Structure and Microwave Dielectric Properties of Gillespite-Type ACuSi4O10 (A = Ca, Sr, Ba) Ceramics and Quantitative Prediction of the Q × f Value via Machine Learning

Structure and dielectric properties of gillespite-type ceramics ACuSi₄O₁₀ (A = Ca, Sr, Ba) were investigated by crystal structure refinement, far-infrared reflectivity spectroscopy, and microwave dielectric measurements. A series of (Ca_xSr_1-x)CuSi₄O₁₀ (0 < x < 1) ceramics with relative permittivities of 5.70-5.82, Q × f values of 20391-48794 GHz (@ ∼ 13.5 GHz), and τ_f of -46.3 to -38.9 ppm/°C were synthesized. By Ca²⁺ substitution for Sr²⁺ at the A-site, the rigid double-layered copper silicate framework remains stable, resulting in the nearly unchanged relative permittivity, while the [(Ca,Sr)O₈] dodecahedron undergoes shrinkage and distortion, which is correlated to the changes in the Q × f and τ_f values. The normalized bond valence sums indicate that almost all ions are rattling, weakening the bond strengths and enlarging the molecular dielectric polarizability. The fitting of far-infrared reflectivity spectra reveals that the local structure changes suppress the intermediate and low-frequency vibrational modes significantly and improves the contribution from electronic polarization to permittivity. Symmetry breaking of the [(Ca,Sr)O₈] dodecahedron conforms to the elevated restoring forces acting on the ions and improves the τ_f value. The large span in Q × f value may have intricate correlations to local structure changes and defects. Machine learning methods were introduced to explore the decisive structural factors for the Q × f value. A Q × f value prediction model correlated with the A-O2 bond length and the variance of A-O bond lengths was established. The Q × f values of isostructural (Ba_ySr_1-y)CuSi₄O₁₀ ceramics were predicted and verified by experiments.