Figure 1 exhibits the XRD patterns of the Li3(Mg1 − *x*Zn*x*)2SbO6 (0.00 ≤ *x* ≤ 0.08) ceramics sintered at 1325 ℃ for 5 h. All the observed reflection peaks are indexed in terms of the Li3Mg2SbO6 phase (JCPDS-PDF No. 36-1019) with the Fddd space group. No secondary phase diffraction peaks can be detected, indicating that a complete solid solution is formed in all compositions. Figure 1(b) shows that the (1 1 1) diffraction peak shifts towards lower angles with *x* increasing from 0.00 to 0.08. Such variation indicates that larger Zn2+ (ion radius = 0.74 Å) successfully substitute for Mg2+ (ion radius = 0.72 Å) sites [16, 17].

Figure 2 illustrates the SEM photos of the Li3(Mg1 − *x*Zn*x*)2SbO6 (0.00 ≤ *x* ≤ 0.08) ceramics sintered at 1325 ℃ for 5 h. As shown in Fig. 2(a)-(c), the samples presented homogeneous morphology with few pores detected and the average grain size rises slightly with *x* increasing from 0.00 to 0.04. However, further increasing of the *x* value contributes nothing to the grain distribution but abnormal grain size distribution, as shown in Fig. 2(d-e). A case study of the sample with *x* = 0.04 sintered at 1350 °C manifests the abnormal morphology, as Fig. 2(f-g) shows. Therefore, a small amount of Zn2+ substitution for Mg2+ plays an important role in promoting the grain growth and morphology optimization. But excessive Zn2+ substitution inhibits the grain growth and deteriorate the homogeneous distribution of grains, which will deteriorate the dielectric properties. Linear intercept method is adopted to calculate the average grain size [18, 19]:

where *M*, *L*, and *N* represent the actual magnification, the length of the test line, and the number of intersections, respectively. The calculated average grain size for the optimal densified sample is about 10.7 µm, which is obtained at the sintering temperature of 1325 ℃ and *x* = 0.04, as shown in Fig. 2(k).

Figure 3 presents the variation of the bulk density and permittivity of the Li3(Mg1 − *x*Zn*x*)2SbO6 (0.00 ≤ *x* ≤ 0.08) ceramics sintered at different temperatures. The density curves of different samples behave similar variation tendency, as shown in Fig. 3(a). Specifically, each density curve increases initially and reaches to a maximum value at 1325 oC~1350 oC, then decreases with the sintering temperature. In addition, the density values for different sample increase with *x* and reaches to a maximum at *x* = 0.02. The increase of the bulk density is mainly attributed to the elimination of pores and grain growth. However, abnormal grain size distribution induced by further Zn2+ substitution reduces the density, which matches well with the SEM results. The highest density value of 3.43 g/cm3 was obtained in the sample of *x* = 0.02 at the sintering temperature of 1325 °C. Figure 3(b) shows the variation of the permittivity of the Li3(Mg1 − *x*Zn*x*)2SbO6 (0.00 ≤ *x* ≤ 0.08) ceramics sintered at different temperatures, which presents a similar tendency with the bulk density. In general, the dielectric permittivity is relevant to the porosity, phase constitution, and ionic polarizability [20, 21]. To eliminate the contribution of the porosity to the relative permittivity, the dielectric constant is corrected using the Eq. (3) [22]:

where *p* is the porosity fraction; *ε*rm, *ε*2, and *ε*corr are the air, measured, and porosity corrected dielectric constants, respectively. The molecule polarizabilities are calculated according to Shannon by the ion polarizabilities, as described in Eq. (4) [21]:

where *α*(Sb5+), *α*(Zn2+), *α*(Mg2+), *α*(O2−), and *α*(Li+) represent corresponding ion polarizability reported by Shannon [23]. The observed dielectric polarizabilities (αobs) are obtained by the Clausius-Mossotti equation derived from Eq. (5) [24]:

where *V*m and *b* indicate the molar volume and constant value (4π/3), respectively. The calculated results of *ɛ*corr, *α*theo, and *α*obs values of the Li3(Mg1 − *x*Zn*x*)2SbO6 ceramics sintered at 1325 °C are listed in Table 1. It is observed that the *α*obs and *α*theo values present different variation trends, while the *ε*r and *ɛ*corr values exhibit similar tendency. As no secondary phases are detected via the XRD, the permittivity of the Li3(Mg1 − *x*Zn*x*)2SbO6 ceramics is mainly determined by the compactness. It is well known that higher density means lower porosity, which usually contributes to higher permittivity.

Figure 4 shows the Q × f values of the Li3(Mg1 − *x*Zn*x*)2SbO6 (0.00 ≤ *x* ≤ 0.08) ceramics sintered at different temperatures. The Q × f curves for different specimens present similar variation trends, increasing firstly and reaching to maximum values then declining with the sintering temperature. The maximum Q × f value of 97,719 GHz is obtained in the sample of *x* = 0.04 sintered at 1325 ℃, which is enhanced significantly compared with that of the previous study on Li3Mg2SbO6 [15]. In general, the dielectric loss of the microwave ceramics is dominated by two primary factors: intrinsic structural characteristics such as packing fraction; and extrinsic factors such as the density, grain size, porosity, grain boundaries, and secondary phases [25–27]. As Li3(Mg1 − *x*Zn*x*)2SbO6 pure phase is detected, the Q × f values are mainly determined by the rest of the extrinsic factors except the secondary phase contribution. It is noticed that the maximum Q × f values for all samples except Li3Mg2SbO6 are obtained at the sintering temperature of 1325 oC, slightly lower than their optimal densification temperature. The increment of the Q × f values can be attributed to the densification and grain growth with the sintering temperature, which eliminates some pores and defects, as shown in Fig. 2(a)-(e) and Fig. 3 [28, 29]. However, fuzzy grain boundaries emerge with further increasing of the sintering temperature to above 1325 ℃, which could deteriorate dielectric loss, as manifested in Fig. 2(f-g). Therefore, the comprehensive impacts on the Q × f value are related with the grain size, grain boundaries, and porosity [10].

Figure 5 exhibits the τf values of the Li3(Mg1 − *x*Zn*x*)2SbO6 (0.00 ≤ *x* ≤ 0.08) ceramics sintered at 1325 °C for 5 h. It is observed that the τf value ranges from − 12 to -1 ppm/°C in the range of 0.00 ≤ *x* ≤ 0.08, presenting an enhanced tendency with *x*. The introduction of Zn2+ into the Li3Mg2SbO6 matrix for substituting Mg2+ could tune the τf value towards zero, implying that Zn2+ can effectively stabilize the crystal structure. Therefore, the substitution of Zn2+ for Mg2+ is considered as an effective solution to adjust the τf and improve the Q × f values of the Li3Mg2SbO6 based systems, which is promising for 5G communication technology.