# A Study of the Thermodynamic Properties of Nd-C and Ce-C TRISO Fission Product Binary Systems
## 1 Introduction  
### 1.1 Background  
TRi-structural ISOtropic (TRISO) particle fuel is purported to change the application of traditional defense in depth concepts on the operational safety of nuclear power reactors, primarily through increased reliance on fuel-driven fission product retention. Typical nuclear power reactors credit a super structure, usually of reinforced concrete and air-tight, as a containment boundary against radiological releases. However, many TRISO applications rely upon a functional containment design, where the fuel itself is credited towards this function. Therefore, it is imperative that fuel performance modeling is developed at a higher level of predictability than conventional fuels to ensure the safety of TRISO-fueled reactors.  
The basic structure of a TRISO fuel particle is shown in Figure 1, illustrating the size of each layer. The fuel kernel most commonly proposed in the commercial sector is a solid Uranium Oxycarbide (UCO) mixture of uranium carbide and uranium oxide. The kernel provides the fissile material for the fuel and assists in fission product retention, while theporous buffer layer provides some accommodation for fission product gases and kernel swelling, permitting gaseous volumetric expansion and mitigating overpressurization of the fuel particle [1]. The Inner Pyrolytic Carbon (IPyC) layer assists in fission product retention within the particle, seals the fuel kernel from external contaminants during fabrication, and provides a deposition surface for the outer layers [1,2]. The SiC layer, which is deposited on the exterior of the IPyC layer, provides structural integrity to the fuel and is the primary barrier to solid fission product release [1,3]. Finally, the Outer Pyrolytic Carbon (OPyC) layer protects the SiC layer from external hazards, provides an additional barrier to fission product release, and can be used as a bond surface for large fuel compact fabrication [1].  
Pressure vessel failure due to fission gas overpressurization [1,2,4,5,6];  
Kernel migration [1,2,4];  
Fission product chemical attack of the SiC layer [1,2,5,7,8,9,10,11,12,13,14,15,16,17,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19  
Needymium and cerium carbides are such compounds that have significant gaps in experimental data to validate predicted behavior. These compounds play a significant role in TRISO fuel performance as insufficient oxygen stoichiometry in the fuel kernel has been proven to lead to neodymium and cerium directly attacking the SiC layer through carbide compound precipitation [1; 9; 15; 16]. Cerium is also an important fission product as low inventories can be indicative of abnormal fuel kernel size or low initial fissile content, thereby implying anomalies in the manufacturing process [17].  
Needymium and cerium are rare earth elements that fall under the lanthanoid group of elements, and follow similar thermodynamic behavior to their parent element and its compounds [18]. The lanthanum carbide system has been extensively investigated experimentally by [PERSON] et al. [18], providing data to validate most phase transition temperatures predicted by the calculated phase diagram by [PERSON] et al. [19]. The La-C phase diagram proposed by [PERSON] et al. [19] is provided in Figure 2. The La-C system contains a low-temperature eutectic transition at approximately 20 mol%C and 806.9 \({}^{\circ}\)C, and a high temperature eutectic transition at approximately 68-70 mol%C and 2268.6 \({}^{\circ}\)C [19]. Two stoichiometric phases are also present, the sesquicarbide phase at 60 mol%C and 1415.8 \({}^{\circ}\)C and the dicarbide phase at 67 mol%C and 1081.8 \({}^{\circ}\)C [19]. The La-C system contains numerous experimental data to validate the predicted phase diagram by [PERSON] et al. [19], with specific emphasis on the liquidus and eutectic transition from 0 to 67 mol%C.