## 3 Results and Discussion  
Figure 1a shows the XRD patterns of BaZn\({}_{2-x}\)Co\({}_{x}\)Fe\({}_{16}\)O\({}_{27}\) (BaZn\({}_{2-x}\)Co\({}_{x}\)W) samples synthesized via the conventional solid-state method (\(x\) = 0.4, 0.5, 0.6, 0.75, 1.0, 1.25, 1.5), while Figure 1b presents the XRD patterns of samples with \(x\) = 0.75, 1.0, and 1.25 synthesized using the molten-salt (M-S) method. The diffraction patterns of the samples were matched with the peak positions of BaW from the International Center for Diffraction Data (ICDD, 01-084-0927), and the corresponding Miller indices are labeled at the top of each diffraction pattern. All sample compositions were confirmed to have an almost single-phase W structure. Using the \(d_{hkl}\) values obtained from the 2\(\theta\) positions of the (110), (1010), (116), and (1011) planes, the lattice constants \(a\) and \(c\), along with the cell volume of the W-type hexaferrite phase, were calculated and are presented in Table 1. It can be observed that as Co, which has a slightly smaller ionic radius, substitutes for Zn, the cell volume continuously decreases with increasing \(x\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Composition** & **x** & **a (Å)** & **c (Å)** & **Vol. (Å3)** & **\(M_{S}\)** & **\(H_{C}\)** \\  & 0.4 & 5.913 & 32.97 & 998.3 & 77.08 & 86.98 \\  & 0.5 & 5.910 & 32.98 & 997.5 & 78.44 & 83.89 \\ BaZn\({}_{2-x}\)Co\({}_{x}\)W & 0.6 & 5.910 & 32.96 & 997.1 & 78.77 & 67.01 \\ (non M-S) & 0.75 & 5.904 & 32.94 & 994.3 & 78.06 & 32.64 \\  & 1.00 & 5.903 & 32.90 & 993.5 & 80.34 & 38.42 \\  & 1.25 & 5.902 & 32.92 & 993.1 & 77.77 & 48.69 \\  & 1.50 & 5.902 & 32.91 & 992.8 & 75.64 & 58.56 \\ \hline BaZn\({}_{2-x}\)Co\({}_{x}\)W & 0.75 & 5.898 & 32.91 & 991.3 & - & - \\ (M-S) & 1.00 & 5.987 & 32.91 & 991.2 & - & - \\  & 1.25 & 5.898 & 32.89 & 990.9 & - & - \\ \hline \hline \end{tabular} The error bar for \(M_{S}\) is \(\pm\)0.2%, and for \(H_{C}\) is \(\pm\)1%, of the original values. M-H for M-S samples were not measured. M-H measurements for M-S samples were not taken.  
\end{table} 
Table 1: Lattice parameters (\(a\), \(c\)), cell volume (Vol. ), saturation magnetization (\(M_{S}\)), and coercivity (\(H_{C}\)) values of the BaZn\({}_{2-x}\)Co\({}_{x}\)Fe\({}_{16}\)O\({}_{27}\) samples after the second calcination, with and without the application of the M-S method. Figure 2a-f presents BaZn\({}_{2-x}\)Co\({}_{x}\)W samples synthesized using the conventional solid-state method for \(x\) = 0.4, 0.5, 0.6, 0.75, 1.0, and 1.25. The images display plate-like crystallites after grinding, with sizes ranging from small fragments to approximately 10 \(\upmu\)m. No significant variation in average crystallite size is observed with changes in the \(x\) value. Figure 2g-i shows samples with compositions \(x\) = 0.75, 1.0, and 1.25 produced using the M-S method. It is evident that secondary calcination caused substantial crystallite growth compared to those synthesized by the conventional solid-state method. Numerous large, flat, plate-like particles exceeding 10 \(\upmu\)m are visible, with no clear trend of microstructural change as the \(x\) value increases. In Figure 3, the particle size distribution of BaZn\({}_{2-x}\)Co\({}_{x}\)W powder samples is presented as a histogram derived from SEM micrographs. Owing to the grinding process following secondary calcination, the grain sizes exhibit an irregular morphology. Grain size was quantified using the average line intercept method, with the mean particle size indicated in each figure panel.