Rare Earth Carbide (Nd-C and Ce-C) Synthesis and Characterization to Inform Phase Equilibrium in Advanced Nuclear Fuels

Abstract

As advances are being made regarding the performance of nuclear fuels, uranium carbides, and composites, such as (U,Zr)C and ${\mathrm{UO}}_2$ + ${\mathrm{UC}}_x$, have recently gained significant interest for deployment in nuclear space propulsion and high temperature gas-cooled reactors, respectively. However, the phase equilibria of several fission products in carbide systems remain unknown and may impact the overall fuel performance, specifically for particle nuclear fuels that are designed for commercial nuclear energy. Furthermore, comprehensive thermodynamic data on Rare Earth (RE) carbides, such as the Nd-C and Ce-C binary systems, remain limited. Presented in this study are the synthesis methods and characterizations of several Nd-C and Ce-C compositions. The findings from this research provide insights on the stability of RE-C binaries that form in irradiated nuclear fuels and address a critical knowledge gap in the current state of thermodynamics for two key RE-C systems.

1. Introduction

Uranium carbides have emerged as promising candidates for advanced nuclear fuel applications for their high thermal conductivity, high melting point, and high uranium density compared to traditional ${\mathrm{UO}}_2$ [1,2,3,4]. In high temperature gas-cooled reactors, uranium carbides enhance fuel performance in particle fuels when fabricated as an uranium oxycarbide composite (${\mathrm{UO}}_2$ + ${\mathrm{UC}}_x$) [5,6,7,8]. Additionally, uranium carbides such as ${\mathrm{UC}}_2$ have previously been studied in early nuclear fueled rocketry [9,10], and advances in uranium carbide fuels are currently being explored for nuclear thermal propulsion as a solid solution with zirconium carbide (U,Zr)C [11,12,13]. In both applications, the formation of fission products will be of concern for either fuel performance or nuclear waste management.

Rare Earth (RE) fission product migration in traditional ${\mathrm{UO}}_2$ fuels are of minimal concern, considering that RE elements tend to be most stable as oxides, as shown from the Ellingham diagram in Figure 1 [14]. This conclusion was supported in recent modeling approaches from Perriot et al. [15], where the diffusivities of RE elements in ${\mathrm{UO}}_2$ were determined to be relatively slow due to high RE solubility in ${\mathrm{O}}_2$. Of the RE elements, neodymium (Nd) is used as a Post Irradiation Examination (PIE) standard to evaluate fuel burn up, as it is generally agreed that Nd is immobile in ${\mathrm{UO}}_2$ [16]. Minimal RE diffusion cannot be assumed for uranium carbide fuels. In early irradiation tests using ${\mathrm{UC}}_2$ particle fuels, RE fission products were observed during PIEs to migrate from the carbide fuel kernel to the protective SiC layer, causing corrosion and damage to the structural integrity of the fuel particle [17]. While RE migration was suppressed by introducing ${\mathrm{UO}}_2$ in uranium oxycarbide particle fuels (${\mathrm{UO}}_2$ + ${\mathrm{UC}}_x$), there still exists a considerable knowledge gap on RE-C phase equilibrium through experimental verification.

Nd and cerium (Ce) are two fission products of interest in irradiated carbide bearing nuclear fuels and are the primary metals studied here. The phase equilibria for binary Nd-C and Ce-C thermodynamic systems have previously been assessed from Bian et al. and Peng et al., respectively [18,19]. The phase diagrams for both systems provide insight on the current state of knowledge on Nd-C and Ce-C, which is incomplete, as can be shown by the limited available experimental data on their various predicted phases. The lack of experimental verification on calculating the Nd-C and Ce-C phase diagrams provides implications for predicting the phase equilibria of RE-C species that may exist in irradiated uranium carbide fuels.

Without available oxygen in the fuel, the fate of RE fission products is not very well understood. Furthermore, the phase diagrams of key RE fission products in carbide binary systems lack experimental calorimetry assessments, specifically for Nd-C and Ce-C systems. This research demonstrates fabrication methods using arc melting synthesis, followed by SEM and XRD characterization of several Nd-C and Ce-C stoichiometries. A deeper understanding of the phases identified in the RE–carbide system will ultimately inform thermodynamic models by providing microstructural and crystallographic data for each stoichiometry process.

2. Materials and Methods

Several species of Nd-C and Ce-C were synthesized in this study to assess the calculated phases in the phase diagrams. Sample synthesis of the RE-carbides was conducted using arc melting techniques of the pure metals and ultra-high purity graphite. The facilities used for the binary compound syntheses have been previously reported in [20,21] and are discussed in greater detail in Section 2.2.

2.1. Composition Selection

Thermodynamic parameters for the Nd-C and Ce-C systems were obtained from [18] and [19] respectively. The binary phase diagrams for both systems were calculated using Thermo-Calc (version 2021a) [22]. The available experimental data for the Nd-C phase diagram were superimposed on the Nd-C phase diagram using data from [18,23,24,25,26] as depicted in Figure 2.

Similarly, the available experimental data for the Ce-C phase diagram were superimposed on the Ce-C phase diagram using data from [27,28,29,30] as summarized in [19] as depicted in Figure 3.

The melt temperatures of the chosen stoichiometries of interest in this study were superimposed on both phase diagrams in blue. Seven stoichiometries of the Nd-C system were synthesized: ${\mathrm{Nd}}_{0.95}$${\mathrm{C}}_{0.05}$, ${\mathrm{Nd}}_{0.9}$${\mathrm{C}}_{0.1}$, ${\mathrm{Nd}}_{0.8}$${\mathrm{C}}_{0.2}$, ${\mathrm{Nd}}_{0.7}$${\mathrm{C}}_{0.3}$, ${\mathrm{Nd}}_{0.6}$${\mathrm{C}}_{0.4}$, ${\mathrm{Nd}}_{0.4}$${\mathrm{C}}_{0.6}$, and ${\mathrm{Nd}}_{0.333}$${\mathrm{C}}_{0.667}$. Five stoichiometries of the Ce-C system were synthesized: ${\mathrm{Ce}}_{0.95}$${\mathrm{C}}_{0.05}$, ${\mathrm{Ce}}_{0.8}$${\mathrm{C}}_{0.2}$, ${\mathrm{Ce}}_{0.6}$${\mathrm{C}}_{0.4}$, ${\mathrm{Ce}}_{0.33}$${\mathrm{C}}_{0.67}$, and ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$.

2.2. Arc Melt Fabrication

Nd foil (99.9% purity (REO), LOT W04G022, sourced from Alfa Aesar, Haverhill, MA, USA) and Ce foil (99.9% purity (REO), LOT X06I025, sourced from Thermo Fisher Scientific, Waltham, MA, USA) were stored and handled in a MBraun argon (Ar) atmosphere glovebox. The Mbraun atmosphere was continuously monitored for ${\mathrm{pH}}_2$O and ${\mathrm{pO}}_2$, where both parameters were typically <1 parts per million (ppm) during sample preparations. Nd and Ce pieces were segmented using shears and weighed using a Mettler Toledo (Columbus, OH, USA, calibrated to 0.1 mg) mass balance. The segmented metals were then separated in sample bags and sealed under Ar to limit volatilization due to oxidation when removed from the glovebox chambers. Ultra-high purity (UHP) graphite (99.997%, sourced from Goodfellow Cambridge Limited, Huntingdon, UK) samples were weighed externally on a benchtop balance Ohaus Balance (Parsippany, NJ, USA), calibrated to 0.00001 g) and were weighed to match various at % of RE-C. A relatively small additional mass (≤0.0003 g) was included in the initial graphite segmentation to account for graphite refinement and handling. The segmented graphite samples were refined by washing with methanol, then heat treated for 20 min using a Corning Laboratory Hot Plate/Stirrer (model PC-162, Corning, NY, USA). Once the mass measurements were completed, the samples were prepared for the arc melt synthesis.

A customized tri-arc melt furnace (model 5TA, Centorr Vacuum Industries, Nashua, NH, USA) with gettered UHP Ar gas supply and hearth water cooling was used for the RE-carbide synthesis. The Ar supply lines were externally gettered for ${\mathrm{O}}_2$ contamination using titanium heating in a jewlers furnace held at 650 °C. Three copper jacketed tungsten welding tip electrodes (Miller Maxstar 210 STR Stick Welder, Appleton, WI, USA) provided the power supply to the arc furnace system. A stoichiometric RE metal and graphite sample occupied two of the three customized pockets on a copper hearth with a brass furnace base and cap. During synthesis, the hearth was continuously cooled using a 10.5 kW recirculating chiller (PolyScience DuraChill, Niles, IL, USA). A titanium slug (99.995% purity, LOT Y08F055, sourced from Alfa Aesar) occupied the third pocket inside the furnace to serve as an internal (molten) ${\mathrm{O}}_2$ getter. Prior to initiating the arc, the furnace was evacuated and backfilled with UHP Ar gas. The furnace atmosphere was continuously monitored using zirconia oxygen sensors (RapidOx Series, CEA instruments, Westwood, NJ, USA) for inlet and outlet ${\mathrm{pO}}_2$ monitoring. The evacuation and Ar backfill process was repeated 7 times or until ${\mathrm{pO}}_2$ measurements were within ${10}^{-14}$ to ${10}^{-16}$ ppm. Once the furnace was purged of ${\mathrm{O}}_2$, Ar was set to continuously flow into the furnace at about 2 LPM. An ultra-violet visor was placed around the furnace, then the initial arc was established. The arc was created by striking the hearth with an electrode and guiding the arc to the titanium getter. Once the titanium getter was molten, a second arc was ignited and guided to the RE metal. The RE metals were refined by continuously melting to remove volatile impurities. During the RE metal refinement, the arc current was set to 30–40 A, and the sample remained in the molten state for 5 min. The current was lowered to zero, and the hearth cooled prior to opening. The samples were quickly removed from their pockets, and the hearth was cleaned to remove soot and volatile products using a methanol-soaked cotton swab. The samples were then placed back in their respective pockets to begin the evacuation and UHP Ar backfill process again, as previously described. The RE metal refinement process was complete after 3 consecutive melts, or until soot was no longer observed on the copper hearth. After completing the refinement and allowing the chamber to cool, the RE metal was shifted into the pocket with graphite using the electrodes as manipulators inside the furnace. An arc was established, and precursors were consolidated using two electrodes on one pocket, with each electrode set to 25–30 A (50–60 A total). A high current was required to establish “pinwheeling" of the molten RE-C; this is a historically accepted indicator of a homogenized compound in the molten state, where pinwheeling is a visual description of molten mass swirling during arc melting. After consolidation, the current was reduced to zero, and the sample was convectively cooled. Again, using the electrodes as manipulators, the RE-C ingot was flipped and remelted to further ensure homogeneity. Remelting was performed an additional three times. Upon completion of the arc melting process, the cooled RE-C samples were exposed to air briefly for transfer to the glovebox and weighed in an inert atmosphere.

2.3. Characterization Methods

Prior to characterization, the RE-C ingots were fragmented in a glovebox using a 100 mL agate mortar and pestle (Fisher Scientific, Pittsburgh, PA, USA). One fragment was triturated and prepared for X-ray Diffraction (XRD), while a second fragment was mounted in epoxy resin or mounted on a stainless steel stub using Crystal Bond (Electron Microscopy Sciences, Hatfield, PA, USA) for Scanning Electron Microscopy (SEM).

2.3.1. Scanning Electron Microscopy

The synthesized RE-C ingots were mounted on stainless steel stubs using Crystal Bond or epoxy resin. Both methods required RE-C specimens to be exposed to ambient air during bonding or resin molding, which introduced oxidation, as discussed in Section 3.1 and Section 3.2. The mounted RE-C ingots were polished prior to SEM using Allied silicon carbide grinding papers starting at 600 grit and ending at 1200 grit. Finer polishing steps used diamond suspension from 6 to 3 microns on an Allied TechCloth. A scanning electron microscope (Hitachi FlexSEM 1000, Tokyo, Japan) was used to examine the microstructures of the RE-C ingots in vacuum. The FlexSEM 1000 was equipped with a backscatter electron (BSE) imaging detector and an Oxford Instruments X-ray Energy Dispersive Spectrometer (EDS) detector. The RE-C ingots were examined using 15–20 kV accelerating voltages.

2.3.2. X-Ray Diffraction

All samples were prepared for XRD inside an Ar-filled glovebox to prevent oxidation. After the segmented RE-C samples were triturated, the powder was enclosed in an Ar-filled airtight polymer dome and then removed from the glovebox and placed in a Benchtop X-ray Powder Diffraction Bruker D2 Phaser (Serial Number: 250084, Part Number: A26-X1, Karlsruhe, Germany) equipped with a LYNXEYE XE-T Detector and Cu anode. Samples were scanned from 10–95 2$\theta$ in 0.24 angle increments every 1 s.

3. Results

3.1. Nd-C Characterization

Seven neodymium carbide compounds were synthesized, varying in C at %, to comprehensively assess the Nd-C phase diagram. Utilizing thermodynamic parameters from [18], the phase diagram was calculated, and stoichiometries of interest were identified, as illustrated in Figure 2, with the relevant stoichiometries denoted in blue. The phases identified in the calculated phase diagram are ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ (space group I$\overline{4}$3d), $\alpha$${\mathrm{NdC}}_2$ (space group I4/mmm), $\alpha$Nd (space group P6₃/mmc), and $\beta$Nd (space group Im$\overline{3}m$). The space group for $\beta$${\mathrm{NdC}}_2$ is currently unknown as discussed in Bian et al. [18]. XRD patterns for all seven samples were collected and displayed in Figure 4.

Figure 4 shows phase identification of ${\mathrm{Nd}}_2$${\mathrm{C}}_3$, ${\mathrm{NdC}}_2$, pure Nd, and an unidentified peak. Unidentified peaks were only observed for Nd-C samples lower than 40 at% C. SEM micrographs for all seven samples were collected and are shown in Figure 5, where the ${\mathrm{Nd}}_{0.9}$${\mathrm{C}}_{0.1}$ and ${\mathrm{Nd}}_{0.333}$${\mathrm{C}}_{0.667}$ micrographs are presented at a relatively lower magnification (300 $\mathsf{\mu }$m vs. 200 $\mathsf{\mu }$m scale bars) as a result of multiple SEM users during data acquisition. For several samples, oxidation is observed on the microstructural surfaces as a result of sample handling, polishing methods, and SEM specimen preparation. Nd-C-O compounds were not identified during the XRD acquisition, since XRD samples were prepared and sealed in an Ar environment.

Two phases, pure Nd and neodymium sesquicarbide (${\mathrm{Nd}}_2$${\mathrm{C}}_3$), were identified in the ${\mathrm{Nd}}_{0.95}$${\mathrm{C}}_{0.05}$ microstructure and in the XRD pattern. The ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ phase appears as a darker contrast within the pure Nd matrix. The ${\mathrm{Nd}}_{0.9}$${\mathrm{C}}_{0.1}$ microstructure has similar SEM and XRD results, with the exception of having a greater ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ phase distribution in the microstructure. The ${\mathrm{Nd}}_{0.8}$${\mathrm{C}}_{0.2}$ microstructure exhibited a eutectic multi-phase complex as a primary matrix, consisting of a darker contrast ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ and bright contrast of pure Nd. The third phase existing within the eutectic was determined as ${\mathrm{NdC}}_2$ and confirmed in the XRD pattern. The ${\mathrm{Nd}}_{0.7}$${\mathrm{C}}_{0.3}$ microstructure contained bright phases of pure Nd, while the primary matrix consisted of a mixture of ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ and ${\mathrm{NdC}}_2$, as confirmed by the XRD pattern. The dark streaks were attributed to polishing fluid contamination. The ${\mathrm{Nd}}_{0.6}$${\mathrm{C}}_{0.4}$ sample exhibited surface oxidation, and the microstructure primary matrix was identified as ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ with smaller phases being ${\mathrm{NdC}}_2$, as shown in the XRD pattern. The ${\mathrm{Nd}}_{0.4}$${\mathrm{C}}_{0.6}$ XRD pattern shows highly crystalline ${\mathrm{Nd}}_2$${\mathrm{C}}_3$ with lower counts of ${\mathrm{NdC}}_2$, as expected from the phase diagram. The phase distribution in the microstructure was not observed due to significant surface oxidation as showed from the SEM microstructure. The ${\mathrm{Nd}}_{0.333}$${\mathrm{C}}_{0.667}$ sample is the only stoichiometry examined that existed as a line compound until its melting temperature, according to the phase diagram. Although the sample microstructure appeared heavily oxidized, the XRD pattern exhibited highly crystalline features for ${\mathrm{NdC}}_2$. No other phases are detected in this sample.

3.2. Ce-C Characterization

Five cerium carbides with varying C at % are synthesized for this study to comprehensively assess the Ce-C phase diagram. Using thermodynamic parameters from [19], the phase diagram was calculated and used to identify stoichiometries of interest, where the stoichiometries chosen to synthesize in this study are denoted in blue in Figure 3. The phases identified in the calculated phase diagram are ${\mathrm{Ce}}_2$${\mathrm{C}}_3$ (space group I4-3D), $\alpha$${\mathrm{CeC}}_2$ (space group I4/mmm), $\beta$${\mathrm{CeC}}_2$ (space group Fm-3m), $\delta$Ce (space group Im-3m), and $\gamma$Ce (space group Fm-3m). XRD patterns for the five cerium carbide samples have been collected and are shown in Figure 6.

SEM micrographs were collected for the five cerium carbides and are shown in Figure 7.

All five cerium carbide microstructures exhibited surface oxidation as a possible result of polishing and handling outside of the glovebox. Ce-C-O compounds were not identified in the synthesized samples, as shown from the XRD acquisition.

While the XRD pattern had minimal detection of ${\mathrm{Ce}}_2$${\mathrm{C}}_3$, two phases, pure Ce and ${\mathrm{Ce}}_2$${\mathrm{C}}_3$, were identified in the ${\mathrm{Ce}}_{0.95}$${\mathrm{C}}_{0.05}$ microstructure according to the phase diagram. The ${\mathrm{Ce}}_{0.8}$${\mathrm{C}}_{0.02}$ microstructure had two identified phases, ${\mathrm{Ce}}_2$${\mathrm{C}}_3$ and pure Ce, supported by the XRD pattern. The ${\mathrm{Ce}}_{0.6}$${\mathrm{C}}_{0.4}$ XRD pattern consists of Ce, ${\mathrm{Ce}}_2$${\mathrm{C}}_3$, and ${\mathrm{CeC}}_2$. The primary matrix in the microstructure was identified as ${\mathrm{Ce}}_2$${\mathrm{C}}_3$. The unique surface oxidation pattern in the microstructure prevented phase identification using SEM. The ${\mathrm{Ce}}_{0.33}$${\mathrm{C}}_{0.67}$ microstructure showed significant oxidation, although the two peaks identified in the XRD were ${\mathrm{Ce}}_2$${\mathrm{C}}_3$ and ${\mathrm{CeC}}_2$ and correspond well with the phase diagram calculations. Although the ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ microstructure exhibited severe surface oxidation, the XRD pattern had significant counts of ${\mathrm{CeC}}_2$.

4. Discussion

4.1. X-Ray Diffraction of the RE-C Alloys

The higher metal-to-carbon compounds were experimentally challenging to triturate using a traditional agate mortar and pestle, and thus, this resulted in powders that were not finely ground. The varying size in powder particulate size produced XRD patterns similar to what would be observed in an amorphous phase, although the amorphous behavior was only an artifact. The irregularly shaped powder caused noise in several Nd-C and Ce-C XRD patterns. However, the noise in the XRD patterns was decreased as the carbon content was increased, as seen by the XRD patterns for ${\mathrm{Nd}}_{0.4}$${\mathrm{C}}_{0.6}$ and ${\mathrm{Nd}}_{0.333}$${\mathrm{C}}_{0.667}$ in Figure 4, and for ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ in Figure 6. The higher carbide compounds were more brittle and easier to triturate into fine powders, and hence, they had less noise in their patterns.

In this study, the XRD patterns for many of the Nd-C stoichiometries exhibited different peak intensities in comparison to their Powder Diffraction Files (PDFs), particularly in the samples characterized with the pure Nd and ${\mathrm{NdC}}_2$ phases. A clear example of this preferred orientation is seen in Figure 8, where the calculated ${\mathrm{NdC}}_2$ XRD pattern is compared to the experimental XRD of ${\mathrm{Nd}}_{0.333}$${\mathrm{C}}_{0.667}$.

Although the experimental ${\mathrm{Nd}}_{0.333}$${\mathrm{C}}_{0.667}$ XRD pattern seen in Figure 8 exhibited noise in the lower 2$\theta$ (2$\theta \le$ 40 deg.), the noise did not impact the identification of the preferred orientation observed at the primary peak intensity. A possible explanation for the varying primary peak intensities can be attributed to the formation of the high temperature $\beta$-${\mathrm{NdC}}_2$ phase. From the phase diagram, the ${\mathrm{NdC}}_2$ was stable at lower temperatures as an $\alpha$-${\mathrm{NdC}}_2$ phase below 1192 °C. Previous reporting on the Nd-C system demonstrated experimental evidence of a tetragonal $\alpha$-${\mathrm{NdC}}_2$ phase and predicted the existence of a cubic $\beta$-${\mathrm{NdC}}_2$ phase, but the actual crystal structure and phase transition from tetragonal $\alpha$-${\mathrm{NdC}}_2$ to cubic $\beta$-${\mathrm{NdC}}_2$ have yet to be confirmed [24,32]. In addition, the unidentified peaks in Figure 4 appear only for Nd-C compositions with ≤40 at%. Given the lack of experimental verification for the Nd-C phase diagram, it is possible that these peaks correlate to a new phase that has yet to be identified, but additional structural studies will need to be explored on the lower C compositions to confirm.

The XRD patterns for ${\mathrm{CeC}}_2$ also display preferred orientation, as seen in Figure 9, where the experimental XRD of ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ sample is being compared to the calculated XRD pattern.

The melting temperature of ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ was predicted to be ≈ 3500 °C, which is relatively higher than what can be achieved using arc melting techniques. However, the ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ composition demonstrated an XRD pattern that resembles the calculated ${\mathrm{CeC}}_2$ XRD pattern. Additional microscopy on the ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ sample revealed a large formation of ${\mathrm{CeC}}_2$ + C, which is supported by the phase diagram predictions, as seen in Figure 10.

Considering the large amounts of C that were observed in the SEM micrographs, C peaks should have been observed in the XRD but were not. This is most likely because a fragment of the ${\mathrm{CeC}}_2$ was used for XRD characterization. The ${\mathrm{CeC}}_2$ fragment was observably more brittle compared to the higher Ce compounds during trituration. The fine powder results in distinct peaks for the ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ XRD pattern compared to the other Ce-C compounds that were synthesized in this study. Still, the 2$\theta$ peaks from the XRD results were offset compared to the calculated XRD pattern. Additionally, preferred orientation on the second peak was observed in the ${\mathrm{Ce}}_{0.2}$${\mathrm{C}}_{0.8}$ sample. Unlike the ${\mathrm{NdC}}_2$ system, it has been documented in the literature that the $\beta$-${\mathrm{CeC}}_2$ phase exists in a cubic crystal structure [33]. However, an experimental XRD pattern for this phase is not available; only atomic spacing parameters are produced from [28]. While this research provides an XRD pattern for the possible high temperature cubic $\beta$-${\mathrm{NdC}}_2$ phase and the $\beta$-${\mathrm{CeC}}_2$ phase, ab initio calculations using potentials to simulate the cubic crystal structure may benefit this experimental result.

4.2. Oxidation Behavior

While XRD characterization on the RE-C systems provided an advantage over EDS due to the rapid oxidation following metallurgical preparation, EDS analysis was done on the ${\mathrm{Ce}}_{0.6}$${\mathrm{C}}_{0.4}$ sample for its unique oxidized surface layer. Although nearly all RE-C samples exhibited surface oxidation, it was observed that the higher carbide content samples, specifically samples containing greater phase distributions of ${\mathrm{RE}}_2$${\mathrm{C}}_3$ and ${\mathrm{REC}}_2$, tended to oxidize significantly faster compared to the lower carbide content samples. Figure 11 of the ${\mathrm{Ce}}_{0.6}$${\mathrm{C}}_{0.4}$ sample identifies two distinct phases in its microstructure, where the oxide layer tended to favor growth on the ${\mathrm{Ce}}_2$${\mathrm{C}}_3$ phase.

These findings suggest that the BCC crystal structures of the higher carbides within the RE-C systems tend to experience greater oxidation because of the compact short range ordering of atoms in comparison to the tetragonal crystal structures found at lower temperatures. It has been known that the RE elements tend to form oxides because of their abundance of valence electrons [34], but there are minimal studies reported on the oxidation performance of RE-C.

4.3. Impact on Advanced Nuclear Fuels

The phase analysis presented in this work can be leveraged to support phase equilibria predictions in PIE of advanced nuclear fuels, such as particle fuels. An important thermodynamic system is the RE-Si-C ternary, as the SiC layer has a primary purpose of metallic fission product retention in Tristructural Isotropic (TRISO) particles [35]. In addition to the SiC layer, several graphite layers coat the actinide fuel, providing additional fission product retention and structural integrity [36,37]. The Inner Pyrolytic Carbon (IPyC) layer creates an interface against the SiC layer, and considerable attention is given at this interface during PIE to assess the retention performance of the SiC layer [38,39]. The RE fission products were previously reported to corrode the SiC layer in irradiated ${\mathrm{UC}}_2$ fuels [17]. However, the formation of RE fission products into stable carbides within the IPyC-SiC interface, such as ${\mathrm{REC}}_2$ or ${\mathrm{RE}}_2$${\mathrm{C}}_3$, is not discussed in Grübmeier et al.’s report, because it is assumed that the chemical bond of any lanthanide RE-C is very weak. More recent studies support this claim of preferential RE oxide formation over carbide formation, as it was determined that the oxygen potentials for Nd and Ce were relatively high in oxide nuclear fuels [14]. The findings in the current study suggest that not only do stable RE-carbides form at relevant reactor operating temperatures, but there is also a significant gap in knowledge on the phase equilibrium of several key RE fission product species as carbides, suggesting that our current understandings of the RE-C systems are either limited or outdated. A stronger understanding on the RE-C systems is needed, as nearly all TRISO PIEs have identified REs either in the kernel or within the SiC layer. Furthermore. The XRD results from this current study indicate that various RE-C compounds are stable in absence of ${\mathrm{O}}_2$, which opens speculation on RE fission product diffusion in uranium carbide fuels. In an effort to fully understand the impact of RE-C in advanced carbide nuclear fuels, the U-RE-C ternaries need to be considered. However, there currently exists no comprehensive thermodynamic treatment on the U-Nd-C or U-Ce-C ternaries, resulting in more knowledge gaps in key actinide thermodynamic systems but allowing for additional research to be conducted in unexplored systems.

5. Conclusions

Experimentally acquired XRD patterns and SEM microstructures for various stoichiometries in the Nd-C and Ce-C system were obtained during this study. Seven Nd-C compounds and five Ce-C compounds were synthesized using arc melting techniques and characterized using SEM and XRD in an effort to explore the microstructures and phase equilibrium of these rare earth carbide systems. XRD results for the Nd-C system demonstrated experimental evidence of a cubic structure for $\beta$-${\mathrm{NdC}}_2$, which has been reported as a theoretical crystal structure. Using EDS results from the Ce-C system, specifically ${\mathrm{Ce}}_{0.6}$${\mathrm{C}}_{0.4}$, it was observed that the ${\mathrm{Ce}}_2$${\mathrm{C}}_3$ phases preferentially oxidized compared to the lower C phases. This is hypothesized to be due to the abundance of RE valence electrons available in the cubic ${\mathrm{Ce}}_2$${\mathrm{C}}_3$ crystal structure.

A comprehensive evaluation on the Nd-C and Ce-C binary systems was given in this study. The experimental XRD and phase identification using SEM agree well with the calculated phase diagrams for the Nd-C and Ce-C binary systems. Prior to the investigations provided in this study, the state of knowledge of these systems was limited in experimental data. This work expands the existing knowledge by discovering the high temperature cubic crystal structure of $\beta$-${\mathrm{NdC}}_2$, which was previously theorized. Further, this research provides the most comprehensive set of experimentally acquired XRD patterns for key compositions in the the Nd-C and Ce-C binary systems.

Due to the limited structural studies reported in the literature, the results of this study encourage ab initio calculations to be performed on the potential high temperature cubic $\beta$-${\mathrm{NdC}}_2$ and $\beta$-${\mathrm{CeC}}_2$ systems. Additionally, a future investigation should include synthesis and calorimetry of the U-Nd-C and U-Ce-C ternary system to fully assess the potential interactions of RE fission products in proposed advanced carbide nuclear fuels.