The thermal conductivity of ThO2 up to 1,800 K is reasonably well established (Table 12). Most of the data were derived from thermal diffusivity measurements. Peterson and Curtis [26] compiled data on thermal conductivity of ThO2 to about 2,000 K. Bakker et al. [38] systematically evaluated the data of various authors. They analyzed the data of Pears [102], Rodriguez et al. [82], McEwan and Stoute [103], Belle et al. [104], Peterson et al. [105], Faucher et al. [108], Kingery et al. [109], McElroy et al. [110], ARF [111], Weilbacher [112] and DeBoskey [113].

Assessing the A and B parameters has the advantage that data sets that were determined in different temperature ranges can easily be compared and that data sets with extremely large or small A and B parameters can be rejected. On this basis, Bakker et al. [38] rejected many data and accepted only that data which shows a small variation between the A and B parameters. Hence data of Murabayashi [114], McElroy et al. [110], Koenig [115] and Springer et al. [57] are only used in their assessment. The A and B parameters were averaged, which yielded A = 4.20 x 10-4 mKW-1 and B = 2.25 x 10-4 mW-1 and these values can be used as the recommended values for 95 % dense ThO2 in the temperature

range between 300 and 1,800 K. Hence, thermal conductivity of pure ThO2 can be expressed as:

kThO2 (W/mK) = (4.20 x 10-4 + 2.25 x 10-4 T) 1 (49)

Belle and Berman [12] reported the following equation for the thermal con­ductivity of 100 % dense ThO2 in the temperature range 298-2,950 K,

kThO2(W/mK) = (0.0213 + 1.597 x 10-4 Г)-1 (50)

To evaluate the thermal conductivity beyond 2,950 K, Belle and Berman first obtained an expression for thermal diffusivity up to 2,950 K as

«ThO2 (m2/s) = (-34191.1 + 561.28 T)-1 (51)

Assuming there is no discontinuity, Belle and Berman [12] extrapolated thermal diffusivity data values from 2,950 to 3,400 K. Their results along with others are shown in Fig. 12. The only high temperature data available is that of Weilbacher [112] which was fitted by a dashed line. The fitted data of Cozzo et al. [95] and Kutty et al. [84] represent the lowest and highest values in the low temperature range.

Figure 13 shows the calculated value of thermal conductivity for fully dense ThO2 from ambient to 3,400 K. There is a sudden increase in conductivity at 2,950 K discontinuity, from 2.03 to 3.05 W/m K, which represents the change in the heat capacity occurring at that point. The lowest thermal conductivity in the

Fig. 12 Thermal diffusivity of ThO2 as a function of temperature. Data of various authors are plotted together. Dotted line are fitted data of Cozzo et al. [95], dashed line that of Weilbacher [112] and solid line that of Kutty et al. [84]

entire temperature range was 2.03 W/m-K at 2,950 K. Belle and Berman [12] estimated minimum values in conductivity using Eq. (36). They assumed that:

1. Phonon velocity can be approximated to (E/q)05,

2. Equation dealing temperature variation in E can be extrapolated to higher temperatures, and

3. Minimum value of phonon mean free path can be approximated to lattice parameter.

They calculated the minimum in thermal conductivity for ThO2 at 2,950 K as 2.07 W/m-K which is very near to the value (2.03 W/m-K) shown in Fig 13. Thermal conductivity data of UO2 [50] and PuO2 [6, 40] are also shown in the same figure. The lowest value for UO2 is 2.19 W/m-K at 1,970 K. The upswing in

20

■ Murabayashi et al. • Moore et al. a Pillai and Raj

♦ ARF ^ Kingery a Bakker et al. v Jain et al. Ф Murti and Mathews 4- Lu et al. > Czzo et al. Ф Tecdoc-1496 ☆ Weilbacher ев Kutty et al.

і14 —

A*"

2

500 1000 1500 2000 2500 3000

Temperature, K

thermal conductivity in UO2 at * 1,970 K can be explained in terms of the electronic contribution. On the other hand, increase in thermal conductivity beyond 2,950 K in ThO2 is not result of electronic contribution, but is associated with increase in heat capacity. Thermal conductivity data of ThO2 reported by various authors are shown in Fig. 14.