# A Study of the Thermodynamic Properties of Nd-C and Ce-C TRISO Fission Product Binary Systems
## 3 Results
### Experimental Results
#### 3.4.1 Neodymium-Carbon
\begin{table}
\begin{tabular}{c c c c} \hline
**Compound** & **Phase Transition** & **Transition Temperature [\({}^{\circ}\)C]** & **References** \\ \hline Ce\({}_{0.8}\)C\({}_{0.2}\) & Eutectic & 878.6 & This work \\ Ce\({}_{0.68}\)C\({}_{0.32}\) & \(\gamma\)Ce + Ce\({}_{2}\)C\({}_{3}\) \(\rightleftharpoons\) Ce\({}_{2}\)C\({}_{3}\) + L & 714.7 & This work \\ Liquidus & 857 & This work \\ Ce\({}_{0.4}\)C\({}_{0.6}\) & Ce\({}_{2}\)C\({}_{3}\) \(\rightleftharpoons\)\(\beta\)CeC\({}_{2}\) + L & 1529.9 \(\pm\) 50 & [19; 39] \\ Ce\({}_{0.4}\)C\({}_{0.6}\) & Ce\({}_{2}\)C\({}_{3}\) \(\rightleftharpoons\) L & 1700 & [32] \\ Ce\({}_{0.33}\)C\({}_{0.67}\) & \(\alpha\)CeC\({}_{2}\) \(\rightleftharpoons\)\(\beta\)CeC\({}_{2}\) & \(1100\pm 10\) & [33] \\  & & 1138.7 & This work \\ Ce\({}_{0.33}\)C\({}_{0.67}\) & \(\beta\)CeC\({}_{2}\) \(\rightleftharpoons\) L & 2250 \(\pm\) 20 & [25] \\  & & 2270 \(\pm\) 20 & [33] \\  & & 2290.3 \(\pm\) 60 & [19; 39] \\ Ce\({}_{0.3}\)C\({}_{0.7}\) & Ce\({}_{2}\)C\({}_{2.34}\) \(\rightleftharpoons\) L & 2270 \(\pm\) 15 & [25; 32] \\ \hline \end{tabular}
\end{table} 
Table 9: Measured phase transition temperatures of Ce-C from this work and the open literature. transitions from [PERSON] et al. are largely speculative and should be considered for reference only. The 40 mol%C sample provides the only point for direct comparison with [PERSON] et al. at 39 mol%C. The liquidus phase transition temperature for this work was found to be 1274.6 \({}^{\circ}\)C compared to 1200 \({}^{\circ}\)C reported experimentally by [PERSON] et al., and aligned well with the predicted phase transition [22]. Nd\({}_{2}\)C\({}_{3}\) exists as a body-centered cubic similar to the Pu\({}_{2}\)C\({}_{3}\)[24], whereas the low-temperature Nd phase exists in the hexagonal close-packed crystal structure [22]. [PERSON] et al. noted that the body centered cubic structures of rare earth carbide compounds of higher carbon molarity appear to experience greater oxidation [43]. Therefore, potential oxidation would be expected to react with Nd\({}_{2}\)C\({}_{3}\) to a greater extent in the solid solution at 40 mol%C than the hexagonal Nd, which is expected to be seen as an increase in the measured phase transition temperature. Additionally, it appears that the eutectic temperature is experimentally higher than predicted. Average values of the onset temperatures of the eutectic phase transition for Nd1.5, Nd2, Nd2.5, and Nd3 gives a eutectic phase transition of 725.1 \({}^{\circ}\)C. Nd1 and Nd3.5 were omitted as their low-temperature phase transitions are significantly higher and may indicate a need to repeat the DSC measurements of these data. The low-temperature phase transitions found from tests of these samples were very inconsistent. Nd3.5 showed a strong DSC peak at 825.1 \({}^{\circ}\)C; however, a change in the DSC response is observed occurring at approximately 730 \({}^{\circ}\)C, aligning well with the neighboring molar composition eutectic temperature, but an onset temperature could not be reported. The La-C system also has a higher eutectic of approximately 806.9 \({}^{\circ}\)C [18], which may indicate similarly higher eutectic transitions for other rare earth carbides. Phase transitions at compositions near the eutectic composition are known to be difficult to measure [54]. Therefore, Nd1 and Nd3 should be re-tested with a lower heating rate of 1 \({}^{\circ}\)C/min or less, as suggested by [PERSON] [54], to improve DSC responses in mixed solids. [PERSON] et al. noted that axial ratios, c/a, of lanthanum and neodymium converged at 1.619 and 1.621 at observed phase transition temperatures, and both exhibit a hexagonal close-packed crystal structure in the low-temperature phase, indicating likely similar phase transition behavior [18]. Additionally, the outer valence electrons of neodymium and lanthanum exist in the same configuration, but their electron configurations can vary in other orbitals [55]. Therefore, they are expected to share some bonding and phase transition behavior.