# A Study of the Thermodynamic Properties of Nd-C and Ce-C TRISO Fission Product Binary Systems
## 2 Materials and Methods
### DSC Calibration  
The STA DSC-TGA was calibrated with one measurement crucible containing the calibrant and one empty, reference crucible, using the Netzsch DSC/DTA calibration kit (sourced from [PERSON] part no. 6.223.5-91.3.00, Bavaria, Germany). The calibrants used in this study and their melting temperatures are: In (156.60 \({}^{\circ}\)C), Zn (419.53 \({}^{\circ}\)C), Al (660.32 \({}^{\circ}\)C), Ag (961.78 \({}^{\circ}\)C), and Au (1064.18 \({}^{\circ}\)C). Experiments above the gold melting temperature should be reviewed with care due to potential extrapolation errors in the DSC measurements. Nickel, with a melting temperature of 1455.00 \({}^{\circ}\)C, was initially included as a calibrant but was found to chemically react with the boron nitride crucibles and excluded. An optical image of the reacted nickel calibrant and boron nitride crucible is shown in Figure 9. A study by [PERSON] et al. [48] reacted hexagonal BN powder with nickel(II) nitrate hexahydrate in an aqueous solution to form Ni(II) modified porous BN, which was eventually annealed into a solid solution. It was shown that the nickel adhered to the outer surface of the BN via B-O-Ni bonding [48]. Therefore, it is suspected that oxygen played a role in the chemical interaction observed, either via an oxide layer on the nickel calibrant or the BN crucible. Another study by [PERSON] et al. [49] demonstrated that nickel oxide can decompose hexagonal BN into boron oxide, which may have also contributed to the observed phenomenon. Calibrant melting temperatures were confirmed through three heating cycles 100 \({}^{\circ}\)C above and below the reported melting temperature at a heating rate of 5 \({}^{\circ}\)C/min, per the recommendation by [PERSON] [50] and previous DSC experience using the STA instrument [44,45]. The onset temperature from the first heating cycle was discarded as the test system had not reached thermodynamic equilibrium. The average of the onset temperatures of the second and third heating cycles was used to determine the phase transition temperatures of the calibrants, as analyzed by the Netzsch Proteus software v.6.1.0 [51]. The enthalpy of formation values were calculated as the area under the second and third heating cycle peaks similarly using the Netzsch Proteus software [50,51]. Figure 10 shows the DSC plot obtained from the silver calibration test, demonstrating the difference in DSC response of the first heating cycle compared to the second and third, while Figure 11 demonstrates the determination of the phase transition onset temperature and enthalpy values. Figure 8: Schematic of the STA interior showing placement of crucibles and thermocouple. Figure 11: Onset temperature and enthalpy measurements of the second heating cycle of the silver calibrant. Figure 10: DSC response of the silver calibrant from the [PERSON] calibration kit 6.223.5–91.3.00 using boron nitride crucibles. Figure 9: Test Ni-2-1 post-DSC measurement of nickel calibrant using BN crucibles. Sample appears to have reacted with the crucible. The Netzsch Temperature Calibration program [50] was used to fit a second-order polynomial to the calibrant phase transition temperatures. This was chosen over the linear approximation as it was more accurate for the 600 \({}^{\circ}\)C to 900 \({}^{\circ}\)C range that encompassed the majority of the planned experiments. The calibration curve is shown in Figure 12 as fit to Equation (1) and the results of the calibration analysis using the Netzsch Proteus software are shown in Table 5. Note that the scale is relatively small, with the largest deviation from the regression being the silver calibrant at approximately 1.8 \({}^{\circ}\)C. The regression fit of the temperature calibration curve is represented by  
\[T_{Corr}=10^{-3}b_{0}+10^{-5}b_{1}T_{Exp}+10^{-8}b_{2}T_{Exp}{}^{2}, \tag{1}\]  
where \(b_{0}\), \(b_{1}\), and \(b_{2}\) are the temperature calibration coefficients determined through the regression analysis and \(T_{Exp}\) is the measured temperature [50; 51].