Correlation between crystal structure and dielectric characteristics of Ti4+ substituted CaSnSiO5 ceramics

Principal element design of garnets to access structure stability and excellent microwave dielectric properties

“…The τ f value is strongly dependent on bond valence, and the bond strength and oxygen octahedral distortion have been reported in other works 26,30 . The bond valences of cations can be evaluated using the following equations: $$\begin{equation}{V_i} = \sum\nolimits_j {{V_{ij}}} \end{equation}$$ $$\begin{equation}{V_{ij}} = {\rm{exp}}\left[ {\frac{{{R_{ij}} - {d_{ij}}}}{b}} \right]\end{equation}$$where $${R_{ij}}$$ is the bond valence parameters, $${d_{ij}}$$ is the bond length between the i and j atoms as shown in Table 1, and b is a universal constant (0.37 Å) 31 .…”

“…Based on the previous phase composition, microstructure, and density analysis, the influence of external elements could be ignored due to the absence of the second phase, compact microstructure with low porosity, and similar average grain sizes. As is well known, the intrinsic fundamental contribution of the dielectric constant comes from ion polarization, that is, the theoretical dielectric constant, which can be estimated by the Clausius–Mossotti 25,26 formula as follows: $$\begin{equation}{\varepsilon _{th}} = \frac{{3V + 8\pi \alpha }}{{3V - 4\pi \alpha }}\ \end{equation}$$where α is the polarizability of the whole ions in the compound and the V represents cell volume respectively. For pure phase garnet compounds, the single molecular polarizability of Ca 3 BTiGe 3 O 12 (B = Mg, Zn) can be estimated by Shannon's addition rule 27,28 as follows: $$\begin{eqnarray} {\alpha _{{\rm{theo}}}} &=& 12\alpha \left( {{{\mathop{\rm O}\nolimits} ^{2-}}} \right) + 3\alpha \left( {{\rm{G}}{{\rm{e}}^{4 + }}} \right) + \alpha \left( {{{\mathop{\rm B}\nolimits} ^{2 + }}} \right)\nonumber\\ && + \alpha \left( {{\rm{T}}{{\rm{i}}^{4 + }}} \right) + 3\alpha \left( {{\rm{C}}{{\rm{a}}^{2 + }}} \right)\end{eqnarray}$$…”

“…1,2,25 Based on the previous phase composition, microstructure, and density analysis, the influence of external elements could be ignored due to the absence of the second phase, compact microstructure with low porosity, and similar average grain sizes. As is well known, the intrinsic fundamental contribution of the dielectric constant comes from ion polarization, that is, the theoretical dielectric constant, which can be estimated by the Clausius-Mossotti 25,26 formula as follows:…”

The latest process and challenges of microwave dielectric ceramics based on pseudo phase diagrams

“…As doped ions, (Li 0.5 Ga 0.5 ) 3+ , and a near ℃ -zero τ f of (+4.52)-(+8.03) ppm/ was observed [66]. ℃ Furthermore, phase transition from A2/a to P2 1 /a was observed in new silicate in the formula of CaSn 1-x Ti x SiO 5 , where the variation of τ f values was ascribed to the Sn/TiO 6 octahedral distortion [67]. Secondary phase of SnO 2 and SrSiO 3 appeared at 0.2 ≤ x ≤ 0.45 in Ca 1-x Sr x SnSiO 5 ceramics, which could adjust the positive τ f of CaSnSiO 5 to -1.2 ppm/℃ [68].…”

The relationship between crystal structure and modified microwave dielectric properties of Ca3SnSi2‐xGexO9 ceramics

“…As a τ f resonator, Ti‐based materials cannot be the optimum choice to adjust the τ f of low‐permittivity microwave ceramics to nearer zero for millimeter‐wave applications. We have surveyed the relationships between the τ f and crystal structure of CaSnSiO 5 in detail 11,22,23 . SnO 6 octahedrons are important parts of CaSnSiO 5 , 24 and the τ f of CaSnSiO 5 can be controlled by regulating SnO 6 octahedral distortion.…”