Security and Privacy Notice Disclaimer

Emissivity and Optical Constants of Uranium Dioxide

Emissivity

The experiments of Bober et al.^1-6 for the emissivity, reflectivity, and optical constants of UO₂ in the solid and liquid phases provide the most reliable data for these properties. Bober, Karow, and Mueller³ commented that, within the limits of experimental error, their data for solid UO₂ agree with earlier emissivity measurements by Cabannes et al.,⁷ Held and Wilder,⁸ and Schoenes.⁹ The data in the range of 1000 K to the melting temperature (3120 K) indicate that the emissivity of both sintered and premelted solid UO₂ varies little with temperature and is only a weak function of wavelength. Thus, the constant total hemispherical emissivity ( ) that was suggested by Gentry¹⁰ and also by Harding et al.¹¹ is recommended:

The equation given by Bober, Karow, and Muller³ for the normal spectral emissivity of premelted solid UO₂ at the wavelength of 630 nm is recommended for wavelengths in the visible range:

For 1000 K 3120 K and 400 nm700 nm,

where T is in K. Values from this equation are given in Table 1 and shown in Figure 1.

Figure 1

The emissivity of liquid UO₂ is a function of both wavelength and temperature. For wavelengths in the visible range, however, the normal spectral emissivity of liquid UO₂ is approximately independent of wavelength. The recommended values as a function of temperature for this wavelength range are those calculated from an equation for a wavelength of 630 nm determined by Fink et al.¹²:

For 3120 K 6000 K and 400 nm 700 nm,

. Normal spectral emissivities calculated with this equation are tabulated in Table 2 and are included in Figure 1. Although Eq.(3) was derived to fit the data of Bober, Karow, and Muller³ at a wavelength of 630 nm, it also gives a good fit to more recent data^{1, 2} at wavelengths of 548, 514.5, 647, and 752.5 nm. However, the behavior of the emissivity in the infrared region differs considerably from Eq.(3). Bober et al.^{3, 6} found that the normal spectral emissivity at a wavelength of 10600 nm falls from 0.85 at 3120 K to 0.64 at 3670 K and to 0.4 at 4000 K. Further emissivity measurements of liquid UO₂ are needed in the infrared and far infrared region to confirm these results.

Optical Constants

Provisional recommendations are available from measurements by Bober, Singer, and Wagner.^{1, 2} They determined the optical constants for liquid UO₂ from 3100 to 3600 K and for single-crystal UO₂ at room temperature from reflectivity measurements in the spectral range of 450 to 750 nm. Their room temperature index of refraction values confirm the values of Ackermann et al.¹³ The average values for the index of refraction (n) and absorption coefficient (k) of UO₂ at room temperature and in the liquid region are

For T = 300 K,

For 3100 3600 K,

The uncertainty in the total hemispherical emissivity is ± 0.05.^10,11 Experimental uncertainties given by Karow and Bober⁶ for the normal spectral emissivity of premelted solid UO₂ at the wavelength of 630 nm increase from ~1% at 1500 K to 2% at 3000 K. In the liquid region, their uncertainties are 2.5 to 3%. Uncertainties of +3%/-10% are suggested¹² for extrapolation of Eq.(2) above 4200 K. Large scatter in the reflectivity data from which the optical constants are derived lead to uncertainties in the refractive index (n) of ± 10% and in the absorption constant (k) of ± 20%.

Emissivity of Solid UO₂

Data of Bober et al.^1-6 provide normal spectral emissivities of solid and molten UO₂ from 1000 to 4200 K and optical constants of molten UO₂ from 3000 to 4000 K. These are the most recent and reliable data and cover the largest temperature range. The normal spectral emissivities at a wavelength of 630 nm determined by Bober et al.^{3, 6} are in reasonable agreement with normal spectral emissivities of Cabannes et al.⁷ at a wavelength of 650 nm, and of Held and Wilder⁸ at wavelengths of 656 and 700 nm but disagree with earlier data of Claudson^14,15 and of Ehlert and Margrave,^15,16 as shown in Figure 1. The data of Claudson,^14,15 which show a decrease in the emissivity in the temperature range of 1000 to 2000 K, have been rejected in reviews by Fink et al.,¹² Gentry,^10,11 and Harding et al.¹¹ Cabannes et al.⁷ have suggested that the decrease with temperature observed by Claudson^{14, 15} was due to errors in the experimental technique. Unlike the data of Held and Wilder,⁸ which decrease with temperature above 2000 K, the data of Bober et al.^{3, 6} show little temperature dependence and no decrease with temperature above 2000 K.

Bober, Karow, and Muller³ found that the normal spectral emissivity of sintered UO₂ at a wavelength of 630 nm is slightly higher than that for premelted UO₂. From 1000 to 3120 K, they obtained an emissivity of 0.87 for sintered UO₂ and recommended Eq.(1) to represent the emissivity of premelted UO₂. Their data are supported by the measurements of Babelot et al.,¹⁷ who obtained an emissivity of 0.84 at a wavelength of 650 nm at the melting point, 3120 K.

Cabannes et al.⁷ determined emissivities at 300, 1200, and 1600 K for wavelengths ranging from 500 nm to the infrared region (10000 nm). They found little variation in emissivity with wavelength or temperature. From these data, they obtained total emissivities of 0.86, 0.90, and 0.90 at 300, 1200 and 1600 K, respectively. These total emissivities are consistent with the recommendation of Gentry^{10, 11} for a total emissivity of 0.85 ± 0.05. The temperature-dependent total emissivity for solid UO₂ determined by Mason¹⁸ is given in MATPRO:¹⁹

Total emissivities calculated with Eq.(6) increase from 0.79 at 300 K to 0.80 at 1000 K and 0.83 at 3120 K. These emissivities are consistently lower than the value given by Gentry.^{10, 11} However, above 700 K, they are within the uncertainty for the total emissivity recommended by Gentry.

Emissivity of Liquid UO₂

Bober, Karow, and Muller³ fit their data for the normal spectral emissivity of liquid UO₂ at a wavelength of 630 nm to a quartic equation:

where , and T is in K. Although Eq.(7) represents the experimental data of Bober, Karow, and Muller,³ this equation should not be used to extrapolate beyond 4200 K because it goes through an inflection point at 4831 K followed by an increasing slope that results in values greater than unity for temperatures above 5668 K. Consequently, Fink et al.¹² fit the data of Bober, Karow, and Muller³ to an equation with a functional form appropriate for extrapolation beyond the range of experimental data without introducing unphysical behavior. That equation is the recommended equation, Eq.(3). In the temperature range of experimental data, Eq.(3) reproduces the values given by Eq.(7) to within 0.14%. Equation (3) also provides a good fit to liquid emissivity data for other wavelengths in the visible range (= 459, 514.5, 647, and 752.5 nm).

The normal spectral emissivity of liquid UO₂ at wavelengths in the far infrared range shows an entirely different temperature behavior from that at wavelengths in the visible range. Data of Karow and Bober^{3, 6} show that for =10600 nm the normal spectral emissivity of liquid UO₂ falls from 0.85 at 3120 K to 0.64 at 3670 K and to 0.4 at 4000 K. Further data are required at wavelengths in the infrared region to confirm these results and determine total emissivities for the liquid.

Optical Constants

Figure 2

Optical constants of single-crystal UO₂ were determined at 300 K by Bober et al.^{1, 2,4} for comparison with values obtained by Ackermann et al.¹³ Ackermann et al. determined the index of refraction at room temperature in the ultraviolet region (at the wavelength of 260 nm) and in the visible range (at wavelengths from 450 to 800 nm). Figure 2 shows refraction indexes obtained from these measurements at wavelengths in the visible range. Room temperature values obtained from measurements by Ackermann et al. are consistently higher than those given by Bober et al. but these data are usually within the estimated 10% experimental uncertainty. The average of the values for the room temperature index of refraction from the data of Bober et al.¹ is 2.24. The average index of refraction from the values of Ackermann et al.¹³ is 2.45. These averages are within the 10% uncertainty given by Bober et al.^{1, 2} They are both higher than the room temperature index of refraction at a wavelength of 260 nm given by Ackermann et al. (1.95). Figure 2 shows that they are also consistently higher than values for liquid UO₂ at wavelengths in the visible spectrum. Absorption coefficients for UO₂ at room temperature, determined by Bober et al., decreased from 0.84 at a wavelngth of 458 nm to 0.60 at a wavelength of 752.5 nm with an average value of 0.7.

Figure 3

Bober, Singer, and Wagner^{1, 2} determined the optical constants for liquid UO₂ from reflectivity measurements with polarized light in the temperature range of 3000 to 4000 K at four visible wavelengths (458, 514.5, 647, and 752.5 nm) and at three angles of incidence (45^o, 58^o, and 71^o). Reflectivities measured as a function of temperature and wavelength showed considerable scatter with angle of incidence. Optical constants were calculated from the reflectivities at each temperature and wavelength for each of the three possible pairs of measurement angles (45^o and 58^o, 45^o and 71^o, 58^o and 71^o). Then these three sets of values were averaged to obtain optical constants for each wavelength and temperature. Figures 3 and 4 show, respectively, the average refractive index and average absorption coefficient for liquid UO₂ for four visible wavelengths as a function of temperature. Both optical constants decrease with increasing temperature. Based on these data, Bober et al.^{1, 2} proposed average values for the refractive index and absorption coefficient for wavelengths in the visible range and temperatures from 3100 to 3600 K. Their average values are n=1.7 and k = 0.8.

Figure 4

From the scatter in their reflectance data, Bober et al.^{1, 2} estimated the uncertainty in the refractive index, n, as ± 10% and the uncertainty in the absorption coefficient, k, as ± 20%. Bober et al.¹ commented that the accuracy of the absorption coefficient, k, is influenced more by measurement errors than that of the refractive index, n. The equations used to calculate the optical constants are based on the assumption of an ideal optically smooth surface, which is difficult to attain. Scatter in the experimental data was attributed to imperfections of the reflecting surface, variations in the angle of incidence arising from oscillations of the liquid surface, and the formation of a meniscus. With increased temperature, surface disturbances from vaporization and gas bursts added to the difficulty of the measurements. The increased difficulty is apparent in the decreased consistency in the reflectance data above 3500 K.

1. M. Bober, J. Singer, and K. Wagner, Determination of the Optical Constants of Liquid UO₂ from Reflectivity Measurements, Proc. Eighth Symp. on Thermophysical Properties, Gaithersburg, MD, 1981, Vol II, pp. 234-244, ASME (1982).



2. M. Bober, J. Singer, and K. Wagner, Bestimmung der Optischen Konstanten von Geschmolzenen Kernbrennstoffen, J Nucl. Mater. 124, 120-128 (1984).



3. M. Bober, H. U. Karow, and K. Muller, Study of the Spectral Reflectivity and Emisssivity of Liquid Ceramics, High Temp. - High Pressures 12, 161-168 (1980).



4. M. Bober, Spectral Reflectivity and Emissivity of Solid and Liquid UO₂ as a Function of Wavelength, Angle of Incidence, and Polarization, High Temp. - High Pressures 12, 297-306 (1980).



5. M. Bober and H. U. Karow, Measurements of Spectral Emissivity of UO₂ Above the Melting Point, Proc. Seventh Symp. on Thermophysical Properties, Gaithersburg, MD, 1977, pp. 344-350, ASME (1978).



6. H. U. Karow, and M. Bober, Experimental Investigations into the Spectral Relectivities and Emissivities of Liquid UO₂, UC, ThO₂, and Nd₂O₃, Thermodynamics of Nuclear Materials 1979 Vol I, Proc. Symp. Julich, 1979, pp. 155-169, IAEA (1980).



7. F. Cabannes, J. P. Stora, and J. Tsakiris, Facteurs de Reflexion et d'Emission de UO₂ a Haute Temperature, C. R. Acad. Sc. Paris, 264B, 45-48 (1967).



8. P. C. Held and D.R. Wilder, High-Temperature Hemispherical Spectral Emittance of Uranium Oxides at 0.65 and 0.70 µm, J. Am. Ceramic Society 52, 152-185 (1969).



9. J. Schoenes, Optical Properties and Electronic Structure of UO₂, J. Appl. Phys. 49 1463-1465 (1978).



10. P. J. Gentry, Report ND-P-6887 (W) (1981), as referenced by 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).



11. 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).



12. J. K. Fink, M. G. Chasanov, and L. Leibowitz, Transport Properties of Uranium Dioxide, ANL-CEN-RSD-80-4, Argonne National Laboratory (April 1981).



13. R. J. Ackermann, R. J. Thorn, and G. H. Winslow, Visible and Ultraviolet Absorption Properties of Uranium Dioxide Films, J. Opt. Soc. Am. 49, 1107 (1959).



14. T. T. Claudson, Emissivity Data for Uranium Dioxide, Report AW-55414 (Nov. 1958), as referenced in Uranium Dioxide Properties and Nuclear Applications, J. Belle, Ed.,. pp. 196-197, USAEC (1961).



15. J. Belle, Ed., Uranium Dioxide Properties and Nuclear Applications, pp. 196-197, US AEC (1961).



16. T. C. Ehlert and J. L. Margrave, Melting Point and Spectral Emissivity of Uranium Dioxide, J. Am. Ceram. Soc. 41, 330 (1958), as referenced in Uranium Dioxide Properties and Nuclear Applications, J. Belle, Ed., pp. 196-197, USAEC (1961).



17. J. F. Babelot, G. D. Brunne, P. R. Kinsman, and R. W. Ohse, Atomwirt-Atomtech 22, (No. 7-8), 387 (1977).



18. R. E. Mason, Fuel Emissivity, CDAP-TR-78-039, Idaho Engineering Laboratory (1978).



19. J. K. Hohorst, Ed., SCADAP/RELAP5/MOD2 Code Manual, Vol. 4: MATPRO- a Library of Materials Properties for Light-Water-Reactor Accident Analysis, NUREG/CR-5273 (1990).