## 3 Results and Discussion
Two kinds of grains possessed Mg, Zn, Ni, Ti, and O ions with different stoichiometric compositions (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)TiO\({}_{3}\) and (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)Ti\({}_{2}\)O\({}_{5}\), respectively, were clearly distinguished in the multiphase ceramics. The grain composition analysis observed from points A-F demonstrated that (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)TiO\({}_{3}\) and (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)Ti\({}_{2}\)O\({}_{5}\) form solid solutions to a certain degree, which is consistent with XRD analysis. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**y** & **Sintering** & **a (nm)** & **c (nm)** \\ \hline
**Value** & **Temperature**(\({}^{\circ}\)**C) & **a (nm)** & **c (nm)** \\ \hline
0.01 & 1175 & 0.50656 \(\pm\) 0.00051 & 1.39113 \(\pm\) 0.00082 \\  & 1200 & 0.50702 \(\pm\) 0.00900 & 1.39242 \(\pm\) 0.00146 \\  & 1225 & 0.50481 \(\pm\) 0.00055 & 1.38946 \(\pm\) 0.00089 \\
0.03 & 1175 & 0.50650 \(\pm\) 0.00079 & 1.39209 \(\pm\) 0.00170 \\  & 1200 & 0.50713 \(\pm\) 0.00057 & 1.39041 \(\pm\) 0.00121 \\  & 1225 & 0.50689 \(\pm\) 0.00054 & 1.39147 \(\pm\) 0.00087 \\
0.05 & 1175 & 0.50671 \(\pm\) 0.00057 & 1.39158 \(\pm\) 0.00122 \\  & 1200 & 0.50670 \(\pm\) 0.00032 & 1.39196 \(\pm\) 0.00069 \\  & 1225 & 0.50545 \(\pm\) 0.00063 & 1.39144 \(\pm\) 0.00103 \\
0.07 & 1175 & 0.50632 \(\pm\) 0.00045 & 1.39188 \(\pm\) 0.00096 \\  & 1200 & 0.50585 \(\pm\) 0.00106 & 1.38861 \(\pm\) 0.00227 \\  & 1225 & 0.50565 \(\pm\) 0.00039 & 1.39175 \(\pm\) 0.00064 \\
0.1 & 1200 & 0.50577 \(\pm\) 0.00068 & 1.39031 \(\pm\) 0.00110 \\
0.2 & 1200 & 0.50593 \(\pm\) 0.00090 & 1.38992 \(\pm\) 0.00146 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The calculated lattice parameter of (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{1-y}\)Ni\({}_{y}\)TiO\({}_{3}\) ceramic with y = 0.01–0.2. Figure 4: The EDS analysis of (**a**) (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)TiO\({}_{3}\) sintered at 1200 \({}^{\circ}\)C (**b**) (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\) Ni\({}_{0.05}\)Ti\({}_{2}\)O\({}_{5}\) sintered at 1250 \({}^{\circ}\)C for 4 h.  
Figure 3: SEM photographs of (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)TiO\({}_{3}\) sintered at temperature range (**a**) 1125, (**b**) 1150, (**c**) 1175, (**d**) 1200, (**e**) 1225 and (**f**) 1250 \({}^{\circ}\)C for 4 h.  
The apparent and relative density of the (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{1-y}\)Ni\({}_{y}\)TiO\({}_{3}\) with y = 0.01-0.2 sintered at different temperatures (1125-1250 \({}^{\circ}\)C) for 4 h is demonstrated in Figure 5. The relative density of the (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{1-y}\)Ni\({}_{y}\)TiO\({}_{3}\) exceeded 91.6% of the theoretical density (TD) in all specimens. The apparent density of the samples increased when the temperature increased from 1125 to 1200 \({}^{\circ}\)C. This increase in the apparent density can be attributed to the formation of dense microstructures, as observed in Figure 3d. The apparent density decreased when the temperature exceeded 1200 \({}^{\circ}\)C.  
This decrease in the apparent density could result from the formation of a porous microstructure with large pores, as observed in Figure 3e.f. The apparent density and its corresponding TD increased from 4.15 g/cm\({}^{3}\) (94.32% TD) to its maximum value of 4.39 g/cm\({}^{3}\) (99.77%TD), and then decreased to 4.33 g/cm\({}^{3}\) (98.41%TD) for the (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{0.95}\)Ni\({}_{0.05}\)TiO\({}_{3}\) ceramics. The permittivity and quality factor (Q\(f\)) of (Mg\({}_{0.6}\)Zn\({}_{0.4}\))\({}_{1-y}\)Ni\({}_{y}\)TiO\({}_{3}\) ceramics sintered at temperatures for 4 h with various y values (0.01-0.2) are shown in Figure 6. The relationship between permittivity (\(\varepsilon_{r}\)) values and temperature reveals the same trend between densities and temperature since higher density means lower porosity inside samples.