Temperature Coefficient Of Resonant Frequency Research Articles

Acceleration of optimizing the dielectric properties of (Ca0.7Nd0.2)1−x(Li0.5Nd0.5)xTi1−y(Mg1/3Nb2/3)yO3 with the aid of machine learning

AbstractThe three key properties required for microwave dielectric ceramics are suitable dielectric constant (εr), high quality factor (Q × f), and near‐zero temperature coefficient of resonant frequency (τf). Due to the intricate coupling relationship among these three properties, regulating one often leads to the deterioration of the remaining two. In this study, the synergetic regulation of dielectric properties of Ca0.7Nd0.2TiO3 was investigated to reduce τf to near‐zero while maintaining its high εr by A‐ and B‐site substitutions. To avoid the seesaw effect and improve the efficiency of composition optimization, machine learning method was introduced in this study. First, the models for predicting dielectric properties were fitted based on a small amount of high‐quality data gathered via a uniform experimental design. Then the dielectric properties of 1037 compositions of (Ca0.7Nd0.2)1−x(Li0.5Nd0.5)xTi1−y(Mg1/3Nb2/3)yO3 were predicted, from which 69 microwave dielectric ceramics with near‐zero τf and adjustable εr of 95–125 were quickly picked out, and 5 of them were proved by experiments with very high prediction accuracy. This work was finished within a period of 1 month, which proves the obvious acceleration of composition designing process of microwave dielectric ceramics with the aid of machine learning.

Effects of Zr4+ and Hf4+ substitution on the structure and dielectric response of Ba4Sm9.33Ti18O54 ceramics

Microwave dielectric ceramics with high relative permittivity (εr) are commonly used for the miniaturation of microwave devices. The dielectric loss mechanism of microwave dielectric ceramics, as well as the property modification, has been a concerned topic among scholars. Herein, the lattice structure, defects, and broadband dielectric response of Zr4+ and Hf4+ substituted Ba4Sm9.33Ti18O54 (BST) ceramics are systematically examined. The negative temperature coefficient of resonant frequency (τf) of BST ceramics can be tuned to near zero via ion substitution, owing to the Sm2Ti2O7 second phase with a large positive τf. Optimal microwave dielectric properties of εr = 81.3, Q × f = 10,800 GHz, and τf = −4.6 ppm/°C are achieved. The lattice vibration behavior and defect concentration are analyzed by Raman spectra and thermally stimulated depolarization currents (TSDC), respectively. The increasing volume of the unit cell and TiO6 octahedra, which is because of the large-radius substitution ions, leads to an increase in lattice vibration damping factor and the generation of more oxygen vacancies (VO∙∙). Therefore, the dielectric losses in the microwave and terahertz (THz) bands increase after substitution. Meanwhile, the low-frequency dielectric losses at high temperatures also increase due to the weak restraint of carriers by the lattice. The broadband loss mechanism of Zr4+ and Hf4+ substituted BST ceramics related to lattice vibration and defects might be referenced for developing low-loss dielectric ceramics.

Spinel-trirutile microwave dielectric ceramics with high Q and excellent temperature stability based on MgO-Al2O3-Ta2O5 ternary systems

(1-x)MgAl2O4-xMgTa2O6 composite ceramics based on the MgO-Al2O3-Ta2O5 pseudoternary phase diagram were prepared by the solid-state reaction. MgAl2O4 and MgTa2O6 could coexist due to their different crystal structures. MgAl2O4 inhibited the rapid growth of MgTa2O6 grains, and dense microstructures (ρ > 95%) with a uniform grain size distribution was obtained, with an optimal densification temperature of 1550 - 1575 °C. The temperature coefficient of resonant frequency (τf) and quality factor (Q×f) were optimized by introducing MgTa2O6 phases with low dielectric loss and positive τf. In addition, the partial solid solutions of Al3+ into Ta5+ sites resulted in loosening bonds within [Al/TaO6] octahedra and abnormally large polarizabilities, which was confirmed by the decrease in VTa-O and the redshift of A1 g(Ta-O) mode. Consequently, the relative permittivity (εr) and τf values of MgAl2O4-MgTa2O6 composite ceramics were further enhanced, exceeding the predicted ones. The 0.6MgAl2O4-0.4MgTa2O6 composition sintered at 1550 °C achieved excellent performance, with a near-zero τf value of 3.3 ± 1.7 ppm/°C, a low εr of 16.4 ± 0.3 and an ultra-high Q×f of 179,000 ± 6700 GHz @ 8.94 ± 0.04 GHz. These findings hold promising applications in the field of 5 G/6 G high-frequency communication.

Ilmenite-type structure and pervoskite structure mix-phase ceramics at microwave frequency

ABSTRACT The impact of CuB2O4 additive used as a sintering aid on the microstructures and microwave dielectric characteristics of mixed phase (Mg0.95Zn0.05)Co0.05TiO3-Ca0.6(La0.9Y0.1)0.2667TiO3 ceramics was investigated. CuB2O4 additives can effectively lower the densification temperature of (Mg0.95Zn0.05)Co0.05TiO3-Ca0.6(La0.9Y0.1)0.2667TiO3 from 1450°C to the range of 1050°C ~ 1175°C. Doping CuB2O4 (0.25 ~ 2 wt%) in 0.875(Mg0.95Zn0.05)Co0.05TiO3-0.125Ca0.6(La0.9Y0.1)0.2667TiO3 ceramics can substantially enhance their microwave dielectric properties and density. With the addition of 1% and 0.25% CuB2O4, Q × f values of 43,000 GHz and 7700 GHz were obtained at 1050–1175°C, respectively. Different additions of CuB2O4 have a significant effect on the Q × f value. Temperature coefficient of resonant frequency of 0.875(Mg0.95Zn0.05)Co0.05TiO3-0.125Ca0.6(La0.9Y0.1)0.2667TiO3 (0.875MZCT–0.125CLYT) varied from 16 to 30.9 ppm/°C when adding different CuB2O4 (0.25 ~ 2 wt%).

Re2TiO5: Special dielectric titanates exhibiting abnormally low permittivity and a positive coefficient of resonance frequency

AbstractIn this study, a series of rare‐earth titanates with the general formula Re2TiO5 (Re = Er, Tm, Yb, and Lu) were synthesized and their microwave dielectric properties were reported. The impact of differences in rare‐earth cation radii on the structure and dielectric properties was systematically analyzed. The findings indicated that ceramics of Re2TiO5 (Re = Er, Tm, Yb, and Lu) were crystallized into a cubic structure with space group Fd‐3m, as confirmed by Rietveld refinement and selected‐area electron diffraction patterns. The rare‐earth elements were analyzed for their impact on microwave dielectric properties, considering factors such as ionic polarizability, packing fraction, and bond valence theory. The resulting materials exhibited excellent microwave dielectric properties with a low permittivity (6.95–7.21), high‐quality factors (19 451–20 115 GHz), and low positive temperature coefficient of resonance frequency (19.34–20.90 ppm/°C). The origin of low permittivity was elucidated through the analysis of bond length, X‐ray photoelectron spectroscopy, and impedance spectroscopy. This series of titanates exhibited unusually low permittivity characteristics in the microwave frequency range, which could meet the low signal transmission delay requirements in wireless communication.

Crystal structure and microwave dielectric properties of A- and B-site co-substituted NdNbO4 ceramics

The microwave dielectric properties of NdNbO4 (NN) ceramics were optimized by substituting Ca2+ at the A-site and W6+ at the B-site. (1-x)NdNbO4-xCaWO4 (NNCWx) (x = 0–0.3) ceramics crystallize in the monoclinic fergusonite structure (space group I2/a), whereas NNCW-0.4 exhibits a tetragonal scheelite structure (space group I41/a), suggesting that Ca2+/W6+ doping effectively contributed to the ferroelastic phase transition. A near-zero temperature coefficient of resonant frequency (τf) of +7.8 ppm/°C, a high Q×f value of 59,190 GHz, and a low permittivity (εr) of 17.51 were obtained for the NNCW-0.3 ceramic. With the increase of x, the permittivity decreases gradually, while τf shows the opposite trend. The permittivity is mainly affected by the polarizability per unit molar volume (α/Vm) and the rattling effect of A-site cations (Nd3+ and Ca2+). The Q×f values of NNCWx ceramics are mainly affected by relative density, packing fraction, and lattice energy (U). The influencing mechanism of τf is a combination of an increase in the temperature coefficient of ion polarizability (ταm), lattice strain, and phase transition.

High-Q, temperature-stable, and medium-permittivity composite ceramics of tungstenbronze-type and perovskite titanates through layer-stacking process

High-Q and temperature-stable ceramics are indispensable in microwave engineering. However, medium-permittivity (εr ∼ 60, named as K60) microwave dielectric ceramics that meet the above demands are yet to be synthesized. High-Q Ba4Sm9.33Ti16.5Al2O54 (BSTA) and Ca0.6Sm0.27Ti0.8Al0.27O3 (CSTA) ceramics have large resonant frequency temperature coefficients (τf) with opposite signs. The composites of the two are expected to have good dielectric properties, but there will be obvious diffusion when they are compounded with each other by sintering after directly mixing the raw powder, which would lead to severe deterioration in dielectric properties. In this work, the undesired diffusion can be effectively avoided by stacking two or three ceramic layers together, which are achieved by two methods named adhesive bonding and spark-plasma-sintering (SPS) cofiring. The finite element method (FEM) analysis with COMSOL Multiphysics proposed in this work can precisely predict the microwave dielectric properties of layered ceramics, helping to determine the ratio of different layers to reach near-zero τf. The adhesive-bonded layered ceramics exhibit excellent dielectric properties: εr = 62.2, Q×f = 21,400 GHz, and τf = –0.7 ppm/°C. The SPS-cofired layered ceramics can be fabricated in one time, partially solving the problem of sintering mismatch between different layers, together with superior properties of εr = 59.8, Q×f = 19,780 GHz, and τf = –0.6 ppm/°C. These layered ceramics could fill the gap of high-Q and temperature-stable K60 microwave dielectric ceramics. The layer-stacking process and related FEM simulations can be used to design more high-Q and temperature-stable microwave dielectric ceramics and devices.

Improvement of τf in HfTiO4 microwave dielectric ceramics with Zr‐ and Sn‐substitution

Abstract(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.

Effects of ion occupancy and polarizability on the crystal structure and microwave dielectric properties of CaEuCO4 (C[dbnd]Ga, Al) ceramics

CaEuCO4 (CGa, Al) microwave dielectric ceramics were produced through a solid-state reaction. Orthorhombic olivine CaEuGaO4 (pnma) exhibits a lower permittivity (εr = 9.7), a higher quality factor (Q × f = 82,049 GHz), and a larger negative resonant frequency temperature coefficient (τf = −54.6 ppm/°C). CaEuAlO4, which has a similar chemical formula, exhibits a perovskite-like structure (I4/mmm, K2NiF4-type), and its microwave dielectric properties are εr = 18.9, Q × f = 43,132 GHz, and τf = −1.6 ppm/°C. The difference in their structures is mainly caused by the properties of the Ga (III) atom. The difference in their dielectric properties can be proved to be affected by the “rattling” effect of Eu3+ through the bond valence theory. The relationship between the covalence (fc) and the bond strength (S) was investigated, and the higher bond strength might be the main reason for the higher Q × f in CaEuGaO4 ceramic.

Low‐k dielectric materials derived from ZSM‐5 zeolite

AbstractLow‐k dielectric materials were prepared by sintering ZSM‐5 zeolite powder compacts at temperatures ranged 1200–1300°C, and the microwave dielectric characteristics were investigated together with the structure evolution during sintering. It was failed to obtain ZSM‐5 ceramics by high temperature sintering because the densification could never occur below the tolerable temperature and the ordered porous structure completely collapsed above the tolerable temperature. The structure changed from ZSM‐5 zeolite to SiO2‐Al2O3 glass at 1240°C, and finally to SiO2‐based cristobalite ceramics above 1275°C. A low dielectric constant (2.63‐2.78) combined with low dielectric loss (< 0.0005 at 18 GHz) and small temperature coefficient of resonant frequency (varied from ‐18.6 to ‐8.1 ppm/°C) was achieved in the present materials, and the value of dielectric loss was the lowest one achieved so far in the dielectric materials with a dielectric constant lower than 3. With the structure evolution from ZSM‐5 zeolite to SiO2‐Al2O3 glass and finally to SiO2‐based cristobalite ceramics, the dielectric constant increased from 2.27 to 2.78, while the Qf value indicated a complicated variation tendency, and the higher Qf values were achieved in the amorphous and crystalline states, while significant drop was determined in the partial amorphous state. It should be a great challenge to prepare dense zeolite ceramics without collapse of ordered porous structure, and then the ultra‐low dielectric constant materials with high Q could be expected.

AlScN-on-SiC Diaphragm Multimode Micromechanical Resonators for High-Temperature Sensing Applications

We demonstrate circular diaphragm multimode micromechanical resonators made of heterostructure thin film of aluminum scandium nitride (AlScN) sputtered on cubic silicon carbide (3C-SiC). We systematically characterize the multimode resonators from room temperature up to 600ºC high-temperature environment. We observe clear consistency in resonances measured in heating up and cooling down processes, validating that the AlScN/SiC diaphragm resonators can operate robustly in high-temperature environment up to 600°C without observable degradation. Raman spectroscopy results indicate that the turning points of the peak positions of the longitudinal optical (LO) phonon modes of both 3C-SiC and AlScN occur in almost the same temperature region where the turning point of temperature coefficient of resonance frequency (TCf) is observed. We calibrate the device temperature by measuring Raman peak of the silicon (Si) substrate of the chip, yielding a crystal lattice temperature of 410ºC at the heater setting temperature being 600ºC. The heating efficiency can be improved by clamping the chip using a clip or jig with lower thermal conductivity.

Improved temperature stability of low-fired Li2Mg3SnO6 microwave dielectric ceramics by using (La0.5Na0.5)TiO3 additives

The (1-x)Li2Mg3SnO6-x(La0.5Na0.5)TiO3-4wt%LiF (x = 0.05, 0.10, 0.15, 0.20) ceramics were prepared in order to produce an alternative material for communication components. Its phase structure composition, sintering properties, microstructure and dielectric performances with the addition of (La0.5Na0.5)TiO3 were studied. All sintered samples exhibit a phase structure composed of main phases Li2Mg3SnO6 and La2Sn2O7 with a small amount of Li2SnO3. The sample showed a densification sintering in 875 °C–950 °C sintering range. Influenced by the amount of (La0.5Na0.5)TiO3 added, the value of temperature coefficient of resonant frequency (τf) is gradually adjusted from negative to positive. When x is equal to 0.15, the good comprehensive property of dielectric constant (εr) ∼ 11.9, quality factor (Q×f) ∼ 10400 GHz, and τf ∼ −6.4 ppm/°C can be obtained for 0.85Li2Mg3SnO6-0.15(La0.5Na0.5)TiO3-4wt%LiF ceramics at 900 °C. This material is suitable for development as an alternative to LTCC applications.

Analysis of structural and dielectric properties of A-site substituted magnesium titanate synthesized using auto-ignition combustion method

The structural and dielectric properties of magnesium titanate solid solutions substituted with zinc or cobalt (M x Mg1− x ) TiO3 (M = Zn/Co and x = 0.00, 0.05) were investigated. MgTiO3 formed as a single phase, according to X-ray diffraction analysis. Low porosity, tightly packed grains were detected using scanning electron microscopy (SEM) and energy-dispersive X-ray (EDX) analyses. The dielectric properties reveal that (M x Mg1− x ) TiO3 with Zn = 0.05 shows a good combination of relative permittivity (ε r) of 15.10, loss tangent (tan) of 1.11 × 10–3, and temperature coefficient of resonant frequency (τ f) of –42.70 ppm/°C at 1 MHz was reported.

Tuning the temperature coefficient of the resonant frequency of the AlPO4–BPO4–SiO2 ternaries with TiO2 addition and sintering atmosphere control

Microwave ceramics with low relative dielectric permittivities (εr), high-quality factors (Q×f values), and near-zero temperature coefficients of resonant frequency (τf) are strongly required for the 5 G and forthcoming 6 G wireless communication system. Effects of the TiO2 addition and atmosphere control on the microstructures and microwave dielectric properties of 0.05AlPO4-0.05BPO4-0.90SiO2 (5A5B90S) and 0.45AlPO4-0.45BPO4-0.10SiO2 (45A45B10S) ternaries were investigated in this paper to achieve the above objective. Adding TiO2 produced the TiP2O7 and/or (TiO)2P2O7 secondary phases in the 5A5B90S, and TiP2O7 in the 45A45B10S sintered bodies, respectively, which improved their sinterabilities. Near zero-τf value (τf∼ −2.0(8) ppm/°C) whilst retaining low εr (∼4.97(7)) and high Q×f value (54,000 ± 1619 GHz) could be attained for the 5A5B90S with the addition of 15 wt% TiO2. In contrast, both the Q×f and τf values deteriorated with the addition of TiO2 for the 45A45B10S. Sintering in the B2O3 protection atmosphere helps suppress the formation of TiP2O7 and/or (TiO)2P2O7 secondary phases for both samples, specifically in the surface layer of the sample, which increased the tunability of τf to be near zero. Combined good microwave dielectric properties with εr∼4.47(6)，Q×f ∼ 48000 ± 950 GHz，τf∼ − 2.1(8) ppm/°C; εr∼ 5.05(8)，Q×f ∼ 45,326 ± 900 GHz，τf∼ − 7.6 ± 1.2 ppm/°C could be attained for the 5A5B90S + 10 wt% TiO2 and 45A45B10S + 15 wt% TiO2 ceramics, respectively by sintering in B2O3 protection atmosphere.

Dielectric properties of ZnNb2O6-ZnTiNb2O8 composites for microwave applications

In this study, the dielectric properties were evaluated in the microwave region for a ZnNb2O6 (ZNO) matrix with added TiO2. X-ray diffraction analysis demonstrated that the addition of TiO2 to ZNO led to formation of the ZnTiNb2O8 (ZTNO) phase. Evaluation of the dielectric properties in the microwave region for the ZNO-ZTNO ceramic composites showed that the permittivity (εr) ranged between 23.08 and 26.19 and the dielectric loss (tan δ) was 7.20 × 10−5 to 3.25 × 10−4. The temperature coefficient of resonant frequency (τf) ranged from −97.64 ppm °C−1 to −62.93 ppm °C−1, thereby demonstrating that adding TiO2 increased the τf value. The ZNO-ZTNO composites were evaluated as dielectric resonator antennas and their far-field parameters obtained based on numerical simulations indicated a gain between 4.69 and 5.60 dBi, bandwidth of 125.00–164.00 MHz, and efficiency above 98%. These results demonstrate that the ceramics investigated in this study have great potential for application in devices that operate in the C-band.

Sintering Behavior, Microstructure and Microwave Dielectric Properties of Li2TiO3-Based Solid Solution Ceramics with Lithium Fluoride Addition for Low-Temperature Co-Fired Ceramic Applications

Nowadays, low-temperature co-fired ceramic (LTCC) technology has become one of the main forms of manufacturing electronic devices. However, a majority of microwave dielectric ceramics are not suitable as LTCC materials due to their high sintering temperatures. Developing novel LTCC materials with good microwave dielectric properties is extremely urgent. In this paper, an LiF sintering aid was added to Li2Ti0.8(Co1/3Nb2/3)0.2O3 (LTCN) ceramics to explore new LTCC materials. The sintering behavior, microstructure and microwave dielectric properties of LTCN + x wt% LiF ceramics were investigated in detail. The results indicated that the addition of LiF increased the degree of disorder in the LTCN matrix, transforming it from a monoclinic to a cubic crystal system. The ceramics exhibited relatively dense and homogeneous microstructures at the sintering temperature of 950 °C as the LiF doping amount was not less than 2 wt%. By LiF doping, the quality factor (Q × f) value was significantly enhanced due to the improved microstructure. Meanwhile, the temperature coefficient of resonant frequency (τf) of LTCN ceramics was successfully regulated to the near zero value owing to the negative τf characteristic of LiF. Excellent microwave dielectric properties of dielectric constant (εr) = 19.01, Q × f = 144,890 GHz, τf = −1.52 ppm/°C were obtained when the sample doped 3 wt% LiF was sintered at 950 °C for 3 h. Furthermore, the good chemical compatibility of the LTCN-3 wt% LiF ceramic with silver electrodes suggested that the ceramic was a potential material for LTCC applications.

Crystal structure and ultra-high quality factor of MgTi1-x(Co1/3Nb2/3)xO3 solid-solution microwave ceramics

MgTi1-x(Co1/3Nb2/3)xO3 (x = 0–0.3) ceramics were prepared by a solid-state reaction method. The (Co,Mg)4Nb2O9 and MgTiO3 phases formed solid solutions, which presented an ilmenite-type with R-3 space group. In low (Co1/3Nb2/3)4+ ion content, the (Co,Mg)4Nb2O9 dissolves in MgTiO3 matrix, whereas the MgTiO3 dissolves in (Co,Mg)4Nb2O9 with high (Co1/3Nb2/3)4+ ion content. In the transition from MgTiO3 to (Co,Mg)4Nb2O9 matrix, MgTiO3 and (Co,Mg)4Nb2O9 phases can coexist. A secondary phase, MgTi2O5, existed in the x = 0 sample. The introduction of (Co1/3Nb2/3)4+ inhibited the formation of the second phase and promoted grain growth. The variation trend of the dielectric constant (εr) was the same as the theoretical dielectric constant (εtheo), indicating that the εr was dominated by the ion polarizability. The stable microstructure, which was caused by the high total lattice energy, enhanced the quality factor (Qf) value. And an ultrahigh Qf value (∼492 500 GHz) was obtained for MgTi0.96(Co1/3Nb2/3)0.04O3 ceramics sintered at 1250 °C. Moreover, the TiO6 octahedral distortion, which is caused by the ion substitution, contributes to the change in bond restoring force. The TiO6 octahedral distortion conduces to the fluctuations of the temperature coefficient of resonance frequency (τf) value.

Superior temperature stability of electromechanical properties and resonant frequency in PYN-PZT piezoelectric ceramics

In this study, the Pb(Yb1/2Nb1/2)O3 (PYN) relaxor with high Curie temperature (TC ∼300 °C) was incorporated into PbZrO3-PbTiO3 (PZ-PT) ceramics to form 0.1PYN-(1-x)PZ-xPT ternary ceramics, and their phase compositions were systematically investigated, providing the more detailed phase diagrams, dielectric, piezoelectric, and ferroelectric properties. Excellent piezoelectric performance (d33 ∼ 450 pC/N, d33* ∼714 pm/V), with high coercive field (EC ∼17.5 kV/cm) and TC (∼398 °C) were simultaneously achieved in the 0.1PYN-0.41PZ-0.49PT composition near the morphotropic phase boundary (MPB). The value of d33 × EC, which exhibits higher than commercial PZT ceramics, indicates its suitability for high-field excitation devices. Additionally, the temperature stability of the resonant frequency (fr) is qualitatively studied by analyzing the main factors influencing fr from a theoretical perspective. Superior stability is achieved in the 0.1PYN-0.38PZ-0.52PT composition (TC ∼ 405 °C) with tetragonal phase, and the temperature coefficient of resonant frequency (Δfr /fr25 °C) remains within 0.5% up to 300 °C, far outperformance than previous reports.

One-step preparation of ultra-low temperature Ag2SrV4O12 ceramics with promising dielectric properties

The pure Ag2SrV4O12 powder with tetragonal structure was directly synthesized via high-energy milling. The dense Ag2SrV4O12 ceramics, sintered at as low temperature as 420 °C, have a low relative permittivity (εr) of 6.39, a high quality factor (Q × f) of 51,584 GHz (f = 13.66 GHz), and a temperature coefficient of resonance frequency (τf) of −79.8 ppm/°C. For practical applications, a composite with balanced microwave dielectric properties (εr = 11.86, Q × f = 38,061 GHz, τf = −8.2 ppm/°C) was realized at 460 °C by adding TiO2 with positive τf to Ag2SrV4O12 ceramics. There was no chemical reaction between Ag2SrV4O12 ceramic and Ag/Al, which shows the good chemical compatibility of Ag2SrV4O12 and Ag/Al. All results indicate that Ag2SrV4O12 has a promising future as an ultra-low temperature co-fired ceramic.

Structure evolution and adjustment of τf in (Ba, Sr)HfO3 and (Sr, Ca)HfO3 microwave dielectric ceramics

AbstractThe crystal structure evaluation of Ba1−xSrxHfO3 and Sr1−yCayHfO3 ceramics with varying composition was determined together with its influence on microwave dielectric characteristics. The variation mechanism of temperature coefficient of resonant frequency (τf) was discussed in details, and the strong correlation between τf and bond valence sum (BVS) and tolerance factor (t) was interpreted from the view point of energy. With increasing Sr‐content, the stable phase of Ba1−xSrxHfO3 at room temperature changed from Pmm (x ≤ 0.25) to I4/mcm (0.35 ≤ x ≤ 0.40), then to Imma (0.50 ≤x < 0.75) and finally to Pnma (0.75 ≤ x ≤ 1.0). The peak temperature of dielectric constant changed due to the structure transition, resulting in that τf rapidly declined at first, reached near zero, then slowly decreased, and finally rapidly decreased. Sr1−yCayHfO3 (0 ≤ y ≤ 1.0) belonged to space group Pnma. As the bond lengths and bond angles between B‐atom and O‐atom became more and more changeable (or BVS became smaller), the crystal could store more input heat energy through bond vibrational energy, and consequently τf became closer to zero with increasing Ca‐content, which was consistent with the physical meaning of the rattling effect on τf. With decreasing t, the dominant mechanisms responsible for tuning τf changed from (i) phase transition and (ii) dilution of ion polarizability to (iii) rattling effect. One could investigate what were the dominant mechanisms tuning τf and hopefully predict its trend with the help of τf–t graph. These findings provided a new idea for developing solid solution ceramics with excellent temperature stability.