# A Study of the Thermodynamic Properties of Nd-C and Ce-C TRISO Fission Product Binary Systems
## 1 Introduction
### Review of Neodymium-Carbon Predicted and Experimental Data  
The neodymium-carbon system has been reported sparingly in the open literature with little experimental data to characterize the full phase diagram. Figure 3 illustrates the predicted phase diagram by [PERSON] et al. [22] with limited experimental data in reference to the following discussion. Thermodynamic properties have been approximated via phase equilibria modeling and prediction based on trends in the La-C, Ce-C, and Pr-C systems [22; 23; 24]. [PERSON] et al. [18] reported hexagonal Nd and cubic Nd\({}_{2}\)C\({}_{3}\) phases in the 0 to 50 mol%C range via X-ray diffraction. [PERSON] et al. [22] added new data within this range by melting neodymium ingots in a graphite crucible at 1100 \({}^{\circ}\)C, 1200 \({}^{\circ}\)C, 1350 \({}^{\circ}\)C, and 1500 \({}^{\circ}\)C until carbon-saturated alloys were produced at 37, 39.3, 44.8, 49.7, and 49.2 mol%C, respectively [22]. The phases present in these samples were confirmed via back-scattering scanning electron microscopy (BSEM) [22].  
Figure 2: La-C predicted phase diagram by [PERSON] et al. [19], with experimental data by [PERSON] et al. [20] and [PERSON] et al. [21].  
All other data available in the literature focus on the 50 to 100 mol%C range of the phase diagram with emphasis on the stoichiometric compounds NdC\({}_{2}\) and Nd\({}_{2}\)C\({}_{3}\). [PERSON] and [PERSON] [24] performed an analysis of this system and described the Nd\({}_{2}\)C\({}_{3}\) as cubic, analogous to the Pu\({}_{2}\)C\({}_{3}\) crystal structure, existing in the 54 to 60 mol%C range with an approximate melting temperature of 1620 \(\pm\) 50 \({}^{\circ}\)C. The low-temperature \(\alpha\)NdC\({}_{2}\) phase is reported as tetragonal with the CaC\({}_{2}\) crystal structure, and experiences a phase transition to \(\beta\)NdC\({}_{2}\), which has a cubic CaF\({}_{2}\) structure [24]. Various temperatures were reported for this phase transition, with the assessed value reported by [PERSON] and [PERSON] as 1150 \(\pm\) 20 \({}^{\circ}\)C for the \(\alpha\)NdC\({}_{2}\) to \(\beta\)NdC\({}_{2}\) phase transition and a postulated melting temperature greater than 2260 \({}^{\circ}\)C [24]. They also reported an assessed NdC\({}_{2}\)-C eutectic phase transition at 2260 \(\pm\) 30 \({}^{\circ}\)C [24].  
[PERSON] and [PERSON] synthesized Nd\({}_{2}\) by combining Nd and C powders into pressed pellets and heating them to 1200 \(\pm\) 2 \({}^{\circ}\)C, confirming the presence of the tetragonal crystal structure at this temperature and reporting an enthalpy of formation of \(-\)29.2 \(\pm\) 1.4 kJ/mol [23; 28]. [PERSON] et al. [25] also provided additional phase transition temperatures and enthalpies of formation measurements around the NdC\({}_{2}\) compound that aligned well with those reported by [PERSON] and [PERSON]. [PERSON] et al. [29] mixed NdO and graphite into pellets and heated the samples to produce a desired partial pressure of CO\({}_{\text{(g)}}\) and measured the resulting NdC\({}_{2}\) enthalpy of formation as \(-\)90.8 \(\pm\) 6 kJ/mol. This measurement appears as an outlier compared to other enthalpy measurements of the same compound, which is similarly true for the CeC\({}_{2}\) measurement also by [PERSON] et al. [30]. [PERSON] et al. [19] excluded this enthalpy data from their assessment of the Ce-C system for this reason. Therefore, these data are included for completeness but are excluded for comparison with this work. A summary of phase transition temperatures and enthalpies found in the open literature for the Nd-C system is provided in Tables 1 and 2.