# A Study of the Thermodynamic Properties of Nd-C and Ce-C TRISO Fission Product Binary Systems
## 1 Introduction
### Objectives  
The thermodynamic assessment by [PERSON] et al. [22] demonstrated the most complete phase diagram reported in the open literature for the Nd-C system, incorporating existing measurements of specific molar concentrations and adding new experimental data. Similarly, [PERSON] et al. [19] performed a comprehensive review of existing literature and applied the Calphad method to generate the most comprehensive phase diagram of the Ce-C system in the open literature. Both thermodynamic systems are similar in structure and behavior, as is expected of light rare earth elements [19; 20; 23; 28; 34]. These two thermodynamic analyses, along with the works described earlier, provide the basis of comparison for the present work. The goal of this work is to report new, experimental phase transition temperatures and enthalpies of fusion for the 0-40 mol\({}^{\circ}\)C range of the Nd-C system and Ce-C systems. Other molarities are used to validate measurements against existing experimental values reported in the open literature. Measurements are performed via Differential Scanning Calorimetry  
Figure 4: Ce-C predicted phase diagram by [PERSON] et al. [19], with experimental data by [PERSON] and [PERSON] [33], and [PERSON] et al. [35]. (DSC), and DSC crucible materials are proposed. The experimental data collected from this campaign are expected to inform the creation of thermodynamic models to accurately predict fission product behavior. The Thermodynamics of Advanced Fuels-International Database (TAF-ID) was developed using the Calphad method to perform thermodynamic calculations of various standard and accident scenarios on nuclear fuel materials [36]. The results from this work will expand the TAF-ID database and improve modeling of Nd-C and Ce-C rare earth carbide compounds in TRISO fuel. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Item** & **Mol\%C** & **Mol\%Nd** & **Equilibrium** & **Temperature [\({}^{\circ}\)C]** & **Method** & **Ref.** \\ \hline
1 & 0 & 1 & \(\alpha\)Nd \(\rightleftharpoons\beta\)Nd & 862 & Calorimetry; & [22] \\
2 & 0 & 1 & \(\beta\)Nd \(\rightleftharpoons\) (L) & 1001.67 & Calorimetry; & [22] \\ \hline
3 & 37 & 63 & Nd\({}_{2}\)C\({}_{3}\) + (L) \(\rightleftharpoons\) (L) & 1100 \(\pm\) 0.5 & BSEM, Elemental Analysis; & [22, 37] \\
4 & 39 & 61 & Nd\({}_{2}\)C\({}_{3}\) + (L) \(\rightleftharpoons\) (L) & 1200 \(\pm\) 0.5 & BSEM, Elemental Analysis; & [22, 37] \\
5 & 45 & 55 & Nd\({}_{2}\)C\({}_{3}\) + (L) \(\rightleftharpoons\) (L) & 1350 \(\pm\) 0.5 & BSEM, Elemental Analysis; & [22, 37] \\
6 & 49 & 51 & Nd\({}_{2}\)C\({}_{3}\) + (L) \(\rightleftharpoons\) (L) & 1500 \(\pm\) 0.5 & BSEM, Elemental Analysis; & [22, 37] \\
7 & 50 & 50 & Nd\({}_{2}\)C\({}_{3}\) + (L) \(\rightleftharpoons\) (L) & 1500 \(\pm\) 0.5 & BSEM, Elemental Analysis; & [22, 37] \\
8 & 60 & 40 & Nd\({}_{2}\)C\({}_{3}\) + (L) & 1620 \(\pm\) 40 & Assessed; & [24] \\ \hline
9 & 67 & 33 & \(\alpha\)NdC\({}_{2}\)\(\rightleftharpoons\beta\)NdC\({}_{2}\) & 1150 \(\pm\) 20 & Assessed; & [24, 38] \\
10 & 67 & 33 & \(\beta\)NdC\({}_{2}\) – C \(\rightleftharpoons\) (L) & 2260 \(\pm\) 30 & Assessed; & [24, 38] \\
11 & 67 & 33 & NdC\({}_{2}\) (L) & 2260 & Estimated; & [23] \\
12 & 67 & 33 & NdC\({}_{2}\) (L) & 2290 \(\pm\) 10 & Knudsen Cell Effusion; & [25] \\ \hline
13 & 70 & 30 & NdC\({}_{2,29}\) (L) & 2300 \(\pm\) 15 & Knudsen Cell Effusion; & [25] \\ \hline \end{tabular}
\end{table} 
Table 1: Neodymium carbide phase transition temperatures in the open literature.