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

Abstract

The crystal structure evaluation of Ba1‐xSrxHfO3 and Sr1‐yCayHfO3 ceramics with varying composition was determined together with its influence on microwave dielectric characteristics. The variation mechanism of temperature coefficient of resonant frequency (τf) was discussed in details, and the strong correlation between τf 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 Pmm (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 τf 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‐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 consequenly τf became closer to zero with increasing Ca‐content, which was consistent with the physical meaning of the rattling effect on τf. With decreasing t, the dominant mechanisms responsible for tuning τf changed from (i) phase transition and (ii) dilution of ion polarizability to (iii) rattling effect. One could investigate what were the dominant mechanisms tuning τf and hopefully predict its trend with the help of τf‐t graph. These findings provided a new idea for developing solid solution ceramics with excellent temperature stability.This article is protected by copyright. All rights reserved

Structure evolution and microwave dielectric characteristics of Hf1−xSnxO2 ceramics

“…First, the consideration could be focused on the structural characteristics that are determined by bond valence. The bond valance is defined as the sum of all the valances for a given atom i and could be calculated by the following formulas 27,28 : $$$$\begin{equation}{V_{\mathrm{i}}} = \mathop \sum \limits_j {\nu _{ij}}\end{equation}$$$$ $$$$\begin{equation}{\nu _{ij}} = {{\mathrm{e}}^{\left( {\frac{{{R_{ij}} - {d_{{\mathrm{i}}j}}}}{{\mathrm{b}}}} \right)}}\end{equation}$$$$where $${R_{ij}}$$ is the bond valance parameter and $${d_{ij}}$$ is the bond length between atoms i and j . b is used as a universal constant (0.37 Å).…”