Phase transition, infrared spectra, and microwave dielectric properties of temperature-stable CaSnSi1-Ge O5 ceramics

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

“…The excess Ge 4+ may substitute for Si 4+ , and the CaSnSiO 5based second phase may be the CaSnSi 1-x Ge x O 5 phase. According to our previous work, 25 the CaSnSi 1-z Ge z O 5 (0 ≤ z ≤ 0.7) solid solution exhibited a monoclinic structure with the A2/a space group and a triclinic structure with A 1 space group could be obtained at CaSnSi 1-z Ge z O 5 (0.8 ≤ z ≤ 1.0). An evident difference in XRD peaks was observed between CaSnSi 1-z Ge z O 5 (0 ≤ z ≤ 0.7) with a monoclinic structure and CaSnSi 1-z Ge z O 5 (0.8 ≤ z ≤ 1.0) with a triclinic structure.…”

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 .…”

“…As illustrated in Figure 6, to speculate the intrinsic contribution of dielectric properties, IR reflection spectra of Ca 3 BTiGe 3 O 12 (B = Mg, Zn) ceramics in the range of 100–1000 cm −1 were recorded and reflectance data were fitted with the Lorentz oscillator model and Fresnel formula: $$\begin{equation}{\varepsilon ^*}\left( \omega \right) = {\varepsilon _\infty } + \sum\nolimits_{j\ = \ 1}^n {\frac{{\omega _{pj}^2}}{{\omega _{oj}^2 - \ {\omega ^2} - j\omega {\gamma _j}}}} = \varepsilon ^{\prime}\left( \omega \right) - i\varepsilon ^{\prime\prime}\left( \omega \right)\end{equation}$$ $$\begin{equation}R\left( \omega \right) = {\left| {\ \frac{{1 - \sqrt {{\varepsilon ^*}\left( \omega \right)} }}{{1 + \sqrt {{\varepsilon ^*}\left( \omega \right)} }}\ } \right|^2}\end{equation}$$where ε *( ω ) represents a complex dielectric function, $${\varepsilon _\infty }$$ is the permittivity caused by the electronic polarization at optical frequencies, n refers to the order of transverse polar‐phonon modes, ω pj , ω oj , and γ j are the plasma frequency, eigen frequency, and damping constant of the j th mode, respectively. The real part ( ɛ ′( ω )) of microwave relative permittivity and loss tangent (tan δ ) can be evaluated as follows 30,39 : …”

“…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:…”

“…As illustrated in Figure 6, to speculate the intrinsic contribution of dielectric properties, IR reflection spectra of Ca 3 BTiGe 3 O 12 (B = Mg, Zn) ceramics in the range of 100-1000 cm −1 were recorded and reflectance data were fitted with the Lorentz oscillator model and Fresnel formula: (9) where ε*(ω) represents a complex dielectric function, 𝜀 ∞ is the permittivity caused by the electronic polarization at optical frequencies, n refers to the order of transverse polar-phonon modes, ω pj , ω oj , and γ j are the plasma frequency, eigen frequency, and damping constant of the jth mode, respectively. The real part (ɛ′(ω)) of microwave relative permittivity and loss tangent (tanδ) can be evaluated as follows 30,39 :…”