## 3 Results and Discussion
Figure 4 shows the SEM micrographs of the cross-sections of the MLLC9.5 ceramics sintered at different temperatures. The micrograph differences between Figure 4a-d could be due to the breaking of the ceramics, leading to different flatnesses. The grain size of the MLLC9.5 ceramic increased with the increase in the sintering temperature, and some pores were \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Phase** & \(D_{t}\) **(g/cm\({}^{3}\))** & \(V_{t}\) **(\(\times\)10\({}^{6}\) pm\({}^{3}\))** & \(\rho_{t}\) **(wt\(\%\))** & \(R_{up}\) **(\%)** & \(R_{p}\) **(\%)** & \(\chi^{2}\) & \(D\) **(g/cm\({}^{3}\))** \\ \hline Mg\({}_{2}\)SiO\({}_{4}\) & 3.311 & 290.337 & 59.07 & & & \\ \hline LiTiO\({}_{2}\) & 4.068 & 70.890 & 24.18 & & & \\ \hline Li\({}_{2}\)TiO\({}_{3}\) & 3.404 & 428.252 & 8.60 & 13.9 & 9.82 & 5.42 & 3.381 \\ \hline Li\({}_{2}\)MgSiO\({}_{4}\) & 2.575 & 336.059 & 6.27 & & & \\ \hline SiO\({}_{2}\) & 2.270 & 175.838 & 1.88 & & & \\ \hline \hline \end{tabular} \(R_{up}\): reliability factor of weighted patterns; \(R_{p}\): reliability factor of patterns; and \(\chi^{2}\): goodness of fit.  
\end{table} 
Table 1: Rietveld refinement result of the MLL ceramic. Figure 2: **(a)** XRD patterns of the MLLC ceramics sintered at 800 \({}^{\circ}\)C. **(b)** Rietveld refinement plots of the MLL ceramic. observed in all the samples except for those sintered at 800 \({}^{\circ}\)C, indicating that 800 \({}^{\circ}\)C was the optimal sintering temperature of the MLLC ceramics. Figure 4: SEM micrographs of the cross-sections of the MLLC9.5 ceramics sintered at different temperatures. (**a**) 775 \({}^{\circ}\)C, (**b**) 800 \({}^{\circ}\)C, (**c**) 825 \({}^{\circ}\)C, and (**d**) 850 \({}^{\circ}\)C.  
Figure 3: SEM micrographs of the cross-sections of the MLLC ceramics sintered at 800 \({}^{\circ}\)C. (**a**) MLL, (**b**) MLLC7.5, (**c**) MLLC8.5, (**d**) MLLC9.5, (**e**) MLLC10.5, and (**f**) MLLC11.5. Figure 5 shows the relative densities, volume densities, dielectric constants, \(Q\)\(\times\)\(f\)s, and \(\tau_{f}\)s of the MLLC ceramics. All the relative densities, volume densities, dielectric constants, and \(Q\)\(\times\)\(f\) values first increased and then decreased with the increase in the sintering temperature and achieved a maximum value in the samples sintered at 800 \({}^{\circ}\)C. When the sintering temperatures were higher than 800 \({}^{\circ}\)C, the air in the ceramics could not escape in time, and isolated pores remained trapped, resulting in higher porosity [38]. The dielectric constants and \(Q\)\(\times\)\(f\) values changed with the relative densities, which indicated that porosity played an important role in the MWDPs. The dielectric constants also varied in the additive amount of CaTiO\({}_{3}\) content due to the high dielectric constant of CaTiO\({}_{3}\) ceramics (~162) [39]. After adding the CaTiO\({}_{3}\) additives, an obvious increase in the relative density, dielectric constant, and \(Q\)\(\times\)\(f\) was observed for all the MLLC ceramics, revealing that the MWDPs were improved with the decrease in porosity. The \(\tau_{f}\)s of the MLLC ceramics sintered at 800 \({}^{\circ}\)C increased linearly with the increase in the CaTiO\({}_{3}\) content. The variation of \(\tau_{f}\)s could mainly be attributed to the CaTiO\({}_{3}\) content and described according to the Lichtenecker empirical rule  
\[\tau_{f}=V_{1}\tau_{f1}+V_{2}\tau_{f2} \tag{5}\]  
where \(V_{1}\) and \(V_{2}\) are the volume fractions and \(\tau_{f1}\) and \(\tau_{f2}\) are the \(\tau_{f}\) value of each phase. The increase in the \(\tau_{f}\) value could be due to the increased concentration of the CaTiO\({}_{3}\) phase, which was reported to have a high positive \(\tau_{f}\) value of +859 ppm/\({}^{\circ}\)C [39]. A near-zero \(\tau_{f}\) value of +5.81 ppm/\({}^{\circ}\)C was obtained for the MLLC11.5 ceramics sintered at 800 \({}^{\circ}\)C with an optimal \(Q\)\(\times\)\(f\) value of 54,581 GHz (at 8.06 GHz) and a low \(\varepsilon_{r}\) value of 14.13.