Structure and microwave dielectric characteristics of (Ba,Sr,Ca)HfO3 ceramics

In the present work, the structure and microwave dielectric properties of (Ba,Sr,Ca)HfO3 ceramics were systematically investigated to understand the general mechanism of tuning the temperature coefficient of resonant frequency, τf in perovskite ceramics. Ba1–xSrxHfO3 and Sr1–yCayHfO3 could form continuous solid solutions while the solid solubility of Ca in Ba1–yCayHfO3 was about 20% (in mole). τf changed nonlinearly with increasing tolerance factor as the result of competition between the increase in the restoring force on the ions and the increase in polarizability. Under the guidance of three microscopic mechanisms affecting τf, a preliminary attempt was made to explore the suitable parameters to predict the variation trend of τf. Normalized ionic radii and the τf values of the end members were selected as independent variables, and τf was calculated by using multiple linear regression method. For Ba1–xSrxHfO3 and Sr1–yCayHfO3 with orthorhombic structures, the root mean square error between the calculated and measured τf was only 6.8×10–6 °C–1. The good agreement between the calculated τf values and the measured ones in Ba1–x–ySrxCayHfO3 ceramics confirmed its validity where three elements jointly occupy A-site, but it only works when there is no structural phase transition. Progresses in this research field would not only deepen our understanding of mechanism of regulating properties in multi-ion solid solutions, but also boost the developments of closely related fields such as machine learning-assisted design and high-entropy ceramics. Finally, a good combination of microwave dielectric properties was achieved in Sr0.15Ca0.85Hf0.96Ti0.040O3: εr = 27.8, Qf = 36,470 GHz, τf = +5×10–6 °C–1.