## 3 Results and Discussion
### Synthesis of 2-14-1 Phase Through Reduction-Diffusion Process  
Figure 4 shows the XRD results of samples prepared by the modified R-D process with different Ce/Fe ratios (Ce:Fe = 1:5 (a), 1:5.5 (b), 1:6 (c), 1:6.5 (d), and 1:7 (e)). When a Ce:Fe ratio of 1:7 was used, which corresponds to the stoichiometric composition of the 2-14-1 phase, XRD peaks from residual Fe were observed. To decrease the amount of residual Fe, the Ce content was increased. As the amount of Fe was decreased, the intensity of the peak from Fe was decreased, leading to the formation of a pure 2-14-1 phase at a Ce:Fe ratio of 1:5.5 (Figure 4 (b)). Therefore, it can be confirmed that the Ce 2-14-1 phase can be successfully synthesized by the modified R-D process using Ca granules as a reducing agent, followed by washing with distilled water and acetic acid, as shown in Figure 4. It should be noted that no XRD peaks from residual Ca or CaO (the unreacted reducing agent and byproducts of the R-D process, respectively) were observed in the XRD patterns in Figure 4, which indicates that they were completely removed during the washing steps. The significant temperature difference between the peritectic reaction of Ce\({}_{2}\)Fe\({}_{14}\)B (982 \({}^{\circ}\)C) and the eutectic reaction of \(\gamma\)-Fe (1173 \({}^{\circ}\)C) presents a major challenge in syn  
Figure 4: XRD analysis results of samples prepared by the modified reduction-diffusion process with different Ce/Fe ratios (Ce:Fe = 1:5 (a), 1:5.5 (b), 1:6 (c), 1:6.5 (d) and 1:7 (e)). Figure 3: XRD results of precursor samples prepared by solid-state reaction with different heat-treatment temperatures (Ce:Fe = 1:7; 6 h, Ar). thesizing Ce\({}_{2}\)Fe\({}_{14}\)B alloys without the formation of \(\alpha\)-Fe using rapid solidification techniques [8, 20, 21]. However, precise compositional control through solid-state reactions has enabled the synthesis of a pure 2-14-1 phase. This suggests that the stoichiometry of metal alloys produced through the R-D process can be effectively adjusted by manipulating the composition during solid-state reactions. When the Fe content was further reduced, a CeFe\({}_{2}\) phase appeared as a secondary phase. As shown in Figure 5, the Ce-Fe-B system is considerably different from the Nd-Fe-B system in terms of phase formation. _RE_-rich phases play a crucial role in the sintering process, facilitating the densification and the magnetic decoupling of 2-14-1 grains through grain boundary wetting. In Nd-Fe-B magnets, the low melting point of the Nd phase allows for the continuous distribution of the grain boundaries, which enhances coercivity. In contrast, minimizing CeFe\({}_{2}\) formation is crucial, as its high melting temperature of 925 \({}^{\circ}\)C leads to poor wettability at grain boundaries. This results in the weakened magnetic decoupling of grains, ultimately deteriorating the magnetic properties of Ce\({}_{2}\)Fe\({}_{14}\)B [8, 22]. Rietveld refinement analysis was applied for calculation and quantification of the Ce 2-14-1 phase in the sample of Ce:Fe = 15.5, and the results are shown in Figure 6. It can be verified that a single phase of Ce\({}_{2}\)Fe\({}_{14}\)B can be synthesized by the modified R-D process with precise compositional control, since the calculated result is in good agreement with the experimental XRD pattern, and there was a negligible amount of secondary phases. Field-emission scanning electron microscopy (FE-SEM) analyses revealed a polygonal particle morphology of the Ce 2-14-1 particle with sizes in the micrometer range as shown  
Figure 5: Phase diagrams of (**a**) Ce–Fe–B and (**b**) Nd–Fe–B ternary systems [20]. Figure 6: Rietveld refinement of the XRD pattern of the sample with the Fe/Ce of 5.5 prepared by the modified reduction-diffusion process. in Figure 7, which is consistent with previously reported Nd-Fe-B particles synthesized by the R-D process [13]. The solid-state reactions have advantages in the precise elemental control, which can be utilized in the control of the amount of substituted elements.