Microwave dielectric properties of (1‐x)Ba_3.75Nd_9.5Cr_0.25Nb_0.25Ti_17.5O₅₄–xNdAlO₃ ceramics

Abstract

This study presents the microwave dielectric properties calculation of (1-x)Ba 3.75 Nd 9.5 Cr 0.25 Nb 0.25 Ti 17.5 O 54 -xNdAlO 3 ceramics where x denotes the volume molar fraction. From X-ray diffraction results, the solid solution limit is calculated to be about 0.76, where it forms a single BaNd 2 Ti 4 O 12 phase in Region I (0 ≤ x ≤ 0.76), and both BaNd 2 Ti 4 O 12 and NdAlO 3 coexist in Region II (0.76 < x < 1). The solid solution limit is confirmed by independently calculating it from the dielectric constant data. There is less than 4 % deviation between the measured dielectric constant (ε r ) and the one calculated from the Maxwell-Wagner formula. The total quality factor (Q) remains almost constant in Region I and increases rapidly with the volume molar fraction of NdAlO 3 in Region II. The measured Q×f, where f is the resonant frequency, is also consistent with the calculated value in both regions. The temperature coefficient at the resonant frequency is -1.4 ppm/ o C, which agrees well with the calculated value of 0 ppm/ o C. In addition, we observed a close correlation between the bulk density and the phase evolution.

Determining the Quality Factor of Dielectric Ceramic Mixtures with Dielectric Constants in the Microwave Frequency Range

“…Typical microwave ceramics are included, e.g. MgTiO 3 10,53,54 , BaTi 4 O 9 55 , Ba 6-3x Nd 8+2x Ti 18 O 54 4,30,48 , TiO 2 6,8,9,13,15,56,57 , CaTiO 3 11,14,16,22,24,49,50,58,59 , and Li 1/2 Nd 1/2 TiO 3 17,20,22 . These 3 groups are: 1. multiphase composites, 2. single phase solid solutions, 3. equivalent ionic substituted single phase ceramics.…”

“…These applications demand ceramics with high dielectric constant ( ε r ), high quality factor ( Q ) and near-zero temperature coefficient at the resonant frequency ( τ f ) 1–3 . However, most ceramics inherently possess non-zero temperature coefficients at the resonant frequency 3,4 . Therefore, for a ceramic of interest in real applications, another ceramic with τ f of an opposite sign needs to be mixed with it or ionic substitution in it is required, to modify the τ f to zero 5,6 .…”

“…When the material of − τ f is mixed, a binary phase composite could be formed if the structure of the two ceramics are different 6,8–16 . Otherwise, the mixed material will be a single phase solid solution 4,5,17–24 . In previous work, the solid solution was treated as a two-phase composite 16,17,20–24 , where the dielectric constant can be derived from the Maxwell-Wagner equation 7–9,25,26 where V represents the volume molar ratio of the second material, ε r is the dielectric constant of the composite, ε r 1 and ε r 2 are the dielectric constants of the two ceramics, respectively.…”

“…The quality factor of the binary phase composite can be estimated by 4,8,28 where Q represents the quality factor of the mixture system, and Q 1 and Q 2 are the quality factors of the two ceramics, respectively. From the definition of Q (it will be given in equation (8) in the next section) at the microwave frequency range, the quality factor of the mixture is related to both the dielectric constant and the resonant frequency 1,5,6,25,26,29 .…”

“…The solid solution can be treated as the ionic substitution situation at some circumstances 4,18,19 . When the ionic substitution is performed, the original phase can be maintained.…”