## 3 Results and Discussion  
Figure 1a-c show the XRD patterns of undoped (no-Si), pre-Si, and post-Si SCLFCO samples sintered at various temperatures. All no-Si SCLFCO samples were single phase M-type hexaferrites at all sintering temperatures (1200-1250 \({}^{\circ}\)C), with a hexagonal crystal structure and a space group of  
Table 1 shows the cell volume of the SCLFCO hexaferrites, calculated based on XRD patterns (Jade 6.0, V6.2.9200, MDI, Materials Data, Inc., USA). For each sintering temperature, the cell volume was the highest in no-Si samples and the lowest in pre-Si samples. The change in cell volume could be the result of Si substitutions in Fe sites, as the ionic size of Si\({}^{4+}\) is smaller than that of Fe\({}^{3+}\)[35]. In addition, the observation that cell volumes of the pre-Si samples are smaller than those of the post-Si samples at each sintering temperature implies that a larger amount of Si was substituted into the hexaferrite lattice in the pre-Si method than in the post-Si method. The excess Fe atoms form the Fe\({}_{2}\)O\({}_{3}\) secondary phase, which could inhibit grain growth based on the Zener effect, where the movement of the interface and grain boundary is suppressed by a secondary phase on the interface and grain boundary [19; 20]. When Si is added, a liquid phase can form, the structures of the interface and grain boundary can change, and the growth rate of each grain can be altered [14; 20; 22; 28; 29; 30]. Figure 2a-i display SEM micrographs of no-Si, pre-Si, and post-Si SCLFCO samples sintered at various temperatures. The effect of the sintering temperature on the average grain size of each sample type is insignificant. However, the average grain size significantly decreased as SiO\({}_{2}\) was added to all samples. The decrease in average grain size could be explained by the effect of Fe\({}_{2}\)O\({}_{3}\) formation, as the Fe\({}_{2}\)O\({}_{3}\) detected in the XRD patterns can suppress the migration of grain boundaries [19; 20; 24]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sintering** & **1 wt\% SiO\({}_{2}\) Addition** & **Density, g/cm\({}^{3}\)** & **Unit Cell Vol., Å\({}^{3}\)** \\ \hline \multirow{3}{*}{1200 \({}^{\circ}\)C} & no-Si & 4.91 & 688.481 \\  & post-Si & 4.55 & 687.746 \\  & pre-Si & 4.78 & 687.518 \\  & no-Si & 4.89 & 689.005 \\  & post-Si & 4.72 & 688.073 \\  & pre-Si & 4.89 & 687.707 \\  & no-Si & 4.95 & 689.025 \\  & post-Si & 4.82 & 687.144 \\  & pre-Si & 4.93 & 686.250 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Densities and unit cell volumes of sintered samples. Figure 2: SEM micrographs of no-Si, pre-Si, and post-Si SCLFCO samples sintered at **(a)** 1200 \({}^{\circ}\)C, **(b)** 1225 \({}^{\circ}\)C, and **(c)** 1250 \({}^{\circ}\)C.  
The \(H_{c}\) and other extrinsic properties may increase in samples with the addition of SiO\({}_{2}\) due to a decrease in the average grain size [31; 32]. However, the intrinsic properties, such as \(M_{s}\), could also be changed due to the diffusion of Si into the lattice. The unit cell volumes of the samples with SiO\({}_{2}\) addition were changed, as shown in Table 1. This phenomenon can be explained by the diffusion of Si into unit cells which changed the intrinsic properties. As shown in Table 2, the degree of change in the \(M_{s}\) in the pre-Si sample is larger than that in the post-Si sample. This could be due to the larger degree of Si substitution in the hexaferrite lattice in the pre-Si samples than that in the post-Si samples. The microstructures in Figure 3 show that the coarsening behavior changes considerably with the addition of SiO\({}_{2}\) during sintering at 1250 \({}^{\circ}\)C. Here, all the samples were prepared with the pre-Si procedure but used different amounts of SiO\({}_{2}\). The addition of 0.5 wt% SiO\({}_{2}\) caused an exaggerated, abnormal grain growth. In the samples with the addition of 1.0 and 2.0 wt% SiO\({}_{2}\), the grain size decreased compared to the case of the undoped and 0.5 wt% SiO\({}_{2}\)-added sample.