## 3 Results and Discussion  
The XRD patterns of Cu\({}_{x}\)Zn\({}_{1-x}\)Ti\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) ceramics (\(0.0\leq x\leq 0.4\)) sintered at 1050 \({}^{\circ}\)C-1300 \({}^{\circ}\)C for 4 h are shown in Figure 1a. With the increase in \(x\) values, all patterns could be indexed to the ZnZrNb\({}_{2}\)O\({}_{8}\) diffraction profile with JCPDS card #48-0324 [14], and no obvious secondary phase appeared. The second phase, including CuZrNb\({}_{2}\)O\({}_{8}\) and CuTiNb\({}_{2}\)O\({}_{8}\), was not detected, indicating that Cu\({}^{2+}\) entered the ZnTi\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) lattice and formed a solid solution. In addition, it was observed that the (111) and (020) peaks tended towards a higher diffraction angle, as shown in Figure 1b, indicating a gradual decrease in the unit cell volume. This is possibly due to the smaller ionic radius of Cu\({}^{2+}\) (0.73 A) than that of Zn\({}^{2+}\) (0.74 A) [23]. Figure 2 shows the SEM images of the Cu\({}_{x}\)Zn\({}_{1-x}\)Ti\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) (\(0.0\leq x\leq 0.4\)) ceramics after thermal etching treatment. The specimen with \(x=0.0\) exhibits a microstructure consisting of large grains with an average grain size of approximately (12.2 \(\pm\) 4.1) \(\mu\)m (Figure 2a). At \(x=0.2\), the average grain size decreased to around (5.9 \(\pm\) 1.3) \(\mu\)m (Figure 2b), probably because of the appearance of a secondary phase along the grain boundaries, which inhibited the grain growth. As \(x\) values further increased, the grain size decreased significantly and an average grain size of (3.6 \(\pm\) 0.9) \(\mu\)m could be found for \(x=0.4\) (Figure 2d). To recognize the secondary phase along the grain boundaries, EDS mapping analysis was conducted on the specimen with \(x=0.3\) (Figure S1 of the Supplementary Material), and the precipitated phase formed along the grain boundaries could be recognized as a Cu-rich phase. Because CuO is usually employed as the sintering aid for the ceramic densification at lower temperature through the mechanism of liquid-assisted sintering [24; 25; 26], and the current specimens were sintered at a high temperature of 1050-1300 \({}^{\circ}\)C, a liquid phase abundant in Cu readily formed along the grain boundaries. Figure 3 shows the relative densities and microwave dielectric properties of Cu\({}_{x}\)Zn\({}_{1-x}\)Ti\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) ceramics (\(0.0\leq x\leq 0.4\)). The relative densities of all the specimens exhibited high values (\(\geq\)95%), indicating that they were well sintered under the current conditions. A maximum value of \(\sim\)97.5% was achieved at \(x=0.3\). As the \(x\) values increased, the \(\varepsilon_{r}\) values fluctuated within a narrow range of 30-33. As reported by [PERSON] et al., the substitution of Cu\({}^{2+}\) will deteriorate the microwave dielectric properties [24]. Therefore, compared to the specimen with \(x=0.0\) (i.e., ZnTi\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\)), the \(Q\times f\) values decreased obviously. Nevertheless, the \(Q\times f\) values were still higher than 5000 GHz, especially the specimen with \(x=0.3\), which exhibited its highest \(Q\times f\) value of around 28,000 GHz when \(0.1\leq x\leq 0.4\), probably due to its highest relative density. The \(\tau_{f}\) values positively shifted from \(-47\) ppm/\({}^{\circ}\)C to \(-34\) ppm/\({}^{\circ}\)C, probably due to the effect of Cu\({}^{2+}\) substitution. Because the highest \(Q\times f\) value was achieved at \(x=0.3\), in the next step, LiF-added Cu\({}_{0.3}\)Zn\({}_{0.7}\)Ti\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) ceramics were synthesized, and their potential for LTCC applications was further evaluated. Figure 4 shows the XRD patterns of Cu\({}_{0.3}\)Zn\({}_{0.7}\)Ti\({}_{0.2}\)Zr\({}_{0.8}\)Nb\({}_{2}\)O\({}_{8}\) ceramics supplemented with \(y\) mol% LiF (\(10\leq y\leq 50\)) and without LiF (\(z,y=0\)) sintered at 950 \({}^{\circ}\)C and 1100 \({}^{\circ}\)C for 4 h, respectively.