## 3 Results and Discussion  
In this work, the predominant phases observed in the alloys are \(\alpha\)-Fe, Ce\({}_{1.1}\)Fe\({}_{4}\)B\({}_{4}\), Ce\({}_{2}\)(Fe\({}_{17-x}\)T\({}_{x}\)), and Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))B. Annealing at 900 \({}^{\circ}\)C increases the growth of Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))B to above 70%, reducing other phases to insignificant amount as shown in Table 1. Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))B solid solutions crystallize in the tetragonal Nd\({}_{2}\)Fe\({}_{14}\)B-type structure (P4\({}_{2}\)/mnm, #136 space group). As can be seen in Figure 1, substitution of Fe by Ni and Si, which have smaller atomic radii to Fe, decreases the lattice volumes of the Ce\({}_{2}\)Fe\({}_{14}\)B, shifting its peaks positions to higher diffraction angles, whereas Al substitution increases lattice volume of the Ce\({}_{2}\)Fe\({}_{14}\)B, shifting its peak positions to lower angles. The measured unit cell parameters and lattice volume of the Ce\({}_{2}\)Fe\({}_{14}\)B used in Figure 1 are in agreement with literature values [4]. The linear relations between lattice parameter c and lattice volume V versus T concentrations in the Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))B solid solutions are consistent with [PERSON]'s law [38] as shown in Figure 1. The dashed red line in Figure 2 demonstrates the shift in the (140) peak due to substitution of Fe in Ce\({}_{2}\)Fe\({}_{14}\)B by Si, Ni, and Al. This confirms that these elements replace Fe in the Ce\({}_{2}\)Fe\({}_{14}\)B to form solid solutions. Rietveld analysis was carried out on the XRD patterns obtained for all the samples and the relative amount of the Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))B solid solution is listed in Table 1.  
Figure 1: Plots of the (**a**) lattice parameter, \(c\); and (**b**) lattice volume, V, with T content in the Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\)B) solid solutions (T = Al, Ni, and Si). The uncertainties in lattice parameter and volume are smaller than the data points. Figure 2: XRD patterns of the Ce\({}_{2}\)Fe\({}_{14}\)B base compound and Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))B solid solutions. The labelled peaks are for the Ce\({}_{2}\)Fe\({}_{14}\)B and its solid solutions. In this work, \(M_{S}\) of Ce\({}_{2}\)Fe\({}_{14}\)B at 25 \({}^{\circ}\)C was determined as 130 emu/g, and this is approximately 997.1 kA/m using the density of Ce\({}_{2}\)Fe\({}_{14}\)B reported in [4]. This value is somewhat higher than the 931.1 kA/m at 22 \({}^{\circ}\)C that was reported for a Ce\({}_{2}\)Fe\({}_{14}\)B single crystal [3,4]. Our value of 28.1 kOe for H\({}_{A}\) at 25 \({}^{\circ}\)C is also higher than the 26.4 kOe previously reported [5,37] using the same SPD method. This might be due to the presence of other secondary phases, such as iron. This was evident during TGA experiments when the curve did not reach zero force after passing \(T_{C}\) of the Ce\({}_{2}\)Fe\({}_{14}\)B compounds. In addition, the deviation from the single crystal data might be due to the fact that grain size, texture, defects, and precipitates affect many magnetic properties of bulk alloys [39]. The grain boundary increases as the grain size reduces, and increasing or decreasing grain boundaries can either improve or worsen magnetic properties of a material [39, 40, 41]. In this work, the annealing conditions were high enough to produce a high volume of Ce\({}_{2}\)(Fe\({}_{14-x}\)T\({}_{x}\))\({}_{14}\)B, and other phases were reduced to minimum amounts. However, grain boundaries were still present in the current samples, and it is expected that the single crystal sample would have had a higher \(M_{S}\) value if the contribution of the secondary phases was ignored. Therefore, the improvement in \(M_{S}\) in this study is presumably attributed to the contributions of the secondary phases.