# A Study of the Thermodynamic Properties of Nd-C and Ce-C TRISO Fission Product Binary Systems
## 3 Results
### Experimental Results
#### 3.4.2 Cerium-Carbon  
A temperature-composition isobaric phase diagram for the Ce-C system is shown in Figure 20, providing a comparison of the results from the cerium carbide DSC measurements completed in this work against the open literature, and Figure 21 showing the low-temperature eutectic. The basis for the predicted phase changes is derived from the work by [PERSON] et al. [19]. Note that the predicted phase equilibria by [PERSON] et al. [19] are speculative and should be considered for reference only. The 67 mol%C sample provides the only point for direct comparison with [PERSON] and [PERSON] [33]. The \(\alpha\)CeC\({}_{2}\) to \(\beta\)Ce\({}_{2}\) transition at this molar composition is 1138.7 \({}^{\circ}\)C \(\pm\) 32.7 \({}^{\circ}\)C for this work, compared to 1100 \({}^{\circ}\)C experimentally reported by [PERSON] and [PERSON] [33], and the predicted phase transition of 1099.8 \({}^{\circ}\)C reported by [PERSON] et al. [19]. It is suspected that potential oxidation effects delayed the onset of the phase transition. Additionally, the transition in crystal structure from body-centered tetragonal to face-centered cubic results in a density increase of the sample and the associated kinetics may have delayed phase transition measurements. X-ray diffraction and BSEM performed by [PERSON] et al. on similar samples and in particular the 80 mol%C sample demonstrated a decomposition into CeC\({}_{2}\) + C solid solution [43]. A similar decomposition may have occurred with the sample tested in this work, which could affect the thermocouple response and resulting reported phase transition temperature.  
The low-temperature eutectic transition and liquidus measurements from Ce1.5 agree relatively well with the predicted phase transitions by [PERSON] et al. [19]. However, the eutectic temperature appears to be significantly higher than the predicted transition, which is consistent with the Nd-C system. It is likely that this is caused by similar phenomena affecting the Nd-C measurements; however, given the lower-temperature eutectic measured from Ce1.5 and significant differences compared to the predicted phase diagram, Ce2 should be re-tested at a lower heating rate to improve the DSC response and confidence in the measurement.  
Figure 19: Predicted Nd-C phase diagram and experimental data by [PERSON] et al. [22] from 0 to 50 mol%C, with additional experimental data by [PERSON] [27], and this work.  
Similar to neodymium, [PERSON] et al. also noted that the axial ratios of lanthanum and cerium converged at 1.619 and 1.618 at observed phase transition temperatures [18]. However, cerium exists as a face-centered cubic structure at low temperatures, which will differ its behavior relative to lanthanum [18]. While cerium shares the same outer electron configuration with lanthanum, other orbitals differ [55]. Therefore, similar to neodymium, cerium is expected to share some behavior with the lanthanum system, as observed with the results in this study.  
Figure 21: Predicted Ce-C phase diagram by [PERSON] et al. [19], with experimental data points from this work.  
Figure 20: Predicted Ce-C phase diagram and some experimental data by [PERSON] et al. [19], with experimental data points from this work, [PERSON] and [PERSON] [33], [PERSON] et al. [32], [PERSON] et al. [25], [PERSON] and [PERSON] [34], and [PERSON] et al. [35].