Machine-learning-guided discovery of Ca ₃ SnSi ₂ O ₉ -based ceramics with ultra-high 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 (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 of Sn-O and Si-O bonds, along with intensified octahedral distortion and polyhedral chain angles in the single-phase Ca₃Sn1-xGexSi₂O₉ ceramics. Remarkably, the Ca₃Sn1-xGexSi₂O₉ (x = 0.05) ceramic demonstrated outstanding performance, exhibiting an ultra-high 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 ultra-low dielectric loss Ca₃Sn1-xGexSi₂O₉ (x = 0.05) ceramic. 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 GHz to 10.3 GHz. This advancement extends the potential applications of Ca₃SnSi₂O₉-based ceramics to the metasurface filters for high-frequency communication systems.