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Development of high temperature calorimeter: heat capacity measurement by direct heating pulse calorimetry
Journal of Physics and Chemistry of Solids 66 (2005) 231–234 www.elsevier.com/locate/jpcs
Development of high temperature calorimeter: heat capacity measurement by direct heating pulse calorimetry Yuji Aritaa,*, Keisuke Suzukib, Tsuneo Matsuic b
a Research Center for Nuclear Materials Recycle, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan Department of Nuclear Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan c Department of Nuclear Engineering and Quantum Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Accepted 6 September 2004
Abstract The temperature limit for heat capacity measurements with the direct heating pulse calorimeter has been increased up to 2000 K by means of the combination of an optical pyrometer to detect the relative temperature change with tungsten–rhenium thermocouples to determine absolute temperatures. With this improved calorimeter the heat capacities were measured up to 1950 K, for SiC and B4C, and 2000 K for graphite. The heat capacity values obtained in this study were in good agreement, within the error of G5%, with those previous values calculated from the enthalpy data by drop method. The electrical conductivities of SiC, B4C and graphite were also simultaneously determined from the inducted voltage and the current for heat capacity measurement. q 2004 Elsevier Ltd. All rights reserved. Keywords: Electrical conductivity
1. Introduction The heat capacity of energy-related materials at high temperatures is essentially important to predict and understand the thermophysical behavior, especially the behavior of nuclear fuels under normal and abnormal operational conditions of nuclear reactors. Most of the heat capacity data above 1500 K were obtained by means of drop calorimetry; the enthalpy data are first obtained, and then heat capacity was calculated by their differentiation with respect to temperature. The heat capacity of UO2 at high temperatures is one of the most important properties of the fuel materials. Several investigators revealed a pronounced increase in the heat capacity of UO2 at temperatures above around 1600 K. The origin of which has been discussed for many years. Though some representative results for heat capacity of UO2 at high temperatures are reported so far [1–9], the results were different from each other even with
* Corresponding author. Tel.: C81 52 789 5940; fax: C81 52 789 5936. E-mail address: [email protected] (Y. Arita). 0022-3697/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2004.09.004
the same enthalpy data [10]. The drop method has difficulties that the derived values for heat capacity depend on both the selection of the polynomials and the differentiation procedure with respect to temperature, and thermal anomalies such as phase transitions are sometimes overlooked or ignored. Table 1 shows a summary of various methods [10–23] for the precise measurement of heat capacity of mainly ceramic materials, within an error of G2% at temperature above 800 K. Although a direct heating pulse method was developed and improved in our laboratory, temperature is limited up to 1700 K. In this paper, the direct heating pulse calorimeter developed in our laboratory has been improved. The heat capacities of several ceramics are measured up to 2000 K and compared with the results reported previously by other research groups.
2. Modification of apparatus The direct heating pulse calorimeter (DHPC) is schematically shown in Fig. 1. With this calorimeter, the heat
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Y. Arita et al. / Journal of Physics and Chemistry of Solids 66 (2005) 231–234
Table 1 Summary of various methods for precise heat capacity measurements at high temperature above 800 K (excluding the drop method) Methods
Objective materialsa Metal
Ceramics
Adiabatic intermittent heating method (Nernst method) Adiabitic scanning method Laser flash method Direct heating AC method Direct heating pulse (intermittent) method
(a) (a) (a) (a) (a)
High-speed direct heating method Laser autoclave technique High-temperature differential scanning method (triple cells) High-speed cooling method a
Temperature (range/K)
Investigators
(a) (a) (a) (b) (a)
T!1050 T!1000 T!1000 T!3000 T!1700
(a)
(b)
TO1500
(a) (a) (a)
(c) (a) (c)
TO2000 T!1500 TO2000
Grønvold [11] Naito et al. [12] Takahashi et al. [13] Kraftmakher [14] Naito et al. [15] Matsui et al. [10] Cezairliyan[16] Reiter et al. [17] Ohse et al.[18–21] Takahashi et al.[22] Matsui et al. [10,23]
(a) Possible, (b) not suitable, (c) probably needs several improvements.
capacity and electrical conductivity were measured simultaneously. In this calorimeter, the temperature of a sample rod is first increased up to a desired temperature by an external main heater. Two electrode heaters placed at both ends of samples were used to decrease the temperature gradient in the rod sample and, to decrease heat flow from the sample to both ends. After reaching equilibrium (after getting a constant desired temperature), electric power was supplied directly to the sample rod in a short period (usually 0.1–1.2 s) through a regulated d.c. power supply and the temperature rise of the sample (generally 1–5 K) was measured by a Pt/Pt-13%Rh (R-type) thermocouple of 0.15 mm diameter [10,15]. In order to reduce the error in heat capacity due to heat leak from the sample at high temperature, a double cylindrical thermal shield made of molybdenum, placed outside the sample, was simultaneously heated electrically using batteries. So as to obtain the same temperature rise as the sample, adiabatic condition was obtained. The electric potential drop, the current and the temperature rise of the sample rod were simultaneously measured to obtain the heat capacity and the electrical conductivity for a sample.
One of the main difficulties to measure the heat capacity at high temperatures above 1600 K with our DHPC in our previous studies [10] is the increase of noise in the signal of R-type thermocouples. Since use of a thin platinum alloy wire for thermocouple at high temperature above 1500 K was not adequate due to vaporization and reaction with some gaseous spices in a vacuum atmosphere, we tried to use a tungsten–rhenium (W–Re) alloy as a thermocouple to increase the measurable temperature. However, it was difficult to make a small contact with the sample and the fast response with the temperature change was not enough by using the W–Re alloy. Therefore, the temperature of the sample was measured by a W-26%Re/W-5%Re thermocouple of 0.2 mm diameter and the temperature rise of the sample was measured by a pyrometer (TOPCON, OEP-PM650) over the temperature range from 1400 to 2000 K. The output from the pyrometer, E is expressed, c2 E Z 3FCexp K ; (2) AT C B where c2 is the radiation constant, A, B and C are fitting parameters, 3 is the emissivity and F is the geometrical
Fig. 1. Schematic diagram of DHPC.
Y. Arita et al. / Journal of Physics and Chemistry of Solids 66 (2005) 231–234
233
Fig. 2. Heat capacity of SiC. C this study, Chekhovski [24], Barin [25], G5% of Barin.
Fig. 4. Heat capacity of graphite. C this study, , our previous results [10], Butland and Madison [29], Barin[25], G5% of Barin.
factor. The value of A, B and C are determined with a black body and a standard lamp calibrated by Osaka branch, National Research Laboratory of Metrology before temperature measurement for heat capacity. Since 3 and F may change at each measurement, they are calibrated with the W–Re thermocouple which is attached on the sample at every temperature. Since the optical signal from a sample is too small to detect by a pyrometer below 1400 K, measurements of heat capacities are difficult when using W–Re thermocouple. Electrical conductivities, however, is able to be measured below 1400 K.
with temperature, the error is larger in lower temperatures from the reason that the signal output is smaller in lower temperatures. The uncertainty of the absolute temperature is larger in higher temperatures and that of temperature change, which means the heat capacity value, is larger in lower temperatures. From the result obtained in this study the precision of this calorimeter is within 5% of the measured specific heat value. The inaccuracy of DHPC in this study is at the same level as that of the drop calorimeter. The DHPC, however, has the advantage in measuring the heat capacity of the sample which has phase transitions.
3. Result and discussion
3.2. Heat capacity and electrical conductivity measurement
3.1. Performance assessment of the calorimeter
The heat capacity of silicon carbide (SiC; 80 mm long and 10 mm in diameter), boron carbide (B4C; 70 mm long and 8 mm in diameter) and graphite (C; 80 mm long and 10 mm in diameter) measured by a DHPC are shown in Figs. 2–4, respectively. It is seen that the heat capacity data measured by a DHPC are in agreement within G4% of the previous
The improved calorimeter uses W–Re thermocouple and a single wave pyrometer. The inaccuracy in the signal from a thermocouple affects the absolute temperature of a sample and the value will be a few% of the signal. Although the noises in the signal from a pyrometer are almost constant
Fig. 3. Heat capacity of B4C. C this study, , our previous results [26], Sheindlin et al.[27], King [28], Barin[25], G5% of Barin.
Fig. 5. Electrical conductivity B SiC, C B4C, C Graphite, SiC [30], B4C[31], Graphite[32].
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Y. Arita et al. / Journal of Physics and Chemistry of Solids 66 (2005) 231–234
data [10,24–28] up to 2000 K. There are tendencies for the measured values to be larger than those of previous data. The reason of this trend is not clear in this study. The electrical conductivity of each sample is shown in Fig. 5. The temperature dependence of electrical conductivity for SiC, B4C and graphite almost agreed with previously published results, respectively. Since the electrical conductivity varies widely with quantities and kinds of impurities, the absolute values of them are not mentioned here.
4. Conclusion A direct heating pulse calorimeter has been improved. The temperature limit of heat capacity measurement increases up to 2000 K. The electrical conductivity can also be measured up to 2000 K.
Acknowledgements This project is partly supported by the Grant in Aid for Scientific Research No. 08555154 from the Ministry of Education, Science, Sports and Culture.
References [1] P. Grønvold, N.J. Kveseth, A. Svean, J. Tichy, J. Chem. Thermodyn. 2 (1970) 665. [2] D.R. Fredrickson, M.G. Chasanov, J. Chem. Thermodyn. 2 (1970) 623. [3] A.E. Ogard, J.A. Leary, Proc. Symp. Thermodynamics Nucl. Mater. IAEA, Vienna 1967. [4] R.A. Hein, P.N. Flagella, J.B. Conway, J. Am. Ceram. Soc. 25 (1968) 99.
[5] C.A. Affortit, J.P. Marcon, Rev. Int. Hautes Temper. Regrat. 7 (1970) 236. [6] R. Szwarc, J. Phys. Chem. Solids 30 (1969) 705. [7] J.F. Kerrisk, D.G. Clifton, Nucl. Technol. 16 (1972) 531. [8] J. Ralph, G.J. Hyland, J. Nucl. Mater. 132 (1985) 76. [9] M.A. Bredig, Colloq. Int. C.N.R. 205 (1971) 183. [10] T. Matsui, Y. Arita, K. Watanabe, Thermochim. Acta 352-353 (2000) 285. [11] F. Grønvold, Acta Chem. Scand. 21 (1967) 1695. [12] K. Naito, H. Inaba, M. Ishida, Y. Sato, H. Arima, J. Phys. E 7 (1974) 464. [13] Y. Takahashi, J. Nucl. Mater. 51 (1974) 17. [14] Y.A. Kreftmakher, High Temp.-High Press. 5 (1973) 433. [15] K. Nazito, H. Inaba, M. Ishida, K. Seta, J. Phys. E 12 (1979) 712. [16] A. Cezairliyan, M.S. Morse, H.A. Berman, C.W. Beckett, J. Res. Natl Bur. Stand. A 74 (1970) 65. [17] P. Reiter, E. Kaschnitz, High Temp.-High Press. 33 (2001) 505. [18] R.W. Ohse, C. Cercignani, A. Frezzotti, J.P. Hiernaut, M. Hoch, G.J. Magill, T. Matsui, P. Werner, J. Matals, TMS-AIME Annual Meeting 37 (1985) 29. [19] R.W. Ohse, Int. J. Thermophys. 11 (1990) 753. [20] C. Ronchi, J.P. Hiernaut, R. Selfslag, G.J. Hyland, Nucl. Sci. Eng. 113 (1993) 1. [21] J.P. Hiernaut, G.J. Hyland, C. Ronchi, Int. J. Thermophys. 14 (1993) 259. [22] Y. Takahashi, M. Asou, Thermochim. Acta 223 (1993) 7. [23] T. Masui, T. Ishii, R. Sasaki, K. Naito, High Temp.-High Press. 25 (1993) 531. [24] V. Ya, Chekhovski, J. Chem. Thermodyn. 3 (1971) 289. [25] I. Barin, Thermochemical Data of Pure Substances, VCH, Weinheim, Germany, 1989. [26] T. Matsui, Y. Arita, K. Naito, J. Nucl. Mater. 186 (1991) 7. [27] E.G. King, Ind. Eng. Chem. 41 (1949) 1298. [28] A.E. Sheindlin, I.S. Belevich, I.G. Kozevnikov, Tepolofuz. Vys. Temp. 10 (1972) 421. [29] A.T.D. Butland, R.J. Maddison, J. Nucl. Mater. 49 (1973) 45. [30] B. Abeles, K.L. Cheng, G.D. Cody, B.E. Baughan, E.F. Hockings, N.E. Lindenbland, G.M. Muha, RCA Quarterly Prog. Rept. 6 (1960) 9. [31] C. Wood, D. Emin, Phys. Rev. B29 (1984) 4582. [32] N.S. Rasor, WADC-TR-59-439 (1960).
Development of high temperature calorimeter: heat capacity measurement by direct heating pulse calorimetry Yuji Aritaa,*, Keisuke Suzukib, Tsuneo Matsuic b
a Research Center for Nuclear Materials Recycle, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan Department of Nuclear Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan c Department of Nuclear Engineering and Quantum Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
Accepted 6 September 2004
Abstract The temperature limit for heat capacity measurements with the direct heating pulse calorimeter has been increased up to 2000 K by means of the combination of an optical pyrometer to detect the relative temperature change with tungsten–rhenium thermocouples to determine absolute temperatures. With this improved calorimeter the heat capacities were measured up to 1950 K, for SiC and B4C, and 2000 K for graphite. The heat capacity values obtained in this study were in good agreement, within the error of G5%, with those previous values calculated from the enthalpy data by drop method. The electrical conductivities of SiC, B4C and graphite were also simultaneously determined from the inducted voltage and the current for heat capacity measurement. q 2004 Elsevier Ltd. All rights reserved. Keywords: Electrical conductivity
1. Introduction The heat capacity of energy-related materials at high temperatures is essentially important to predict and understand the thermophysical behavior, especially the behavior of nuclear fuels under normal and abnormal operational conditions of nuclear reactors. Most of the heat capacity data above 1500 K were obtained by means of drop calorimetry; the enthalpy data are first obtained, and then heat capacity was calculated by their differentiation with respect to temperature. The heat capacity of UO2 at high temperatures is one of the most important properties of the fuel materials. Several investigators revealed a pronounced increase in the heat capacity of UO2 at temperatures above around 1600 K. The origin of which has been discussed for many years. Though some representative results for heat capacity of UO2 at high temperatures are reported so far [1–9], the results were different from each other even with
* Corresponding author. Tel.: C81 52 789 5940; fax: C81 52 789 5936. E-mail address: [email protected] (Y. Arita). 0022-3697/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2004.09.004
the same enthalpy data [10]. The drop method has difficulties that the derived values for heat capacity depend on both the selection of the polynomials and the differentiation procedure with respect to temperature, and thermal anomalies such as phase transitions are sometimes overlooked or ignored. Table 1 shows a summary of various methods [10–23] for the precise measurement of heat capacity of mainly ceramic materials, within an error of G2% at temperature above 800 K. Although a direct heating pulse method was developed and improved in our laboratory, temperature is limited up to 1700 K. In this paper, the direct heating pulse calorimeter developed in our laboratory has been improved. The heat capacities of several ceramics are measured up to 2000 K and compared with the results reported previously by other research groups.
2. Modification of apparatus The direct heating pulse calorimeter (DHPC) is schematically shown in Fig. 1. With this calorimeter, the heat
232
Y. Arita et al. / Journal of Physics and Chemistry of Solids 66 (2005) 231–234
Table 1 Summary of various methods for precise heat capacity measurements at high temperature above 800 K (excluding the drop method) Methods
Objective materialsa Metal
Ceramics
Adiabatic intermittent heating method (Nernst method) Adiabitic scanning method Laser flash method Direct heating AC method Direct heating pulse (intermittent) method
(a) (a) (a) (a) (a)
High-speed direct heating method Laser autoclave technique High-temperature differential scanning method (triple cells) High-speed cooling method a
Temperature (range/K)
Investigators
(a) (a) (a) (b) (a)
T!1050 T!1000 T!1000 T!3000 T!1700
(a)
(b)
TO1500
(a) (a) (a)
(c) (a) (c)
TO2000 T!1500 TO2000
Grønvold [11] Naito et al. [12] Takahashi et al. [13] Kraftmakher [14] Naito et al. [15] Matsui et al. [10] Cezairliyan[16] Reiter et al. [17] Ohse et al.[18–21] Takahashi et al.[22] Matsui et al. [10,23]
(a) Possible, (b) not suitable, (c) probably needs several improvements.
capacity and electrical conductivity were measured simultaneously. In this calorimeter, the temperature of a sample rod is first increased up to a desired temperature by an external main heater. Two electrode heaters placed at both ends of samples were used to decrease the temperature gradient in the rod sample and, to decrease heat flow from the sample to both ends. After reaching equilibrium (after getting a constant desired temperature), electric power was supplied directly to the sample rod in a short period (usually 0.1–1.2 s) through a regulated d.c. power supply and the temperature rise of the sample (generally 1–5 K) was measured by a Pt/Pt-13%Rh (R-type) thermocouple of 0.15 mm diameter [10,15]. In order to reduce the error in heat capacity due to heat leak from the sample at high temperature, a double cylindrical thermal shield made of molybdenum, placed outside the sample, was simultaneously heated electrically using batteries. So as to obtain the same temperature rise as the sample, adiabatic condition was obtained. The electric potential drop, the current and the temperature rise of the sample rod were simultaneously measured to obtain the heat capacity and the electrical conductivity for a sample.
One of the main difficulties to measure the heat capacity at high temperatures above 1600 K with our DHPC in our previous studies [10] is the increase of noise in the signal of R-type thermocouples. Since use of a thin platinum alloy wire for thermocouple at high temperature above 1500 K was not adequate due to vaporization and reaction with some gaseous spices in a vacuum atmosphere, we tried to use a tungsten–rhenium (W–Re) alloy as a thermocouple to increase the measurable temperature. However, it was difficult to make a small contact with the sample and the fast response with the temperature change was not enough by using the W–Re alloy. Therefore, the temperature of the sample was measured by a W-26%Re/W-5%Re thermocouple of 0.2 mm diameter and the temperature rise of the sample was measured by a pyrometer (TOPCON, OEP-PM650) over the temperature range from 1400 to 2000 K. The output from the pyrometer, E is expressed, c2 E Z 3FCexp K ; (2) AT C B where c2 is the radiation constant, A, B and C are fitting parameters, 3 is the emissivity and F is the geometrical
Fig. 1. Schematic diagram of DHPC.
Y. Arita et al. / Journal of Physics and Chemistry of Solids 66 (2005) 231–234
233
Fig. 2. Heat capacity of SiC. C this study, Chekhovski [24], Barin [25], G5% of Barin.
Fig. 4. Heat capacity of graphite. C this study, , our previous results [10], Butland and Madison [29], Barin[25], G5% of Barin.
factor. The value of A, B and C are determined with a black body and a standard lamp calibrated by Osaka branch, National Research Laboratory of Metrology before temperature measurement for heat capacity. Since 3 and F may change at each measurement, they are calibrated with the W–Re thermocouple which is attached on the sample at every temperature. Since the optical signal from a sample is too small to detect by a pyrometer below 1400 K, measurements of heat capacities are difficult when using W–Re thermocouple. Electrical conductivities, however, is able to be measured below 1400 K.
with temperature, the error is larger in lower temperatures from the reason that the signal output is smaller in lower temperatures. The uncertainty of the absolute temperature is larger in higher temperatures and that of temperature change, which means the heat capacity value, is larger in lower temperatures. From the result obtained in this study the precision of this calorimeter is within 5% of the measured specific heat value. The inaccuracy of DHPC in this study is at the same level as that of the drop calorimeter. The DHPC, however, has the advantage in measuring the heat capacity of the sample which has phase transitions.
3. Result and discussion
3.2. Heat capacity and electrical conductivity measurement
3.1. Performance assessment of the calorimeter
The heat capacity of silicon carbide (SiC; 80 mm long and 10 mm in diameter), boron carbide (B4C; 70 mm long and 8 mm in diameter) and graphite (C; 80 mm long and 10 mm in diameter) measured by a DHPC are shown in Figs. 2–4, respectively. It is seen that the heat capacity data measured by a DHPC are in agreement within G4% of the previous
The improved calorimeter uses W–Re thermocouple and a single wave pyrometer. The inaccuracy in the signal from a thermocouple affects the absolute temperature of a sample and the value will be a few% of the signal. Although the noises in the signal from a pyrometer are almost constant
Fig. 3. Heat capacity of B4C. C this study, , our previous results [26], Sheindlin et al.[27], King [28], Barin[25], G5% of Barin.
Fig. 5. Electrical conductivity B SiC, C B4C, C Graphite, SiC [30], B4C[31], Graphite[32].
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Y. Arita et al. / Journal of Physics and Chemistry of Solids 66 (2005) 231–234
data [10,24–28] up to 2000 K. There are tendencies for the measured values to be larger than those of previous data. The reason of this trend is not clear in this study. The electrical conductivity of each sample is shown in Fig. 5. The temperature dependence of electrical conductivity for SiC, B4C and graphite almost agreed with previously published results, respectively. Since the electrical conductivity varies widely with quantities and kinds of impurities, the absolute values of them are not mentioned here.
4. Conclusion A direct heating pulse calorimeter has been improved. The temperature limit of heat capacity measurement increases up to 2000 K. The electrical conductivity can also be measured up to 2000 K.
Acknowledgements This project is partly supported by the Grant in Aid for Scientific Research No. 08555154 from the Ministry of Education, Science, Sports and Culture.
References [1] P. Grønvold, N.J. Kveseth, A. Svean, J. Tichy, J. Chem. Thermodyn. 2 (1970) 665. [2] D.R. Fredrickson, M.G. Chasanov, J. Chem. Thermodyn. 2 (1970) 623. [3] A.E. Ogard, J.A. Leary, Proc. Symp. Thermodynamics Nucl. Mater. IAEA, Vienna 1967. [4] R.A. Hein, P.N. Flagella, J.B. Conway, J. Am. Ceram. Soc. 25 (1968) 99.
[5] C.A. Affortit, J.P. Marcon, Rev. Int. Hautes Temper. Regrat. 7 (1970) 236. [6] R. Szwarc, J. Phys. Chem. Solids 30 (1969) 705. [7] J.F. Kerrisk, D.G. Clifton, Nucl. Technol. 16 (1972) 531. [8] J. Ralph, G.J. Hyland, J. Nucl. Mater. 132 (1985) 76. [9] M.A. Bredig, Colloq. Int. C.N.R. 205 (1971) 183. [10] T. Matsui, Y. Arita, K. Watanabe, Thermochim. Acta 352-353 (2000) 285. [11] F. Grønvold, Acta Chem. Scand. 21 (1967) 1695. [12] K. Naito, H. Inaba, M. Ishida, Y. Sato, H. Arima, J. Phys. E 7 (1974) 464. [13] Y. Takahashi, J. Nucl. Mater. 51 (1974) 17. [14] Y.A. Kreftmakher, High Temp.-High Press. 5 (1973) 433. [15] K. Nazito, H. Inaba, M. Ishida, K. Seta, J. Phys. E 12 (1979) 712. [16] A. Cezairliyan, M.S. Morse, H.A. Berman, C.W. Beckett, J. Res. Natl Bur. Stand. A 74 (1970) 65. [17] P. Reiter, E. Kaschnitz, High Temp.-High Press. 33 (2001) 505. [18] R.W. Ohse, C. Cercignani, A. Frezzotti, J.P. Hiernaut, M. Hoch, G.J. Magill, T. Matsui, P. Werner, J. Matals, TMS-AIME Annual Meeting 37 (1985) 29. [19] R.W. Ohse, Int. J. Thermophys. 11 (1990) 753. [20] C. Ronchi, J.P. Hiernaut, R. Selfslag, G.J. Hyland, Nucl. Sci. Eng. 113 (1993) 1. [21] J.P. Hiernaut, G.J. Hyland, C. Ronchi, Int. J. Thermophys. 14 (1993) 259. [22] Y. Takahashi, M. Asou, Thermochim. Acta 223 (1993) 7. [23] T. Masui, T. Ishii, R. Sasaki, K. Naito, High Temp.-High Press. 25 (1993) 531. [24] V. Ya, Chekhovski, J. Chem. Thermodyn. 3 (1971) 289. [25] I. Barin, Thermochemical Data of Pure Substances, VCH, Weinheim, Germany, 1989. [26] T. Matsui, Y. Arita, K. Naito, J. Nucl. Mater. 186 (1991) 7. [27] E.G. King, Ind. Eng. Chem. 41 (1949) 1298. [28] A.E. Sheindlin, I.S. Belevich, I.G. Kozevnikov, Tepolofuz. Vys. Temp. 10 (1972) 421. [29] A.T.D. Butland, R.J. Maddison, J. Nucl. Mater. 49 (1973) 45. [30] B. Abeles, K.L. Cheng, G.D. Cody, B.E. Baughan, E.F. Hockings, N.E. Lindenbland, G.M. Muha, RCA Quarterly Prog. Rept. 6 (1960) 9. [31] C. Wood, D. Emin, Phys. Rev. B29 (1984) 4582. [32] N.S. Rasor, WADC-TR-59-439 (1960).