## 3 Results and Discussion  
### Crystalline Structure and Microstructure Analysis  
Figure 1a-d present the XRD patterns of the M-hexaferrite samples synthesized in this study in four series, based on different cationic compositions. All the samples were obtained through calcination at 1100 \({}^{\circ}\)C in an air atmosphere and sintering at 1210 \({}^{\circ}\)C. The XRD patterns of the M-hexaferrite phase were indexed based on the International Center for Diffraction Data (ICDD) with the pdf search number SrM: 00-033-1340. For some samples, the peak positions of the secondary phase Fe\({}_{2}\)O\({}_{3}\) (ICDD, 33-0664) that occurred in certain samples are also indicated. In Figure 1a, the formation of the M-hexaferrite phase in Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{11.-3}\)xMn\({}_{x}\)Al\({}_{x}\)Si\({}_{x}\)O\({}_{19.-d}\), where 20% of Sr in the basic composition of M-hexaferrite SrFe\({}_{12}\)O\({}_{19}\) is substituted with Ca, and Fe is simultaneously substituted with Mn, Al, and Si, is shown. For \(x\) = 0 and 0.05, a pure M-hexaferrite phase is formed, whereas for \(x\) = 0.1, a small Fe\({}_{2}\)O\({}_{3}\) peak is observed, and as \(x\) increases to 0.15 and 0.2, the Fe\({}_{2}\)O\({}_{3}\) peak becomes significantly more pronounced. For the \(x\) = 0 composition, it can be observed that the 00l peaks, such as 006, 008, and 0014, are significantly higher compared to the other compositions. This result can be explained as follows: in samples with large grain growth, wide plate-like hexaferrite grains are abundant even in the powdered state. During the packing of the powder into the sample holder for the XRD measurements, the c-axes of each grain align perpendicular to the sample holder's surface. This phenomenon has been reported in previous studies on hexaferrites [7; 16; 23]. Figure 1b shows the XRD patterns of Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{10.7-3}\)xMn\({}_{0.1+x}\)Al\({}_{0.1+y}\)Si\({}_{0.1}\)O\({}_{19.-d}\) (0 \(\leq\)\(x\), \(y\)\(\leq\) 0.1), in which either of the Mn and Al substitution levels are increased from one of the first series samples, Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{10.7}\)Mn\({}_{0.1}\)Al\({}_{0.1}\)Si\({}_{0.1}\)O\({}_{19.-d}\) (\(x\) = 0). All four samples show the presence of a secondary phase Fe\({}_{2}\)O\({}_{3}\) in small amounts. Figure 1c,d display the XRD patterns of two series samples, Sr\({}_{0.7+x}\)Ca\({}_{0.3-z}\)Fe\({}_{10.2}\)Mn\({}_{0.1}\)Al\({}_{0.2}\)Si\({}_{0.11}\)O\({}_{19.-d}\) and Sr\({}_{0.7+z}\)Ca\({}_{0.3-z}\)Fe\({}_{9.7}\)Mn\({}_{0.1}\)Al\({}_{0.2}\)Si\({}_{0.11}\)O\({}_{19.-d}\) (z = 0.05, 0.1, 0.15, 0.2). In these samples, the  
ratio of Sr:Ca is varied and the Fe content in the formula is reduced from 10.6 to 10.2 and 9.7, respectively. All eight samples in Figure 1c,d are single-phase M-hexaferrites. The phases of each composition confirmed from the XRD analysis are summarized in Table 1.  
Additionally, the lattice constants \(a\), \(c\), and the unit cell volume (V) were calculated from the XRD peaks and are presented in Table 1. The \(a\) and \(c\) are calculated from the values of \(d_{hkl}\) corresponding to the (107) and (114) peaks, according to the following equation:  
\[d_{hkl}=\left\{\frac{4(h^{2}+hk+k^{2})}{3a^{2}}+\frac{l^{2}}{c^{2}}\right\}^{-1/2} \tag{2}\]  
where \(d_{hkl}\) is the interplanar spacing, and \(h\), \(k\), and \(l\) are the Miller indices. As the substitution level \(x\) increases, the unit cell volume generally decreases due to the smaller average ionic radii of Mn\({}^{3+}\), Al\({}^{2+}\), and Si\({}^{4+}\) compared to Fe\({}^{3+}\). Furthermore, since Sr\({}^{2+}\) has a larger ionic radius than Ca\({}^{2+}\), it could be expected that the unit cell volume would increase with increasing \(z\). However, this trend is not observed in this experiment. Figure 2a-e illustrate the changes in the microstructure with increasing \(x\) in sintered Sr\({}_{0.8}\)Ca\({}_{0.2}\)Fe\({}_{11-3x}\)Mn\({}_{x}\)Al\({}_{x}\)Si\({}_{x}\)O\({}_{19-\)d samples.