Structure evolution and adjustment of τ_f in (Ba_, Sr)HfO₃ and (Sr_, Ca)HfO₃ microwave dielectric ceramics

Abstract The crystal structure evaluation of Ba 1− x Sr x HfO 3 and Sr 1− y Ca y HfO 3 ceramics with varying composition was determined together with its influence on microwave dielectric characteristics. The variation mechanism of temperature coefficient of resonant frequency ( τ f ) was discussed in details, and the strong correlation between τ f and bond valence sum (BVS) and tolerance factor ( t ) was interpreted from the view point of energy. With increasing Sr‐content, the stable phase of Ba 1− x Sr x HfO 3 at room temperature changed from Pm m ( x ≤ 0.25) to I 4/ mcm (0.35 ≤ x ≤ 0.40), then to Imma (0.50 ≤ x < 0.75) and finally to Pnma (0.75 ≤ x ≤ 1.0). The peak temperature of dielectric constant changed due to the structure transition, resulting in that τ f rapidly declined at first, reached near zero, then slowly decreased, and finally rapidly decreased. Sr 1− y Ca y HfO 3 (0 ≤ y ≤ 1.0) belonged to space group Pnma . As the bond lengths and bond angles between B‐atom and O‐atom became more and more changeable (or BVS became smaller), the crystal could store more input heat energy through bond vibrational energy, and consequently τ f became closer to zero with increasing Ca‐content, which was consistent with the physical meaning of the rattling effect on τ f . With decreasing t , the dominant mechanisms responsible for tuning τ f changed from (i) phase transition and (ii) dilution of ion polarizability to (iii) rattling effect. One could investigate what were the dominant mechanisms tuning τ f and hopefully predict its trend with the help of τ f – t graph. These findings provided a new idea for developing solid solution ceramics with excellent temperature stability.