TaBLE 3 - uploaded by Robert D. Shannon
Content may be subject to copyright.
Source publication
The dielectric constants and dielectric loss values of a series of garnets were measured at l MHz using a two-terminal method and empirically determined edge corrections. The results are five intermediate pyrope-almandine samples, k'=11.96-12.35; spessartine, k'=11.65; two andradite samples, k'=10.53-10.59; and three grossular samples, k'=8.53-8.8l...
Similar publications
We consider the appearance of a cavitation near a needle-shaped electrode under nanosecond high-voltage impulse. It was shown that the gas–liquid boundary moves in an opposite direction to the needle-shaped electrode under the influence of electric field on this boundary. It leads to an increase of the cavity volume. The comparison with experiment...
Citations
... Each atom corresponds to a distinct vibration, and these atomic vibrations combine to form the Raman vibration mode [41]. For example, the Bg modes are composed of Bg (11) (Ln), Bg (12) (Ln), Bg (21) (Li), Bg (22) (Li), Bg (31) (P), Bg (32) (P), Bg (33) (P), Bg (41) (O1), Bg (42) (O1), Bg (43) (O1), Bg (51) (O2), Bg (52) (O2), Bg (53) (O2), Bg (61) (O3), Bg (62) (O3), Bg (63) (O3), Bg (71) (O4), Bg (72) (O4), Bg (73) (O4), Bg (81) (O5), Bg (82) (O5), Bg (83) (O5), Bg (91) ...
... In addition, it is observed that the εr value in the microwave band is significantly lower than that in the low-frequency band, mainly due to space charge polarization and dipole orientation polarization withdrawal from the dielectric response, and the ion displacement J u s t A c c e p t e d polarization becomes the major mechanism in the microwave range. Consequently, the theoretical permittivity (εth) in the microwave band can be inferred using the Clausius-Mossotti equation, and the molecular polarizability (αD) is calculated by using the following Shannon's additive rule [52]: ...
... The theoretical molecular polarizability (eqn. 1) changes with different substitutions, resulting in a change in ε theo , calculated according to the Clausius-Mossotti equation (eqn. 2) [29,30]. ε theo and ε cor are almost consistent with the measured ε r . ...
... In order to eliminate the effect of air holes, the where P is the porosity, ε r is the measured value of the relative permittivity, and ε pc is porosity corrected dielectric constant. The theoretical polarizability can be calculated by the summation rule proposed by Shannon [29]. ...
An efficient reaction sintering process is engaged to synthesize a series of non-stoichiometric Li2(1+x)Mg3TiO6 (x = 0.01, 0.02, 0.03, 0.04) microwave dielectric ceramics. The single phase of Li2Mg3TiO6 with rock-salt structure is accurately recognized by XRD. Pores left on the surface and inside the sample can be clearly observed from SEM pictures. Excessive Li⁺ affects the local charge distribution, which influences the response of the dielectric material to the electric field. The pores are not the same medium as the matrix material, and the signal is refracted and scattered when it passes through the pores. Refractions and scatterings increase the signal transmission distance and also increase the transmission loss. These residual Li⁺ and pores eventually affect the dielectric properties as well. Finally, at x = 0.02 and a sintering temperature of 1260 °C, the ceramic samples showed good dielectric properties: εr = 10.983, Q×f = 107,367 GHz and τf = − 24.2 ppm/°C.
... Generally, ε r at microwave frequencies is dominated by ionic polarization, which is determined by constituent ions, bond valence, crystal structure, and bulk density. 28,29 In the present work, the theoretical ionic polarizabilities have been calculated by applying Shannon's additive rule, 30 and the polarizabilities of constituent ions of (Hf 1-x Zr x TiO 4 ceramics can be described as the following: ...
Hf1‐xZrx)TiO4 and (Hf1‐xSnx)TiO4 ceramics were prepared through a standard solid‐state reaction route, and the microwave dielectric characteristics were determined together with the microstructures. The single‐phase solid solution in space group Pbcn was obtained in (Hf1‐xZrx)TiO4, while the two‐phase structure with (HfTiO4(s.s.) major phase in space group Pbcn and Sn0.3Ti0.7O2 secondary phase in space group P42/mnm) was determined in (Hf1‐xSnx)TiO4. The temperature coefficient of resonant frequency τf could be significantly improved to near‐zero in both systems, and the best combination of microwave dielectric characteristic was achieved at x = 0.5 in (Hf1‐xZrx)TiO4: εr = 39.0, Qf = 43,150 GHz at 5.3 GHz and τf = 3 ppm/°C, and at x = 0.225 in (Hf1‐xSnx)TiO4: εr = 37.2, Qf = 52,600 GHz at 5.5 GHz and τf = ‐6 ppm/°C. In the solid solutions, the obvious improvement of τf could be deeply linked with the degree of covalency and the restoring forces of structure. While, the intermediate near‐zero τf is achieved by mixing the phases with opposite τf in multiphase materials. The present work provided an effective way to modify the temperature coefficient of resonant frequency in microwave dielectric ceramics.
... In addition, among all the compositions with excess Na, Na1+xSrB5O9+0.5x (x = 0.05, Ts = 800 °C) shows the To further discuss the influence of the Na content on the ε r values of Na 1+x SrB 5 O 9+0.5x ceramics sintered at optimum temperatures, the corrected dielectric constant (ε rc ) was obtained by correcting the measured dielectric constant (ε r ) of the ceramics for porosity, and the theoretical dielectric constant (ε cal ) and the actual molecular polarization (α obs ) were calculated based on the refined results, as shown in Figure 5b. The values were determined as follows [22][23][24]: ε rc = ε r (1 + 1.5P) (12) ...
Microwave dielectric ceramics composed of Na1+xSrB5O9+0.5x (0 ≤ x ≤ 0.125) were synthesized via a traditional solid-state reaction approach. The effects of non-stoichiometric Na on the crystal structures, phase compositions, chemical bond characteristics, and microwave dielectric properties of the Na1+xSrB5O9+0.5x ceramics were systematically studied. All Na1+xSrB5O9+0.5x ceramics sintered at optimum temperatures consisted of a NaSrB5O9 solid-solution phase and a SrB2O4 phase. Appropriate excess Na could suppress the generation of the SrB2O4 phase, and the lowest content of the SrB2O4 phase was achieved at x = 0.075. The εr values of the Na1+xSrB5O9+0.5x ceramics were primarily affected by the relative density and molecular polarization. The Q × f values showed a positive correlation with the lattice energy. The τf value was correlated to the SrB2O4 phase content, bond valence, and bond energy. Typically, the Na1.075SrB5O9.0375 ceramic sintered at 825 °C possessed good microwave dielectric properties of εr = 5.61, Q × f = 31, 937 GHz, and τf = −3.09 ppm/°C, which are suitable for high-frequency, low-temperature co-fired ceramics (LTCCs) substrate applications.
... Å 3 ), germanates (α = 1.63 Å 3 ), and so on. 7,8 Among them, the Si-based melilites have attracted much attention due to their excellent microwave dielectric ceramics and flexible crystal structure. [9][10][11][12] For example, Lei et al. reported that BaCo 2 Si 2 O 7 ceramic sintered at 1060 • C with excellent microwave dielectric properties ε r ∼ 9. 26, Q × f ∼ 31 135 GHz, and τ f ∼ −92.05 ppm/ • C. 9 Ba 2 ZnSi 2 O 7 ceramic also attracted much attention due to its excellent microwave dielectric properties (ε r ∼ 8.09, Q × f ∼ 26 634 GHz, and τ f ∼ −51.46 ppm/ • C) and the weak ferroelectricity. ...
The dielectric properties of a Ga‐based melilite type ceramic Sr2Ga2SiO7 via theoretical prediction based on far‐infrared spectroscopy and experimental measurement by the Hakki–Coleman method were studied in this work. Dense and single‐phase ceramics were fabricated via solid‐state reaction at 1330°C and exhibited comprehensive microwave dielectric properties (εr ∼ 7.6, Q × f ∼ 23 600 GHz, and τf ∼ −35.2 ppm/°C) at 14.3 GHz. Chemical modifications were proposed to adjust the thermal stability and reduce the densification temperature. By adding 10 mol% CaTiO3, the negative τf can be compensated to a near‐zero value of −3.8 ppm/°C. The densification temperature was reduced to 940°C by adding 3 wt.% LiF. A patch antenna was designed using Sr2Ga2SiO7 ceramic with a high radiation efficiency of 99.1% and a gain of 2.788 dBi at the center frequency of 4.371 GHz. All results indicate that the Sr2Ga2SiO7 ceramic has promising application potential for 5G wireless communication technology.
... Many physical properties have a strong functional dependence or correlation with lattice parameter (a), or a derivative metric such as average volume per atom or average bond length. 65,66,67,68,69,70,71,72,73,74,75,76,77,78 The same cations occupy both the tetrahedral and octahedral sites in common ternary garnets such as the rare-earth aluminates (Ln 3 Al 5 O 12 ), ferrates (Ln 3 Fe 5 O 12 ), and gallates (Ln 3 Ga 5 O 12 ). In these garnets a increases linearly with rare-earth ion size. ...
The validity of prediction methods for garnet lattice parameters was tested, and a modified model with best fit to a lattice parameter database with over 1000 garnet compositions was developed. The lattice parameter predictions were used in Shannon and Fischer's model to predict garnet refractive indices. The predictions were compared to refractive index measurements reported for 143 garnet compositions. After calibration of electron overlap factors used in the model, the average prediction error was 1.13%. Sources of error in the models are discussed, as well as applications of the predictive methods.
... Many physical properties have a strong functional dependence or correlation with lattice parameter (a), or a derivative metric such as average volume per atom or average bond length. 65,66,67,68,69,70,71,72,73,74,75,76,77,78 The same cations occupy both the tetrahedral and octahedral sites in common ternary garnets such as the rare-earth aluminates (Ln 3 Al 5 O 12 ), ferrates (Ln 3 Fe 5 O 12 ), and gallates (Ln 3 Ga 5 O 12 ). In these garnets a increases linearly with rare-earth ion size. ...
A series of LiCa2Mg2As3xV3−3xO12 garnet powders (x = 0, 0.25, 0.50, 0.667, 0.75, and 1) were synthesized using solid‐state reaction from mixed precursor powders. A complete solid‐solution series was found between the endmembers. Energy‐dispersive spectroscopy confirmed the homogeneity of the synthesized garnets. The compositions reversibly melted between 1000 and 1160°C and had low sintering temperatures between 650 and 900°C. Thermal diffusivity, heat capacity, thermal conductivity, density, lattice parameter, thermal expansion, index of refraction, and dispersion were measured from room temperature to 800°C.
... where a Mg 2þ =1.33Å 3 , a Ni 2þ =1.23Å 3 , a B 3þ =0.05Å 3 , a O 2À =2.01Å 3 [20,21]. V m is the molar volume. ...
A cold sintering process (150 °C, 90 min, and 800 MPa) is employed to pre-densify (Mg1 − xNix)3B2O6 (0.00 ≤ x < 0.10, MNBO) ceramics to 80% relative density, followed by a post-annealing treatment between 800 and 950 °C. The origin of optimizations of the sintering, microstructure, and dielectric properties of Ni²⁺-substituted Mg3B2O6 ceramic are investigated in detail. All the samples are the single phase of magnesium borate, as confirmed by XRD and Raman spectra. The crystallographic lattice parameters of all compositions are obtained by full-pattern Rietveld refinement. It is found that the εr of MNBO ceramics is related to the relative density and the ionic polarization of chemical bonds. The change of atomic filling fraction and half peak width is found to be an important effect on the Q × f value. The optimum microwave dielectric properties (εr = 6.92, Q × f = 24,336 GHz, τf = − 53.43 ppm/°C) and the relative density of MNBO ceramics (92.4%) are obtained for composition with 4% Ni²⁺.
... According to the calculated data summarized in Table 3 and the relative density curves in Fig. 4, the theoretical ion polarization rate grows continuously with x increasing, however, the e meas , e pc , and a obs follow the same trend as that of relative density, reaching a maximum at x = 0.12, after which they start to decrease. This phenomenon indicates that density contributes the majority to the e r of BaMg 2-V 2?x O 8 ceramics [37][38][39]. Figure 6 depicts Q Â f variation curves of BaMg 2-V 2?x O 8 ceramics sintered at different temperatures. The variation pattern of Q Â f corresponds to the relative density, all of which reach the maximum value at 900°C when x B 0.12. ...
BaMg2V2+xO8 (0.04 ≤ x ≤ 0.16) ceramics with high quality factors were prepared by the conventional solid-state reaction method at 850–925 °C, which can meet the LTCC technology. The effects of non-stoichiometric V⁵⁺ ions on sintering characteristics, phase composition, microstructure, as well as on microwave dielectric properties have been analyzed. All ceramic samples synthesized with different non-stoichiometric ratios of V⁵⁺ ions had a single tetragonal structure phase which belonged to the I41/acd (142) space group. The τf value of BaMg2V2+xO8 (0.04 ≤ x ≤ 0.16) ceramics was adjusted without deteriorating Q×f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q \times f$$\end{document} value by adding excessive V⁵⁺ ions, and Q×f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q \times f$$\end{document} value was found to correlate with relative density and the average lattice energy of V–O bonds while the τf value correlating with the total bond energy. The BaMg2V2.12O8 ceramics sintered at 900 °C showed an optimal Q×f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q \times f$$\end{document} value of 141, 014 GHz, with εr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon_{{\text{r}}}$$\end{document} of 12.4 and τf of − 14.25 ppm/°C.
