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Vapor Pressure of Uranium Dioxide

Vapor Pressure over Liquid UO₂

The recommended equation for the total vapor pressure over liquid UO₂ from the melting point (3120 K) to 8000 K is the equation derived by Breitung and Reil¹ from their in-pile equation-of-state measurements, and their review of the experimental data. Their equation for the logarithm of the saturated vapor pressure over liquid UO₂ is

Figure 1

where the pressure is in MPa and the temperature is in K. Vapor pressures determined from this equation are given as a function of temperature in Table 1 and shown with estimated uncertainties in Figure 1. This equation gives a boiling point of 3815.1 K.

Vapor Pressure over Solid UO₂

The recommended equation for the vapor pressure of UO₂(g) over solid UO₂ is based on measurements by Ackermann, Rauh, and Rand² of the pressure of UO₂(g) over UO₂ in the temperature range from 1800 to 2600 K. Their equation for the logarithm of the vapor pressure of UO₂(g) is

where the vapor pressure, P, is in MPa and the temperature, T, is in K. Ackermann, Rauh, and Rand stated that in the temperature range of their measurements, UO₂(g) comprises approximately 94% of the total vapor pressure over solid UO₂. Therefore, below 2600 K, this equation gives a reasonable estimate of the total vapor pressure over solid UO₂. Because contributions to the total vapor pressure from other species become significant with increasing temperature,³ this equation does not give a good estimate of the total vapor pressure over solid UO₂ near the melting point, 3120 K. The equation of Tetenbaum and Hunt⁴ is recommended for the total vapor pressure over solid UO₂ at temperatures above 2600 K. Tetenbaum and Hunt⁴ measured the total vapor pressure over uranium dioxide as a function of stoichiometry. Their equation for the total vapor pressure over UO₂(s) is

Figure 2

The vapor pressure of UO₂(g) calculated using the equation of Ackermann et al.² and the total vapor pressure over UO₂(s) calculated using the equation of Tetenbaum and Hunt⁴ are tabulated as a function of temperature in Table 2 and shown with estimated uncertainties in Figure 2.

The estimated uncertainties in total vapor pressure over liquid UO₂ calculated from Eq.(1) range from -40%/+60% at 3120 K to -45%/+80% at 6000 K. From 3120 to 6000 K, the negative uncertainties are assumed to decrease linearly: The positive uncertainties are assumed to increase linearly from +60% at 3120 K to +80% at 4500 K: Above 4500 K, the positive uncertainties are assumed constant (+80%). The uncertainties in the pressure of UO₂ (g) over solid UO₂ calculated from Eq.(2) and in the total vapor pressure over solid UO₂ calculated using Eq.(3) are estimated as -40%/+60% from 1700 to 3120 K.

Uranium dioxide can exist over a wide range of compositions (hypostoichiometric to hyperstoichiometric with respect to oxygen), which are temperature dependent. The total vapor pressure depends on the oxygen-to-uranium ratio of the condensed phase, so that the total vapor pressure over UO_2±x will depend on the value of x. The vaporization of UO₂ is not congruent because the O:U ratio in the gas phase is greater than in the condensed phase. The total vapor pressure above solid and liquid UO₂ includes contributions from UO₂(g), UO(g), UO₃(g), U(g), O(g), and UO(g).

Breitung and Reil¹ have recently reviewed the experimental measurements of the total vapor pressure of liquid UO₂. The data used in their assessment are summarized in Table 3. They included both pressure-temperature measurements¹, 5-15 and pressure-enthalpy measurements^16-19,22,23 in their assessment.

Pressure-Temperature Measurements

The transpiration measurements of Reedy and Chasanov⁵ were weighted high in the assessment of Breitung and Reil¹ for the following reasons: (1) they are the only measurements on both solid and liquid UO₂, (2) the technique produces true equilibrium data, and (3) the experimental uncertainties are very small (in pressure; in temperature). In these experiments, the UO₂ was contained in tungsten, which limited the temperature range (2615 - 3390 K). At 2615 and 2860 K, the O:U ratio of the condensed phase was 1.98. At 3390 K, the O:U ratio of the liquid was 1.94.

The laser-heated vapor pressure measurements listed in Table 3 may be divided into two groups: (1) measurements performed far from thermodynamic equilibrium^6-13 and (2) measurements close to thermodynamic equilibrium. ^14,15 Measurements far from thermodynamic equilibrium consist of experiments in which the fuel vapor expands into a vacuum or a rare gas environment. Such experiments require a theoretical model to convert properties of the expanding nonequilibrium plasma into saturation vapor pressures. The large scatter in the data from different experiments of this type is indicative of the difficulty of obtaining saturation vapor pressure data from these nonequilibrium measurements. Measurements close to equilibrium use a boiling point technique that determines the temperature at which a laser-generated UO₂ vapor cloud begins to expand against a xenon cover gas of a given pressure. At this temperature, the UO₂ vapor pressure is assumed to be equal to the gas pressure. The xenon gas atoms initially confine the laser-generated vapor cloud so that evaporation proceeds close to thermodynamic equilibrium. The recent boiling-point experiments by Bober and Singer¹⁵ included corrections for optical absorption (by the vapor cloud) of thermal radiation emitted from the liquid surface. Breitung and Reil concluded that the recent measurements by Bober and Singer are the most reliable saturation vapor pressure data for liquid UO₂ from the laser experiments.

In-Reactor Experiments

The first in-reactor measurements of vapor pressure as a function of adiabatic fuel enthalpy by Reil¹⁶ determined upper and lower bounds for the vapor pressure. Later calculations showed that these values were overly conservative.¹ Benson¹⁷ measured the isobaric expansion of a 25-m-thick layer of UO₂ powder confined by two movable pistons as it was heated to a certain internal energy in one microsecond. Results of this experiment were inconsistent with the expansion of a single-component liquid-vapor system. An unknown source of pressure, such as water vapor, adsorbed by the fine UO₂ powder is believed to have contributed to the measured pressure. Fission heating was used in the eight Commissariat a l'Energie Atomique (CEA) experiments by Limon et al.¹⁸ to heat a thin solid UO₂ disk to boiling under constant argon pressure. The boiling point was determined by the sudden increase in pressure. The average energy deposited in the UO₂ was assumed to be equal to the fuel enthalpy in the boiling zone. This assumption led to deviations of only a few percent in six high-enthalpy tests but the actual enthalpy in the boiling zone may have been on the order of 10% higher for the two low-enthalpy tests.¹

Breitung and Reil¹ measured the saturation vapor pressure of pure UO_2.01, reactor grade UO_2.08, and reactor grade (U_0.77 Pu_0.23)O_2.09 as a function of enthalpy for enthalpies from 2000 to 3700 kJ kg^-1. Their six effective equation-of-state experiments at the annular core research reactor at Sandia National Laboratories determined the saturation vapor pressure as a function of enthalpy at conditions that are very close to those of the disassembly phase of a core disruptive accident. These experiments gave very reproducible results. They found that under these conditions

(1) the fuel saturation vapor pressure for fuel containing uranium-plutonium mixed oxide was essentially identical to that of pure UO₂;

(2) fuel impurities from fabrication did not noticeably contribute to the pressure;

(3) stoichiometry variations have no strong influence on the saturation vapor pressure for UO_2.01, and UO_2.08;

(4) replacement of uranium by plutonium in concentrations equivalent to mixed oxide fuel, e.g., (U_0.77 Pu_0.23)O_2.09, does not significantly affect the measured vapor pressure.

From the data obtained in these six experiments, Breitung and Reil developed an equation for the vapor pressure for all three fuels:

Figure 3

where z = h - h₂₉₈ is the enthalpy increment in kJ kg^-1 and P is the saturation pressure in MPa. This equation fits their data for all three fuel types within their experimental uncertainties of ± 0.5 MPa in pressure and ± 3% in enthalpy. Breitung and Reil¹ converted their pressure-enthalpy equation to a pressure-temperature equation, Eq.(1), using Fischer's²⁰ theoretical prediction for the saturation pressure as a function of internal energy of liquid UO₂ and the melting point enthalpy given by Fink et al.²¹ (1398.6 kJ/kg). Their equation for pressure as a function of temperature, Eq.(1), is slightly different from an earlier equation given by Breitung and Reil^{22, 23} (which was recommended by Harding et al.²⁴) because different equations were used to convert from pressure-enthalpy to pressure-temperature. Breitung and Reil¹ stated that the main uncertainty in the conversion is the choice of equation for the heat capacity. The large variations in the available equations for the heat capacity of liquid UO₂ are shown in Figure 3. The data in Figure 3 are those determined by Ronchi et al.²⁵ from their cooling curve experiments. In the analysis of these experiments, Ronchi et al. assumed a constant thermal conductivity of 2.5 W m^-1 K^-1. The solid line is the fit by Ronchi et al.²⁵ to their data. The dashed line labeled "H+Cp Fit Fink" is a combined fit to the enthalpy data^{26, 27} and the heat capacity data of Ronchi et al.²⁵ from 3100 to 4500 K. The line labeled "Rand et al." is the constant heat capacity obtained from the linear fit by Rand et al.²⁸ to the enthalpy data.^{26, 27} The heat capacities of Fischer²⁰ were preferred by Breitung and Reil to the equation they used previously (labeled "Breitung and Reil KfK 3939") because the model used by Fischer was anchored at experimental results for the vapor pressure and density of liquid UO₂. Figure 3 shows that values from both equations used by Breitung and Reil are high relative to the values given by Ronchi et al.²⁵ Harding et al.²⁴ have pointed out that the heat capacity may be varied without significant effect on the vapor pressure at a given temperature. They stated that a 20% variation in heat capacity at 6000 K gives a 30% change in the vapor pressure.

Comparison of Recommended Equation with Data

In Figure 4, the recommended equation of Breitung and Reil for the total vapor pressure over liquid UO₂ is compared with the most recent and reliable vapor pressure data from each experimental method, with the equation formulated by the 1978 IAEA International Working Group on Fast Reactors (IWGFR),²⁹ and with vapor pressures calculated by Green and Leibowitz.³ The IWGFR equation was based on a review of the data available in 1978 and was recommended for use up to 5000 K. The vapor pressures and vapor compositions above uranium dioxide calculated by Green and Leibowitz³ are based on a statistical-mechanical calculation of the thermodynamic functions of the individual vapor species using molecular energy levels from spectroscopic data and an oxygen potential model. Experimental data included in Figure 4 are: transpiration data of Reedy and Chasanov,⁵ the boiling-point data of Bober and Singer,¹⁵ data from the most recent laser-heating vaporization experiments of Ohse et al.,^{12, 13} and data from the in-pile experiments of Limon et al.¹⁸ The equation recommended by Limon et al. to best describe their data has also been included. Breitung and Reil's earlier vapor pressure equation that was obtained by using a different heat capacity^22,23 to convert their data has been included in Figure 4 to show the effect of differences in choice of heat capacity on the final vapor pressure equation. It is labeled "Breitung KfK3939." Figure 4 shows that at high temperatures, it gives lower pressures than the recommended equation of Breitung and Reil. Therefore, the recommended equation is in better agreement with the high-temperature data of Limon et al.

Figure 4

The IWGFR equation is consistent with the total pressures calculated by Green and Leibowitz³ and with the early laser-vaporization data, which were higher than the 1980 data of Ohse et al.^12. The datum at 4220 K from the 1980 measurements of Ohse et al.¹² is a factor of 3.3 higher than the vapor pressure at 4220 K calculated using the recommended equation of Breitung and Reil.¹ At 4000 K, vapor pressures obtained from the IWGFR equation and calculations by Green and Leibowitz³ are, respectively, factors of 2.1 and 1.6 higher than the vapor pressure calculated with the equation of Breitung and Reil.¹ The recommended equation of Breitung and Reil is in good agreement with the vapor pressures determined from laser-vaporization experiments in 1985 by Ohse et al.,¹³ with the low-temperature data of Reedy and Chasanov,⁵ with the high-temperature data of Limon et al.,¹⁸ and with the data of Bober and Singer.¹⁵ It is a good representation of all equilibrium in-pile and out-of-pile data.

Breitung and Reil¹ noted that if the two low-temperature CEA data points of Limon et al.¹⁸ are disregarded, all in-pile results are located close to an almost linear extension of the transpiration data of Reedy and Chasanov⁵ and the laser boiling point data of Bober and Singer.¹⁵ All these methods provide conditions very close to equilibrium vaporization so that the slope of the line connecting these data should give the heat of vaporization. They attributed the steeper slopes obtained from the earlier laser-vaporization experiments (as characterized by the 1980 data of Ohse et al.) to the use of nonequilibrium pressure models to reduce the data and/or to the neglect of optical absorption of thermal surface radiation in the vapor cloud. Application of the Clausius -Clapeyron equation to their vapor pressure equation gives an effective enthalpy of vaporization:

where is in J mol^-1 and T in K ranges from 3120 to 8000 K. The heat of vaporization at the normal boiling point (3815.1 K) is 413.5 kJ mol^-1.

Although the total vapor pressure above solid UO₂ includes contributions from UO₂(g), UO(g), UO₃(g), U(g), O(g), and UO(g), the greatest contribution is from UO₂(g). Ackermann et al.² measured the vapor pressure of UO₂(g) above solid UO₂ from 1800 to 2600 K and commented that UO₂(g) comprises 94% of the total pressure at 2150 K. Tetenbaum and Hunt⁴ determined the total vapor pressure above UO_2-x in the temperature range 2080 to 2705 K. Green and Leibowitz³ used models for the partial Gibbs free energy of oxygen above UO₂ to determine the contributions of the various vapor species above hypostoichioeteric uranium dioxide for UO_2.00 through UO_1.90.

Measurements of the total vapor pressure above solid UO₂ by Knudson effusion,^30-33 Langmuir surface evaporation,³⁵ and transpiration^{4, 36} methods and have been reviewed by Ackermann et al.² and compared with measurements of the vapor pressure due to UO₂(g) determined from mass-spectrometric measurements by Pattoret et al.³⁷ and by Ackermann et al.^2,30,34 They found reasonable agreement between the different measurements. Table 4 shows the vapor pressures at 2150 K determined from the experiments included in the assessment by Ackermann et al.² Ackermann et al. corrected the data of Alexander et al.³⁶ for a systematic error. Consequently, the vapor pressure attributed to Alexander et al. in Table 4 (which is from the table of Ackermann et al.²) differs from the value given in the original paper by Alexander et al.³⁶ The average of the values, excluding the value from the 1979 mass spectroscopy measurements by Ackermann et al.,² is 1.38 x 10^-7 MPa. This is in good agreement with the vapor pressure of UO₂(g) (1.32 x 10^-7 MPa) determined by Ackermann et al. in 1979.

The recommended equation for the vapor pressure of UO₂(g) over UO₂, Eq.(2), is from the 1979 measurements and assessment of Ackermann et al.² It is in reasonable agreement with other data and was derived with considerations for consistency with the thermodynamic functions for solid UO₂ and the enthalpy of sublimation from the solid. It is consistent with a heat capacity that has a phase transition at 2670 K. In Figure 5, this recommended equation of Ackermann et al.² for the vapor pressure of UO₂(g) over solid UO₂ is compared with vapor pressure equations and data from earlier measurements and with the vapor pressure of UO₂(g) and the total vapor pressure over UO_2.00 calculated by Green and Leibowitz.³ In the legend for Figure 5, the notation UO₂ has been included to distinguish measurements or calculations of the pressure due to the vapor species UO₂(g) from the total vapor pressure over UO₂. Below 2450 K, the 1956 low-temperature data of Ackermann et al.³⁰ and the equation of Tetenbaum and Hunt⁴ are in excellent agreement with the recommended equation of Ackermann et al.² Above 2615 K, the equation of Tetenbaum and Hunt for the total vapor pressure over UO₂ gives higher vapor pressures than the equation of Ackermann et al. for the vapor pressure of UO₂(g). Two data from transpiration measurements of the total vapor pressure over UO_1.98 by Reedy and Chasanov⁵ have been included in Figure 5. These are the only vapor pressure measurements over uranium dioxide in both the liquid and solid phases. The Reedy and Chasanov datum at 2615 K is in good agreement with the equation of Ackermann et al. but their datum at 2860 K is higher than values from both the equation of Ackermann et al. and the equation of Tetenbaum and Hunt. Total vapor pressures over UO₂ measured by Ohse et al.³² are in good agreement with the equation of Ackermann et al. at low temperatures but are higher at high temperatures. Above 2500 K, the data of Ohse et al. approach total pressures calculated by Green and Leibowitz. The contribution to the total vapor pressure from UO₂(g) calculated by Green and Leibowitz is in good agreement with the equation of Ackermann et al.² above 2600 K. However, the total vapor pressure over UO₂ calculated by Green and Leibowitz is consistently higher than the UO₂(g) pressure given by the equation of Ackermann et al. The difference between these values increases with temperature. The contribution to the total vapor pressure from UO₂(g) calculated by Green and Leibowitz decreases with increasing temperature. It is 70% at 2100 K, 54% at 2500 K, and only 37% at 3100 K. These comparisons indicate that the equation for the vapor pressure of UO₂(g) over solid UO₂ is a reasonable approximation of the total vapor pressure over solid UO₂ up to 2600 K but not at higher temperatures. At higher temperatures, extrapolation of the equation of Tetenbaum and Hunt [ Eq. (3)] is a better approximation to the total vapor pressure over solid UO₂.

Figure 5

Figure 6

The logarithm to the base 10 of the vapor pressures determined from a number of vapor pressure equations near the solid/liquid phase boundary are compared in Figure 6. Equations included in Figure 6 are: the 1978 IWGFR equation²⁹ for the vapor pressure over liquid UO₂, the equation of Breitung and Reil¹ for the vapor pressure over liquid UO₂, the equation of Ackermann et al. for the vapor pressure of UO₂(g) over solid UO₂, the equation of Tetenbaum and Hunt⁴ for the total vapor pressure over solid UO₂, and a modified equation of Tetenbaum and Hunt.²¹ The equation of Tetenbaum and Hunt was modified by Fink, Leibowitz, and Chasanov²¹ for continuity at the solid/liquid interface with the IWGFR equation²⁹ for the vapor pressure over liquid urania. The logarithms of the total vapor pressures over UO₂ calculated by Green and Leibowitz³ are also shown in Figure 6. The total vapor pressure data of Reedy and Chasanov⁵ that spans this temperature range and the 1985 liquid vapor pressure data of Ohse et al.¹³ have also been included in the figure. Harding et al.²⁴ have recommended the equation of Ackermann et al.² as an approximation to the total vapor pressure over solid UO₂ up to the melting point. However, Figure 6 shows that extrapolation of the equation of Ackermann et al. to the melting point gives vapor pressures that are lower than the experimental data and 47% lower than the liquid vapor pressures at the melting point calculated from the equation of Breitung and Reil. Extrapolation of the equation of Tetenbaum and Hunt⁴ into the liquid region gives vapor pressures that are consistent with the vapor pressures over the liquid determined in 1985 by Ohse et al.¹³ but the vapor pressure at the melting point calculated with this extrapolated equation is 17% lower than that calculated using the equation of Breitung and Reil. The modified equation of Tetenbaum and Hunt²¹ is consistent with the IWGFR equation and with the data of Reedy and Chasanov but the vapor pressure at the melting point calculated with this modified equation is 19% higher than the vapor pressure calculated with the equation of Breitung and Reil. Thus, the deviations from the equation of Breitung and Reil by the original equation of Tetenbaum and Hunt⁴ and the modified equation of Tetenbaum and Hunt²¹ are similar in magnitude but opposite in sign. The original equation of Tetenbaum and Hunt⁴ is preferred to the modified equation of Tetenbaum and Hunt²¹ because the original equation of Tetenbaum and Hunt was based on experimental data and it agrees better with the low-temperature vapor pressure data over solid UO₂ and with the equation of Ackermann et al. below 2450 K.

1. W. Breitung, and K. O. Reil, Vapor Pressure Measurements on Liquid Uranium Oxide and (U,Pu) Mixed Oxide, Nucl. Sci. Eng. 101, 26-40 (1989).



2. R. J. Ackermann, E. G. Rauh, and M. H. Rand, A Re-Determination and Re-Assessment of the Thermodynamics of Sublimation of Uranium Dioxide, Symp. on Thermodynamics of Nuclear Materials Julich 1979, Vol.1, IAEA, pp.11-27, Vienna (1980).



3. D. W. Green and L. Leibowitz, Vapor Pressures and Vapor Compositions in Equilibrium with Hypostoichiometric Uranium Dioxide at High Temperatures, Argonne National Laboratory Report ANL-CEN-RSD-81-1 (June 1981); also J. Nucl. Mater. 105, 94 (1982).



4. M. Tetenbaum and P. D. Hunt, Total Pressure of Uranium-Bearing Species over Oxygen-Deficient Urania, J. Nucl. Mater. 34, 86-91 (1970).



5. G. T. Reedy and M. G. Chasanov, Total Pressure of Uranium-Bearing Species over Molten Urania, J. Nucl. Mater. 42 341-344 (1972).



6. M. Bober, H. U. Karow, and K. Schretzmann, Evaporation Experiments to Determine the Vapor Pressure of UO2 Fuel (3000 -5000 K), IAEA Symp. on Thermodynamics of Nuclear Materials, Vol. 1, 295 (1975); Nucl. Technol. 26, 237 (1975).



7. M. Bober, W. Breitung, H. U. Karow, and K. Schretzmann, Evaporation Studies of Liquid Oxide Fuel at Very High Temperatures Using Laser Beam Heating, KFK-2366, Kernforschungszentrum Karlsruhe (1976).



8. R. W. Ohse, P. G. Berrie, H. G. Bogensberger, and E. A. Fischer, Thermodyn. Nucl. Mater. 1, 307 (1975).



9. J. F. Babelot, G. D. Brumme, P. R. Kinsman, and R. W. Ohse, Atomwirtsch. Atomtech., 12, 387 (1977), as referenced by W. Breitung, and K. O. Reil,, Nucl. Sci. Eng. 101, 26-40 (1989).



10. H. C. Tsai, A. Convington, and D. R. Olander, Laser Vaporization of UO₂, in Materials and Molecular Research Division Annual Report LBL-6016, Lawrence Berkeley Laboratory, University of California, Berkeley (1976).



11. M. Bober, W. Breitung, and H. U. Karow, Thermodynamic Calculation and Experimental Determination of the Equation of State of Oxide Fuels up to 5000 K, KFK-2689, Kernforschungszentrum Karlsruhe (1978).



12. R. W. Ohse, J. F. Babelot, A. Frezzotti, K. A. Long, and J. Magill, Equation of State of Uranium Oxide: Mach-disk Investigation of Transient Laser-induced Vaporization of UO₂ up to 5000 K, High Temp.-High Pressures 12, 537 (1980).



13. R. W. Ohse, J. F. Babelot, C. Cercignani, J. P. Hiernaut, M. Hoch, G. J. Hyland, and J. Magill, J. Nucl. Mater. 130, 165 (1985).



14. M. Bober and M. Trapp, Bestimmung des Dampfdrucks von flussigem Uranoxid mittels Laseraufheizung, Kernforschungszentrum Karlsruhe (unpublished), as referenced by W. Breitung, and K. O. Reil,, Nucl. Sci. Eng. 101, 26-40 (1989).



15. M. Bober and J. Singer, Nucl. Vapor Pressure Determination of Liquid UO₂ Using a Boiling Point Technique, Nucl. Sci. Eng. 97, 344-352 (1987).



16. K. O. Reil, Effective Equation of State Measurements on Uranium Dioxide, Dissertation, University of New Mexico (May 1977), as referenced by W. Breitung, and K. O. Reil, Vapor Pressure Measurements on Liquid Uranium Oxide and (U,Pu) Mixed Oxide Nucl. Sci. Eng. 101, 26-40 (1989).



17. D. A. Benson, Application of Pulsed Electron Beam Vaporization to Studies of UO₂, SAND77-0429, Sandia National Laboratories (1977).



18. R. Limon, G. Sutren, P. Combetter, and F. Barbry, Equation of State of Non-Irradiated UO₂, Proc. ENA/ANS Topical Meeting on Reactor Safety Aspects of Fuel Behavior, Sun Valley, Idaho, August 2-6, 1981, Vol. 2, pp. 2-576 to 2-583, CEA-CONF-5816, American Nuclear Society (1981).



19. S. A. Wright, d. H. Worledge, G. L. Cano, P. K. Mast, and F. Briscoe, Fuel-Disruption Experiments Under High-Ramp-Rate Heating Conditions, SAND81-0413, Sandia National Laboratories (Oct. 1983).



20. E. A. Fischer, Evaluation of the Urania Equation of State Based on Recent Vapour Pressure Measurements, KfK- 4084 Kernforschungszentrum Karlsruhe (Sept. 1987).



21. J. K. Fink, M. G. Chasanov, and L. Leibowitz, Thermodynamic Properties of Uranium Dioxide, J. Nucl. Mater. 102, 17-25 (1981); see also Thermophysical Properties of Uranium Dioxide, ANL-CEN-RSD-80-3, Argonne National Laboratory (April 1981).



22. W. Breitung and K. O. Reil, In-Pile Vapor Pressure Measurements on UO₂ and (U,Pu)O₂ from 5000 to 8000 K, Proc. of Conf. on Science and Technology of Fast Reactor Safety, Guernsey, U. K., May 12-16, 1986, p. 501.



23. W. Breitung and K. O. Reil, In-Pile Vapor Pressure Measurements on UO₂ and (U,Pu)O₂, KfK-3939 Kernforschungszentrum Karlsruhe (Aug. 1985).



24. J. H. Harding, D. G. Martin, and P. E. Potter, Thermophysical and Thermochemical Properties of Fast Reactor Materials, Commission of the European Communities Report EUR 12402 EN (1989).



25. C. Ronchi, J. P. Hiernaut, R. Selfslag, and G. J. Hyland, Laboratory Measurement of the Heat Capacity of Urania up to 8000 K: I. Experiment, Nucl. Sci. Eng. 113, 1-19 (1993).



26. L. Leibowitz, M. G. Chasanov, L. W. Mishler, and D. F. Fischer, Enthalpy of Liquid Uranium Dioxide to 3500 K, J. Nucl. Mater. 39 115-116 (1971).



27. R. A. Hein and P. N. Flagella, Enthalpy Measurements of UO₂ and Tungsten to 3260 K, General Electric Report GEMP-578 (February 16, 1968).



28. M. H. Rand, R. J. Ackermann, F. Gronvold, F. L. Oetting, and A. Pattoret, The Thermodynamic Properties of the Urania Phase, Rev. Int. Hautes Temp. Refract. 15, 355-365 (1978).



29. International Working Group on Fast Reactors, Specialists' Meeting on Equations of State of Materials of Relevance to the Analysis of Hypothetical Fast Breeder Reactor Accidents, Harwell, U. K., June 19-23, 1978, IWGFR/26, IAEA (1978).



30. R. J. Ackermann, P. W. Giles, R. H. Thorn, J. Chem. Phys. 25, 1089 (1956).



31. V. E. Ivanov, A. A. Kruglykh, V. S. Pavlov, G. P. Kovtin, and V. M. Amonenko, Proc. Symp. On Thermodynamics of Nuclear Materials, Vienna, 1962, IAEA, p. 735, Vienna (1962).



32. R. W. Ohse, J. Chem. Phys. 44, 1375 (1966).



33. Y. A. Gorban, L. V. Pavlinov, and V. N. Vykov, At. Ehnerg. 22, 465 (1955), as referenced by R. J. Ackermann, E. G. Rauh, and M. H. Rand, A Re-Determination and Re-Assessment of the Thermodynamics of Sublimation of Uranium Dioxide, Proc. Symp. on Thermodynamics of Nuclear Materials, Julich, 1979, Vol.1, IAEA, pp.11-27, Vienna (1980).



34. R. J. Ackermann, E. G. Rauh, and M. S. Chandrasekhariah, J. Phys. Chem. 73, 762 (1969).



35. N. M. Voronov, A. S. Danilin, I. T. Kovalev, Symp. on Thermodynamics of Nuclear Materials Vienna 1962, IAEA, p. 789, Vienna (1962).



36. C. A. Alexander, J. S. Ogden, and G. C. Cunningham, Battelle Memorial Institute Report BMI-1789 (Jan. 1967), as referenced by R. J. Ackermann, E. G. Rauh, and M. H. Rand, A Re-Determination and Re-Assessment of the Thermodynamics of Sublimation of Uranium Dioxide, Proc. Symp. on Thermodynamics of Nuclear Materials, Julich, 1979 Vol.1, IAEA, pp.11-27, Vienna (1980).



37. A. Pattoret, J. Drowart, and J. Smoes, Proc. Symp. Thermodynamics of Nuclear Materials, Vienna, 1967, IAEA, p. 613, Vienna (1968).