Abnormal dielectric behavior of glaserite-type Ba_3−xSr_xMgSi₂O₈ solid solution

The temperature coefficient of the resonant frequency (τ_f) of low-permittivity (ε_r) microwave dielectric ceramics is required to be near 0 ppm/°C for practical application. However, owing to the polarization mechanism, τ_f of low-ε_r microwave dielectric ceramics is generally negative. Here, a novel microwave dielectric ceramic, Ba_3−xSr_xMgSi₂O₈, with an abnormal positive τ_f at the applied temperature is presented. In this study, Sr²⁺ with a relatively small ionic radius was introduced to replace Ba²⁺, and a single-phase solid solution was formed (x > 0.5). Ba_3−xSr_xMgSi₂O₈ ceramics were discussed in glaserite-type topology with space groups of P $\overline{3}$ for x ≤ 0.5, relatively high symmetry P $\overline{3}$m1 for 0.5 < x < 2.5, and C2 for x ≥ 2.5. The ε_r peaks as a function of temperature initially shift to low temperatures and then return to high temperatures through an ion substitution strategy. Notably, remarkable microwave dielectric properties for BaSr₂MgSi₂O₈ were observed: ε_r ≈ 14.2, Q×f ≈ 38,900 GHz, and τ_f ≈ +117 ppm/°C, which are superior to those of other low-ε_r silicate ceramics with positive τ_f values. Density functional theory simulation calculations revealed that the preferential occupation of Sr²⁺ ions could decrease the intrinsic formation energy and improve the microwave dielectric properties by mitigating the ionic size mismatch within the crystal structure. The present research offers a strategy for discovering novel microwave dielectric ceramics with abnormal τ_f values, which could serve as τ_f regulators in practical applications because of their low cost and excellent microwave dielectric properties.