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We calculated the temperature variation of this sample using FlexPDE and, as input, the values of thermal conductivity and emissivity given in the manual of ...
Thermal conductivity measurements ANL, rapid communication A. Davila, A.C.C. Villari, J. Greene, T. Burtseva, J.A. Nolen ANL Thermal conductivity measurements were performed at the ANL target laboratory using the method described in the preceding report and the reference [J.P. Greene et al., Nucl. Phys. A746 (2004)425c]. A new grafoil sample was measured in order to determine the characteristics of the electron beam. This procedure was undertaken two times, firstly at the beginning of the measurements series and secondly at the end. This is important in order to verify that the beam properties did not change during the period of measurements. The measurements took place from June 2nd to June 13th. During this period of time, a new sample of UC made at ANL was measured several times. UC sample characteristics: UC2-ALB-C ANL-W Uranium 325 mesh + Alb + C 200 mesh. Sample series number #5. Before heating: 13.03 mm diameter, 0.93 mm thickness, 0.6518 g weight. After heating: 12.45 mm diameter, 0.97 mm thickness, 0.6291 g weight. Grafoil characteristics: 0.030” thickness and ½” diameter.

Grafoil: The Grafoil sample data is presented in Fig. 1 and Fig. 2 for bottom and top temperature behaviors as a function af the electron beam power.

Fig 1 and 2: Top and bottom temperatures of the grafoil sample before and after heating. The continuous lines represent a power function which fits all data obtained independently of the time of the measurement. The reproducibility of the measurements

is relatively good. The error we found for the temperature was estimated by the standard deviation of all data points with respect to the fitting curve. This is equal to σl = 16.5 K for the lower temperature and σh = 19.8 K for the higher one. We calculated the temperature variation of this sample using FlexPDE and, as input, the values of thermal conductivity and emissivity given in the manual of grafoil. The results, compared with the lower and higher temperatures of the samples are shown in figure 3 and 4.

Figure 3: Lower and higher temperature differences plotted as a function of the beam power. The black dots correspond to the fit using FlexPDE. The first and last black dots can match experimental data if the thermal conductivity is decreased/increased by 30% W/m-k of the original value quoted by Graftech.

Figure 4: Lower (red) and Higher (blue) temperatures measured experimentally compared with the calculations using FlexPDE (black dots).

In this calculation, the power distribution of the electron beam was considered to be of Gaussian type with a FWHM = 6.4 mm. Compared with the previous calculations (6.0 mm), it changed by 0.4 mm. This can be explained by a change of the optical conditions

of the beam after the replacement of the filament. This new beam spot value was used in the following calculations for UC samples.

Uranium Carbide: The uranium carbide sample was irradiated four times on different days and after opening and closing the vacuum system. Also the pyrometer was re-positioned for each measurement. We believe that, with this procedure, a good estimation of errors related with the positioning of the pyrometer of the results can be made. This is the main factor which affects the reproducibility of our results. Another factor to be considered is the positioning of the sample in the holder, with respect to the electron beam center. This was verified in all measurements. A clear hottest zone appears in the center of the sample, if it is correctly positioned. Data was taken during heating and cooling of the sample. Also we waited for the equilibrium to be established before reading the pytometer. Fig. 5 and 6 show the data obtained as a function of the electron beam power. The continuous line is the fit using a power law function.

Figure 5 and 6: Lower and Higher temperatures of the UC sample. Different colors represent different sets of measurements, done at different days. The standard variation of the data was calculated as: σl = 10.5 K (lower) and σl = 13.2 K (higher) FlexPDE was used in order to evaluate the thermal conductivity. The diameter and thickness of the sample after heating were used in the calculations. The result of the fit is shown in Fig. 7 and 8.

Figure 7: Lower (red) and Higher (blue) temperatures of the UC sample as a function of the beam power. The black dots correspond to the FlexPDE fit.

Figure 8: Higher and Lower temperature difference as a function of the electron beam power. The red dots represent the FlexPDE fit.

The obtained thermal conductivities, for each calculated beam power (corresponding to an averaged temperature) is plotted in Fig. 9. In these calculations, the emissivity of UC was always set to one. This value gave the best fits of the experimental data. Figure 9: Thermal conductivity of UC sample as a function of the averaged temperature of the sample.

Conclusion: The thermal conductivity of the UC sample studied averaged around 11.5 W/mK. Its variation with temperature seems to be less steep than the preceding one. The sample did not presented any detectable change of thermal conductivity during the period of measurements.