Abstract
Microwave dielectric ceramic materials are extensively utilized in microwave applications because of their high dielectric constants and quality factors. These applications also require ceramics of zero temperature coefficients at the resonant frequency (τf), which can be realized through mixing a ceramic that one is interested in with another ceramic with −τf, or by performing the ionic substitution. With the mixing/ionic substitution, it is indispensable to compute the quality factors precisely. Previous study indicates that the quality factor depends on the grain size, porosity, internal strain, structure, phase evolution, and conductivity etc. Here we derive a quality factor formula based on the definition, which works very well for multiphase composites, single phase solid solutions, and equivalent ionic substituted single phase materials. Our formula calculation and fits to the previous experimental results demonstrate that the quality factor of the ceramic mixtures strongly depend on the dielectric constants and the dielectric constant variation index. Our results suggest that the impacts from grain size, porosity, and internal strain etc. can be summarized to the dielectric constant or dielectric constant variation index, which is of great importance for future design of high performance microwave dielectric ceramics.
Highlights
Microwave dielectric ceramics have been used extensively in resonators, filters, radars, and integrated passive modules for wireless communication applications[1,2,3]
The quality factor of the mixed ceramics should be predicable if we know the microwave properties of the two materials defined in equation (1) and (2), and the new phase(s)
We find that the precise quality factor calculation strongly depends on the dielectric constant when the materials in each group are fabricated by the same or similar process
Summary
Hetuo Chen[1,2], Xuewen Fu2, Qi An 3, Bin Tang[1], Shuren Zhang[1], HaoYang4,Yin Long[1], Mark Harfouche[2], Huolei Wang2 & Yingxiang Li1. The quality factor of the mixed (including binary phase, solid solution and equivalent ionic substitution) ceramics should be predicable if we know the microwave properties (including dielectric constants, quality factors, and the volume molar ratios) of the two materials defined in equation (1) and (2), and the new phase(s). Examples will be grouped into: (1) binary phase composites, where the dielectric constant and quality factor of the two original materials are known; (2) single phase solid solution, e.g. the quality factor of the perovskite structure CaTiO3-NdAlO3 will be calculated through dielectric constants and quality factors of CaTiO3 and NdAlO332; (3) equivalent ionic substitutions, e.g. the quality factors of Ca1-xSrxTiO3 (0 ≤ x ≤ 1) will be calculated via CaTiO3 and SrTiO349. The case of extra new phases co-existing will not be considered because the volume molar ratios were not given in the previous literatures[41,42,43]
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