Microwave dielectric ceramics have emerged as highly promising materials for high-frequency applications due to their exceptional dielectric properties. Nevertheless, achieving an optimal balance among the interdependent parameters of relative permittivity (ε_r), quality factor (Q×f), and temperature coefficient of resonant frequency (τ_f) to satisfy the technical requirements of microwave components continues to pose a substantial challenge. In this work, an interpretable machine learning framework was proposed to elucidate the structure–property relationships, thereby guiding the compositional design of the candidate microwave ceramic Ca₃SnSi₂O₉. Based on the machine learning insights, we developed a Ca₃Sn_1−xGe_xSi₂O₉ (0.025 ≤ x ≤ 0.20) ceramic system where controlled Ge⁴⁺ substitution for Sn⁴⁺ was strategically designed to synergistically optimize both Q×f and τ_f values while maintaining low ε_r. This improvement was achieved through the enhanced relative covalency (r_c) of Sn–O and Si–O bonds, along with intensified octahedral distortion (δ) and polyhedral chain angles (σ) in the single-phase Ca₃Sn_1−xGe_xSi₂O₉ ceramics. Remarkably, the Ca₃Sn_1−xGe_xSi₂O₉ (x = 0.05) ceramics demonstrated outstanding performance, exhibiting an ultrahigh Q×f value of 120,413 GHz coupled with a favorably small negative τ_f value of −25.8 ppm/°C. These results clearly demonstrate that the collaborative optimization strategy can significantly enhance the microwave dielectric properties of Ca₃SnSi₂O₉-based ceramics. Furthermore, a single-mode topological metasurface filter operating in the X-band was designed and fabricated using the ultralow dielectric loss Ca₃Sn_1−xGe_xSi₂O₉ (x = 0.05) ceramics. Leveraging the bulk-edge correspondence, we established a relationship between structural morphology with transitional deformations and operating frequency. Experimental results demonstrated that the topological metasurface filter can operate at any frequency within the range of 9.6–10.3 GHz. This advancement extends the potential applications of Ca₃SnSi₂O₉-based ceramics to metasurface filters for high-frequency communication systems.

Excellent microwave dielectric properties and ultra-low thermal expansion are essential for dielectric ceramics in high-frequency substrate applications. However, the inherent constraints among these three key microwave dielectric properties make it challenging to achieve ultra-low relative permittivity (ε_r), high quality factor (Q×f), and near-zero temperature coefficient of the resonance frequency (τ_f) values simultaneously in existing materials. In particular, the coefficient of thermal expansion (CTE) of microwave dielectric ceramics often reaches approximately 10 ppm/°C, indicating limited tunability. In this work, based on novel osumilite-type BaMg₂Al₆Si₉O₃₀ ceramics with high crystal structural symmetry and excellent stability, we designed a strategy involving the substitution of Si⁴⁺ with larger Ge⁴⁺ ions. Replacing Si⁴⁺ with larger Ge⁴⁺ ions directly elongated the Si/Al(1)–O bond length while reducing the Si/Al(1)–O(1)–Si/Al(1) angle (σ₂). This structural modification suppressed the longitudinal vibration of 2-coordinate O(1) along the a-axis, effectively inhibiting negative thermal expansion and yielding a reduced CTE within the operational temperature range. Simultaneously, the elongation of the Si/Al(1)–O bond cooperatively increased the Si/Al(1)–O(2)–Si/Al(1) angle (σ₁) and enhanced the relative covalency of the Si/Al(1)–O bond, synergistically improving the Q×f values. Importantly, Ge⁴⁺ substitution preserved ultra-low ε_r and near-zero τ_f values by maintaining the polarization characteristics and crystal structural stability of BaMg₂Al₆Si₉O₃₀-based ceramics. The optimized BaMg₂Al₆Si_7.75Ge_1.25O₃₀ ceramics achieved excellent microwave dielectric properties: ε_r = 5.84, Q×f = 32,351 GHz, τ_f = −7.27 ppm/°C, and an ultra-low CTE of +1.07 ppm/°C. The successful co-regulation of the Q×f and CTE values was attributed to the polyhedral coupling strategy, which leveraged the structural features of the osumilite-type ceramics to synergistically optimize the tilting and distortion of critical polyhedra.