Structure evolution and adjustment of tf in (Ba, Sr)HfO3 and (Sr, Ca)HfO3 microwave dielectric ceramics

The crystal structure evaluation of Ba1-xSrxHfO3 and Sr(1-y)CayHfO(3) ceramics with varying composition was determined together with its influence on microwave dielectric characteristics. The variation mechanism of temperature coefficient of resonant frequency (iota(f)) was discussed in details, and the strong correlation between iota(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 Ba1-xSrxHfO3 at room temperature changed from Pm3m (x <= 0.25) to I4/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 tf rapidly declined at first, reached near zero, then slowly decreased, and finally rapidly decreased. Sr1-yCayHfO3 (0 <= y <= 1.0) belonged to space group Pnma. As the bond lengths and bond angles between B-atomandO-atombecame more andmore changeable (or BVS became smaller), the crystal could store more input heat energy through bond vibrational energy, and consequently iota(f) became closer to zero with increasing Ca-content, which was consistent with the physical meaning of the rattling effect on iota(f). With decreasing t, the dominant mechanisms responsible for tuning iota(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 tf and hopefully predict its trend with the help of iota(f)-t graph. These findings provided a new idea for developing solid solution ceramics with excellent temperature stability.

Automated summary

The crystal structure and microwave dielectric characteristics of Ba1-xSrxHfO3 and Sr(1-y)CayHfO(3) ceramics were evaluated. The study found a strong correlation between the temperature coefficient of resonant frequency (iota(f)) and bond valence sum and tolerance factor. The stable phase of Ba1-xSrxHfO3 changed with increasing Sr-content, resulting in changes in the dielectric constant. Additionally, with increasing Ca-content in Sr1-yCayHfO3, iota(f) approached zero, consistent with the rattling effect.