Machine-learning-guided discovery of Ca ₃ SnSi ₂ O ₉ -based ceramics with ultrahigh Q×f values for topological metasurface filters

Abstract 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 (εr), quality factor (Q×f), and temperature coefficient of resonant frequency (τf) 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 Ca3Sn1−xGexSi2O9 (0.025 ≤ x ≤ 0.20) ceramic system where controlled Ge4+ substitution for Sn4+ was strategically designed to synergistically optimize both Q×f and τf values while maintaining low εr. This improvement was achieved through the enhanced relative covalency (rc) of Sn–O and Si–O bonds, along with intensified octahedral distortion (δ) and polyhedral chain angles (σ) in the single-phase Ca3Sn1−xGexSi2O9 ceramics. Remarkably, the Ca3Sn1−xGexSi2O9 (x = 0.05) ceramics demonstrated outstanding performance, exhibiting an ultrahigh Q×f value of 120,413 GHz coupled with a favorably small negative τf 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 Ca3Sn1−xGexSi2O9 (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.