## 3 Results and Discussion
### Characteristics of Randomly Oriented Polycrystalline Samples
#### 3.1.1 Lattice Parameters and Microstructures
The lattice parameters of Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(0.0\leq x\leq 0.30\)) samples are shown in Figure 3.  
As shown in Figure 3, the lattice parameter \(a\) gradually decreases with the increasing \(x\) in Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) from 0.0 to 0.25, and then it turns to slightly increase with a further increasing \(x\), up to 0.30, while the lattice parameter \(c\) monotonously decreases up to \(x\) = 0.30. The unit cell volume (\(V_{cell}\)) monotonously decreases with the increasing \(x\) from 0 to 0.3, as illustrated in Figure 3b. Notably, La\({}^{3+}\) (1.22 A) and Co\({}^{2+}\) (0.75 A) can substitute for Sr\({}^{2+}\) (1.31 A) and Fe\({}^{3+}\) (0.65 A) sites, respectively [33]. The ionic radius of La\({}^{3+}\) is smaller than that of Sr\({}^{2+}\), while the ionic radius of Co\({}^{2+}\) is larger than that of Fe\({}^{3+}\). As La-Co is co-substituted into SrM, and Fe\({}^{2+}\) (0.78 A) is formed due to a local substitution imbalance between La\({}^{3+}\) and Co\({}^{2+}\)[34; 35; 36]. According to [PERSON] et al. [34], with an increasing \(x\), there is a corresponding increase in the concentration of Co\({}^{2+}\) occupying the \(2a\) site of Fe\({}^{3+}\) for \(x\)\(<\) 0.15. Furthermore, it can be inferred that the occupation of Co\({}^{2+}\) at the \(2a\) site results in the formation of Fe\({}^{2+}\) at the \(2a\) site. Figure 3: The lattice parameters (\(a\), \(c\)) (**a**) and unit cell volumes (\(V_{cell}\)) and the \(c/a\) ratio (**b**) for the Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) (\(0.0\leq x\leq 0.3\)) samples sintered at 1230 \({}^{\circ}\)C (filled square) and post-annealed at 1230 \({}^{\circ}\)C (open triangle) for samples in Ref. [37]. In our previous study on La-Co-co-substituted SrM hexaferrites [37], the M-type single phase could be synthesized at 1300 \({}^{\circ}\)C for 2 h in air, without sintering additives. For a comparison with the present results, we performed additional post-annealing at 1230 \({}^{\circ}\)C for 2 h in air for those as-sintered samples in Ref. [37]. The lattice parameters \(a\) and \(c\) of the post-annealed samples are also represented in Figure 3a. Compared with post-annealed samples without sintering additives, the lattice parameter \(a\) showed no significant change, while the decrease in parameter \(c\) became more pronounced with the increasing \(x\), particularly up to \(x=0.25\). Consequently, as shown in Figure 3b, the \(c/a\) ratio exhibited a significant decrease with an increasing \(x\) up to \(x=0.25\), while the \(V_{cell}\) values are somewhat peculiar variation. It is known that Si and Ca, used as sintering additives, can substitute for Fe and Sr sites, respectively [22; 38], which most probably caused the above difference in the lattice parameter \(c\). However, a negligible variation in \(c\) for \(x=0.3\) with sintering additives may be due to a reduced effect of the sintering additives on \(c\) at a much higher La-Co concentration relative to the amounts of sintering additives. Consistent with previous reports on the Sr\({}_{1-x}\)La\({}_{x}\)Fe\({}_{12-x}\)Co\({}_{x}\)O\({}_{19}\) samples with sintering additives of SiO\({}_{2}\) and CaCO\({}_{3}\)[19; 20], the lattice constant \(c\) continuously decreases while the lattice constant \(a\) negligibly changes with the increasing \(x\). [PERSON] et al. [19] and [PERSON] et al. [20] commonly attribute the variations in the lattice parameters only to differences in ionic radii between La\({}^{3+}\) and Co\({}^{2+}\) substituents and Sr\({}^{2+}\) and Fe\({}^{3+}\) ions in SrM, respectively, but not take the effect of sintering additives into account.