changes in the thermal diffusivities and the O/M ratios during the thermal diffusivity measurements in the low-temperature region [16]. From these facts, it is considered that the evaporation occur in high-temperature condition exceeding 1800 K.
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n
O=M ðtþDtÞ
h m io mUO ðtÞ mPuO ðtÞ W ðtÞ m m UO ðtÞ O=M ðtÞ MðtÞ 3 MUO3 þ 2 MUO2 þ MUOðtÞ þ 2 MPuO2 þ MPuOðtÞ UO PuO 3 2 2 ( " #) ¼ ; Xm W ðtÞ iðtÞ M ðtÞ Mi
1.0E-02
(a)
1.0E-04
Vapor Pressure (atm)
In order to infer the relation between the O/M ratio changes of the specimens and the evaporation of vapor species at high temperature, the estimation of these changes based on Knudsen–Langmuir equation [20] was carried out. In this estimation, the main vapor species were assumed to be UO3, UO2, UO, U, PuO2, PuO and Pu. The O/M ratio of specimen in heating and cooling was calculated as a function of time by the following equations:
1.0E-06
1.0E-08 Calculation results
1.0E-10
i
ð4Þ
1.96
UO3 UO2 PuO2 PuO 1.98
at 2241 K
2.00
2.02
2.00
2.05
O/M
ð5Þ
1 pðOÞ ; O2 ðgÞ ¼ OðgÞ; K O2 =O ¼ 2 pðO2 Þ1=2
ð6Þ
1 pðUOÞ UðgÞ þ O2 ðgÞ ¼ UOðgÞ; K U=UO ¼ ; 2 pðUÞ pðO2 Þ1=2
ð7Þ
1 pðUO2 Þ UOðgÞ þ O2 ðgÞ ¼ UO2 ðgÞ; K UO=UO2 ¼ ; 2 pðUOÞ pðO2 Þ1=2
ð8Þ
1 pðUO3 Þ UO2 ðgÞ þ O2 ðgÞ ¼ UO3 ðgÞ; K UO2 =UO3 ¼ ; 2 pðUO2 Þ pðO2 Þ1=2
ð9Þ
1.0E+00
(b) 1.0E-05
VaporPressure (atm)
where W(t), M(t), T(t) and A are, respectively, weight, molecular weight, temperature and surface area of the specimen at time t; Mi, mi(t), and pi(t) are, respectively, molecular weight, evaporation amount and vapor pressure of vapor species i at t; R is the gas constant and Dt is a short interval enough to neglect temperature change in heating and cooling. The vapor pressures of vapor species, pi, were calculated using Rand–Markin model [21] based on thermodynamic equilibrium theory. In hypostoichiometric MOX, the (U1y, Puy)O2x was assumed to be an ideal solid solution of UO2 and PuO2m (m = x/y). The vapor pressures were calculated from the relations (R T lnðK i Þ ¼ Df G0i ) between the Gibbs free energies of formation (Df G0i ) for these species and the equilibrium constants (Ki) for following reactions (6)–(13). The detailed information of the calculation and the Df G0i were given in Ref. [22].
1.0E-10
1.0E-15 p(UO 2) p(UO) p(PuO 2) p(Pu)
1.0E-20
1.0E-25 1.85
p(UO 3) p(U) p(PuO) Total
1.90
1.95
O/M Fig. 6. (a) Comparison between the experimental and calculated vapor pressures of main vapor species of MOX with 20% Pu-content at 2241 K. Marks are the values measured by Battles et al. [23]. Lines are the values calculated theoretically. (b) Vapor pressures of vapor species at 2000 K calculated using Rand–Markin model [21]. Vapor pressure of UO3 is highest in all species when O/M ratio is 2.00.
2.02
2.00
1 pðPuOÞ PuðgÞ þ O2 ðgÞ ¼ PuOðgÞ; K Pu=PuO ¼ ; 2 pðPuÞ pðO2 Þ1=2
ð10Þ
1 pðPuO2 Þ PuOðgÞ þ O2 ðgÞ ¼ PuO2 ðgÞ; K PuO=PuO2 ¼ ; 2 pðPuOÞ pðO2 Þ1=2
ð11Þ
PuO2m ðsÞ þ
1.0E-12 1.94
1.98
O/M ratio
miðtÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Mi ; ¼ piðtÞ Dt A 2 p R T ðtÞ
Experimental results[23]
UO3 UO2 PuO2 PuO
1.96
1.94
1.92
O/M=2.00 O/M=1.95
1.90
m pðPuO2 Þ O2 ðgÞ ¼ PuO2 ðgÞ; K PuO2m ðsÞ=PuO3 ðgÞ ¼ ; 2 y pðO2 Þm=2
0
500
1000
1500
2000
2500
Temperature (K)
ð12Þ ð13Þ
Fig. 7. Calculation results of the O/M ratio changes during the measurements for initial O/M ratios of 2.00 and 1.95. For O/M ratio of 2.00, the calculation was carried out from room temperature to 2220 K. For O/M ratio of 1.95, the calculation was carried out from room temperature to 2270 K.
In this calculation, the influence of Am in the specimen was neglected because the content of it was very small. Fig. 6(a) shows the comparison between the experimental values of main vapor species of MOX measured by Battles et al. [23] and the calculation values of those derived from the above mentioned calculation. In this comparison, the vapor pressures of the vapor species of MOX with 20% Pu-content at 2241 K were adopted because the number of the experimental values was limited.
Although the experimental values at O/M ratio of 2.00 were not shown in the report of Battles et al., they estimated that the vapor pressure of UO3 was highest in this condition. Fig. 6(b) shows the vapor pressures at 2000 K for the vapor species of the specimen in this study calculated using the Rand-Markin model. The main vapor species are UO3, UO2, PuO2, and PuO. When O/M ratio was greater than 1.95, the vapor pressure of
UO2 ðsÞ ¼ UO2 ðgÞ; K UO2 ðsÞ=UO2 ðgÞ ¼
pðUO2 Þ : ð1 yÞ
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Thermal diffusivity (cm2/s)
1.4E-02
1.2E-02
HT-1 O/M=2.000
HT-2 O/M=1.946
HT-3 O/M=1.932
HT-4 O/M=1.926
HT-5 O/M=1.916 1.0E-02
8.0E-03
6.0E-03
4.0E-03
2.0E-03 800
1000 1200 1400 1600 1800 2000 2200 2400
Temperature (K) Fig. 8. Thermal diffusivities measured during the heating of MOX with 30% Pucontent on various O/M ratios.
(2) For specimens with O/M ratio less than 1.946, thermal diffusivities obtained during both the heating and the cooling processes of the high-temperature measurements were almost the same because the O/M ratio did not change during the high-temperature measurements. (3) The O/M ratio changes of specimens during the high-temperature measurements were discussed using the Knudsen–Langmuir equation. Evaluations by the Rand-Markin model showed that the main vapor species were UO3, UO2, PuO2 and PuO. From the calculation results at 2000 K, the vapor pressure of UO3 was the highest among all species in the range of the O/M ratio of about 1.96 or more. Therefore, the O/M ratio decreased because a large amount of oxygen in the specimen was evaporated together with UO3. When the O/M ratios of specimens were less than 1.95, the O/M ratio did not change up to 2200 K because the vapor pressures of the main vapor species were the same order and a little evaporation was expected under these conditions. (4) The measurements of thermal diffusivities of the stoichiometric specimen below 1800 K had high reliability because no significant change of O/M ratio was observed. When the O/M ratio of specimens was less than 1.95, the measurements could be done at temperatures up to 2200 K because the change of O/M ratio was slight.
UO3 was the highest among all species. On the other hand, when O/ M ratio was about 1.95, the vapor pressures of the main vapor species were almost the same order. Fig. 7 shows the calculation results of the O/M ratio changes during the measurements for initial O/M ratios of 2.00 and 1.95. In the former, the O/M ratio started to decrease at about 1800 K and it was about 1.95 after completing the measurement. In the latter, the O/M ratio started to decrease at about 2200 K, but it did not decrease significantly. These calculation results about the O/M ratio change were in good agreement with the experimental results above mentioned.
We are pleased to acknowledge Mr. H. Uno, Mr. T. Tamura, Mr. H. Sugata, Mr. T. Sunaoshi and Mr. K. Shibata for their assistance in the sample preparation, and in carrying out the EPMA, XRD, and other analysis.
4.2. Temperature dependence of thermal diffusivity
References
The thermal diffusivities during the heating process of MOX with 30% Pu-content on various O/M ratios are shown in Fig. 8. In the stoichiometric specimen, the measurements obtained below 1800 K had high reliability because only a little evaporation was expected at such a low temperature region. When the O/M ratios of specimens were less than 1.95, the measurements obtained below 2200 K also had high reliability because a little evaporation was expected under these conditions as shown in Fig. 7. The thermal diffusivities decreased with increasing temperature and with larger deviation of O/M ratios from stoichiometry. In the high-temperature region, the difference in thermal diffusivities of each O/M ratio decreased. At temperatures above 1800 K, the thermal conductivities shown in Fig. 1 increased with increasing temperature, unlike the behavior seen for thermal diffusivities. This high-temperature behavior of thermal conductivity was due to the heat capacity behavior.
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5. Conclusions The thermal diffusivities of (U, Pu)O2.00x solid solutions (x = 0.00–0.08) were measured by the laser flash method in the temperature range from 990 to 2190 K. The measured values were normalized to 100%TD by using the modified Maxwell-Eucken relationship to evaluate the influences of temperature and O/M ratio on thermal diffusivity. These results are summarized as follows: (1) The thermal diffusivities of the stoichiometric specimen obtained during the cooling process of the high-temperature measurements were greatly lower than those in the heating process because the O/M ratio decreased during the hightemperature measurements.
Acknowledgements