## 3 Results and Discussion
### Characteristics of MFP-Processed Samples  
#### 3.2.1 Grain Alignments and Microstructures  
The magnetic easy axis (\(c\)-axis) of M-type hexaferrite grains is aligned parallel to the applied field direction by the MFP process. Figure 7 shows the bulk surface XRD patterns of the MFP-processed Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(x\) = 0.0, 0.15, 0.2, and 0.3) samples. From this figure, one can see that the bulk surface exhibits grain alignment primarily along the \(c\)-axis because the peaks of the (0 0 6), (0 0 8), and (0 0 14) planes are much larger than the main peak of the (1 1 4) plane. However, other peaks, such as the (1 0 7), (1 1 4), and (2 0 11) planes, are not negligible, implying that the \(c\)-axis alignment is insufficient. The degree of orientation along the \(c\)-axis, w(00\(l\)), was calculated according to the following formula [45]:  
\[w(00l)\ =\ \frac{\frac{\sum I(00l)}{\sum I(hkl)}-\frac{\sum I(00l)^{0}}{\sum I( hkl)^{0}}}{1-\frac{\sum I(00l)^{0}}{\sum I(hkl)^{0}}} \tag{6}\]  
where the X-ray-integrated intensities of the (00\(l\)) plane and the (_hkl_) plane are represented by \(\sum I(00l)\) and \(\sum I\) (_hkl_), respectively. Similarly, the X-ray-integrated intensities of the (00\(l\)) plane and the (_hkl_) plane of the non-oriented powder sample are denoted by \(\sum I(00l)^{0}\) and \(\sum I(hkl)^{0}\), respectively. The \(w(00l)\) values evaluated for the MFP samples using Equation (6) are presented in Figure 7. As shown in this figure, the \(w(00l)\) increases from 42.4 to 55.9% with the increasing of \(x\) from 0.0 to 0.3. Figure 8 shows the SEM micrographs of the MFP-processed Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(x\) = 0.0, 0.15, 0.2, and 0.3) samples. Figure 8a-d show the plane view perpendicular to the applied field, while Figure 8e-h show cross-sectional view parallel to the applied field. Consequently, the grains shown in Figure 8a-d predominantly represent the basal planes of hexaferrites, while those in Figure 8e-h represent cross-sectional views of hexagonal plates. Non-MFP1 samples exhibit non-uniform grains due to the random orientations of adjacent grains (see Figure 4). The average grain sizes (\(d_{avg}\)), corresponding to the average length of the hexagonal plate, and the average thickness of the hexagonal plate (\(t_{avg}\)) were determined from the micrographs shown in Figure 8. The values and their standard deviation (SD) of \(d_{avg}\) and \(t_{avg}\) are listed in Table 3. The average aspect ratio calculated by \(d_{avg}/t_{avg}\) and the average volume (V\({}_{avg}\)) are also listed in Table 3, together with the measured sintered density (D) and evaluated relative density (D/D\({}_{\text{th}}\)). As shown in Table 3, the \(d_{avg}\) value slightly increases from 1.30 to 1.38 \(\upmu\)m as \(x\) increases from 0.0 to 0.3, while the SD values are decreased from \(\pm\) 0.35 to 0.20 \(\upmu\)m. Also, the \(t_{avg}\) values of samples decreased from 1.18 to 0.77 \(\upmu\)m with the increasing \(x\) value, and their SD values also decreased from \(\pm\) 0.21 to 0.05 \(\upmu\)m.  
Figure 7: The bulk-surface XRD patterns of the MFP-processed Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(x\) = 0.0, 0.15,0.2 and 0.3) samples sintered at 1230 \({}^{\circ}\)C for 2 h in air. The degrees of orientation, \(w(00l)\), are also represented on the plot. Figure 8: SEM micrographs of the Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(x\) = 0.0, 0.15, 0.2, and 0.3) samples sintered at 1230 \({}^{\circ}\)C for 2 h in air: (**a–d**) plane view and (**e–h**) cross-sectional view.