Crystal structure, chemical bond characteristics and microwave dielectric properties of low-permittivity Ca_1–xMg_xY₂Ge₃O₁₀ ceramics with superlattice

Ca_1–xMg_xY₂Ge₃O₁₀ ceramics were synthesised using the solid-state reaction method. XRD analysis reveals that the solid solubility limit of Mg²⁺ in Ca_1–xMg_xY₂Ge₃O₁₀ lies between x = 0.15 and 0.20. Multiple characterisation approaches, including Phillips–van Vechten–Levine theory and bond valence analysis, were employed to systematically elucidate the crystal structure and microwave dielectric properties. TEM analysis revealed a distinct superlattice structure in the material, characterised by an increased density of (001) planes along the [100] zone axis. The presence of superlattice in Ca_0.9Mg_0.1Y₂Ge₃O₁₀ gives rise to a higher degree of lattice ordering, thereby reducing the intrinsic loss. The corrected dielectric constant shows a trend opposite to the α_D^T/V_m from Clausius–Mossotti (C–M) equation, primarily because of the rattling effect induced by Mg²⁺ substitution, which limits the applicability of the C–M equation. The intrinsic loss of CaY₂Ge₃O₁₀ was assessed by far-infrared spectroscopy. Key factors governing the microwave dielectric properties include total lattice energy (U_t), ion activation energy (E_a), and packing fraction (P.F.), which collectively determine the variation in Q×f, whereas the average distortion of Y–O bonds (Ave(δY–O)), the rattling effect and proportion of Ge–O bonds in total polarizability (χ(Ge–O)/χ), primarily affect τ_f. The Ca_0.9Mg_0.1Y₂Ge₃O₁₀ ceramic exhibits an enhanced Q×f, with microwave dielectric properties of ε_r = 10.1, Q×f = 106,440 GHz, and τ_f = −27.1 × 10⁻⁶ ℃⁻¹. At x = 0.15, a reduced Ave(δ_Y–O), a maximum χ(Ge–O)/χ, and a stronger rattling effect are observed, leading to a near-zero τ_f of −9.7 × 10⁻⁶ ℃⁻¹, with ε_r = 10.3 and Q×f = 91,920 GHz.