Machine-learning-guided discovery of Ca₃SnSi₂O₉-based ceramics with ultrahigh Q×f values for topological metasurface filters

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.