Microwave dielectric properties of temperature-stable (Mg<Subscript>0.95</Subscript>Co<Subscript>0.05</Subscript>)<Subscript>2</Subscript>TiO<Subscript>4</Subscript>–Li<Subscript>2</Subscript>TiO<Subscript>3</Subscript> composite ceramics for LTCC applications

In this paper, the effects of Li₂O–B₂O₃–Bi₂O₃–SiO₂ (LBBS) glass on the phase formation, sintering characteristic, the microstructure and microwave dielectric properties of temperature-stable (Mg_0.95Co_0.05)₂TiO₄–Li₂TiO₃ ceramics were investigated. (Mg_0.95Co_0.05)₂TiO₄–Li₂TiO₃ powders were obtained by using the traditional solid-state process. A small amount of LBBS doping can effectively reduce sintering temperature and promote the densification of the ceramics. X-ray diffraction analysis revealed not only the primary phase (Mg·Co)₂TiO₄ associated with Li₂TiO₃ minor phase but also a third phase (Mg·Co)TiO₃. The dielectric constant and Qf values vary with the doping amount of LBBS and sintering temperatures. With the compensation of the positive temperature coefficient (τ _f ) of Li₂TiO₃ and the negative τ _f of (Mg_0.95Co_0.05)₂TiO₄, the τ _f of the specimens fluctuates around zero. The (Mg_0.95Co_0.05)₂TiO₄ ceramic with 2.5 wt% LBBS addition and sintering at 900?°C for 4 h exhibited excellent microwave dielectric properties: ? _r ?=?19.076, Qf?=?126100 GHz, and τ _f ?=?0.98 ppm/°C.     

Preparation,characterization and dielectric properties of Ba<Subscript>3−x</Subscript>Sr<Subscript>x</Subscript>LiM<Subscript>3</Subscript>Ti<Subscript>5</Subscript>O<Subscript>21</Subscript>[M=Nb and Ta,x = 0 to 3] ceramics

The ceramic compositions Ba_3−xSr_xLiM₃Ti₅O₂₁[M=Nb and Ta, x = 0 to 3] were prepared through conventional solid state ceramic route. A detailed study has been carried out to correlate the structure of Ba_3−xSr_xLiM₃Ti₅O₂₁[M=Nb and Ta, x = 0 to 3] with respect to their dielectric properties. The structure and microstructure of ceramic samples were studied using powder X-ray diffractometer and Scanning Electron Microscopic techniques. The dielectric properties of the sintered ceramic compacts have been studied. The Ba-rich compositions were identified as promising candidates for high frequency applications whereas the Sr-rich compositions were excellent ionic conductors and can be commercially exploited for applications in solid-state batteries.     

Microwave dielectric properties of Sr<Subscript>0.7</Subscript>Ce<Subscript>0.2</Subscript>TiO<Subscript>3</Subscript>–Sr(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> ceramics

xSr_0.7Ce_0.2TiO₃–(1???x)Sr(Mg_1/3Nb_2/3)O₃ ceramics, referred to xSCT–(1???x)SMN, were successfully produced by conventional solid-state sintered technology. The compounds, belonging to perovskites with a secondary phase of CeO₂, can be detected even with x down to 0.1 of SCT composition. The overall trend for grain growth illustrates the increase with increasing SCT doping level. The Raman peak at 825 cm^?1 splits into two peaks and causes red shift phenomenon. XPS spectra indicate that Ti and Nb ions exist respectively in tetravalence and pentavalence, and Ce ions exist in trivalence and tetravalence. Dielectrics constant (ε _r ) of SCT–SMN ceramics gradually increases with increasing theoretical dielectric polarizabilities. A wider width of the 825 cm^?1 for FWHM of A_1g mode Raman peaks suggests to a lower Q?×?f value. The increasing tolerance factor in agreement with temperature coefficient of resonant frequency (τ _f ), denotes that the rise of perovskite symmetry. The 0.1SCT–0.9SMN ceramic sintered at 1450?°C for 4 h illustrates excellent microwave dielectric properties with ε _r ?~?35.4, Q?×?f?~?11282 GHz and τ _f ?~?1.7 ppm/°C. Activation energies of 0.1SCT–0.9SMN ceramic at 100, 300 and 500 V, are ~0.436, 0.427 and 0.331 eV, respectively, indicative of a decreased trend with external electric field.     

Ferroelectric and antiferroelectric polarisation switching characteristics of Bi(Mg<Subscript>0.5</Subscript>Ti<Subscript>0.5</Subscript>)O<Subscript>3</Subscript>–PbTiO<Subscript>3</Subscript> ceramics

Bi(Mg_0.5Ti_0.5)O₃–PbTiO₃ (BMT–PT) ceramics, with BMT–PT ratios ranging from 70-30 to 50-50, were prepared by a conventional solid state reaction process. The 50-50 BMT–PT ceramic possessed a tetragonal perovskite structure with a c/a ratio of ~1.037. Increasing BMT content led to a reduction of tetragonality and a change of structure to a rhombohedral or pseudo-cubic phase. Dielectric measurements, carried out during heating, indicated the occurrence of two phase transformations, which were identified as relaxor ferroelectric to antiferroelectric (at a temperature in the range from 150–300 °C) and antiferroelectric to paraelectric (at a temperature around 500 °C). The antiferroelectric nature of the 60-40 and 70-30 BMT–PT ceramics in the intermediate temperature range was confirmed by polarisation-electric field hysteresis measurements.     

Dielectric and impedance studies of (Pb<Subscript>1−x</Subscript>Ca<Subscript>x</Subscript>)(Fe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>)O<Subscript>3</Subscript> dielectric ceramics

Ceramic samples of (Pb_1?xCa_x)(Fe_0.5Nb_0.5)O₃ with x = 0.20, 0.40, 0.45, 0.50, 0.55 and 0.60 were obtained by columbite precursor method. All the synthesized samples have perovskite structure with pseudo-cubic symmetry. Dielectric properties of all the samples were measured as a function of frequency from room temperature up to 573 K. Two dielectric anomalies were observed in ε_r–T plots at about 400 and 500 K. The impedance analysis depicts a single relaxation process. Activation energies obtained from temperature dependence of relaxation frequency, f₀ and grain resistance, R_g were found to be more or less comparable. The observed relaxation in all the samples seems to be due to electron relaxation associated with oxygen vacancies.     

Phase formation and dielectric properties of ceramics in the BiFeO<Subscript>3</Subscript>–BaTiO<Subscript>3</Subscript>–Bi(Mg<Subscript>0.5</Subscript>Ti<Subscript>0.5</Subscript>)O<Subscript>3</Subscript> system

We have studied the effect of Bi(Mg_0.5Ti_0.5)O₃ additions on the phase formation, structural parameters, microstructure, and dielectric properties of solid solutions in the region of a morphotropic phase boundary in the BiFeO₃–BaTiO₃ system. Single-phase samples with the perovskite structure have been obtained and the addition of Bi(Mg_0.5Ti_0.5)O₃ has been shown to raise the Curie temperature of the ceramics and improve their dielectric properties.     

Piezoelectric properties of [Bi<Subscript>0.5</Subscript>(Na<Subscript>0.7</Subscript>K<Subscript>0.25</Subscript>Li<Subscript>0.05</Subscript>)<Subscript>0.5</Subscript>]TiO<Subscript>3</Subscript>−Ba(Ti,Zr)O<Subscript>3</Subscript> binary system ceramics

Dense lead-free binary system piezoelectric ceramics (1 − x)[Bi_0.5(Na_0.7K_0.25Li_0.05)_0.5]TiO₃−xBa(Ti_0.95Zr_0.05)O₃ (BNKLT–BZT) were prepared by a two-step sintering process. A phase transition from rhombohedral to tetragonal was observed with increasing BZT fraction in the range x = 0.06–0.1 and the morphotropic phase boundary (MPB) between rhombohedral and tetragonal appears in this range. Ceramics containing 10 mol% BZT with tetragonal phase near the MPB region has the maximum piezoelectric constant d ₃₃(151pC/N).     

Sol–gel preparation and high-energy XRD study of (CaO)<Subscript>x</Subscript>(TiO<Subscript>2</Subscript>)<Subscript>0.5−x</Subscript>(P<Subscript>2</Subscript>O<Subscript>5</Subscript>)<Subscript>0.5</Subscript> glasses (x = 0 and 0.25)

Glasses from the CaO–TiO₂–P₂O₅ system have potential use in biomedical applications. Here a method for the sol–gel synthesis of the ternary glass (CaO)_0.25(TiO₂)_0.25(P₂O₅)_0.5 has been developed. The structures of the dried gel and heat-treated glass were studied using high-energy X-ray diffraction. The structure of the binary (TiO₂)_0.5(P₂O₅)_0.5 sol–gel was studied for comparison. The results reveal that the heat-treated (CaO)_0.25(TiO₂)_0.25(P₂O₅)_0.5 glass has a structure based on chains and rings of PO₄ tetrahedra, held together by a combination of electrostatic interaction with Ca²⁺ ions and by corner-sharing oxygen atoms with TiO₆ octahedra. In contrast, the (TiO₂)_0.5(P₂O₅)_0.5 glass has a structure based on isolated P₂O₇ units linked together by corner-sharing with TiO₆ groups. The results suggest that both the dried gels possess open porous structures. For the (CaO)_0.25(TiO₂)_0.25(P₂O₅)_0.5 sample there is a significant increase in Ca–O coordination number with heat treatment.     

Investigation on the synthesis of (Zn<Subscript>1−x</Subscript>Mg<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> and the modulation effect of CaTiO<Subscript>3</Subscript>

(Zn_1−xMg_x)TiO₃ (x = 0.1–0.5) solid solutions were synthesized by solid-state reaction using ZnO, (MgCO₃)₄·Mg(OH)₂·5H₂O and TiO₂ as raw materials. The influences of Zn: Mg ratio and calcining temperature on the properties of (Zn_1−xMg_x)TiO₃ were studied. By adding CaTiO₃ into (Zn_1−xMg_x)TiO₃, the microwave properties and sintering behavior were improved. The ceramics could be sintered at 1150 °C, and the ceramics with excellent microwave properties of τ_f ≈ ±10 ppm/°C, ε ≈ 24, Q × f > 45000 GHz (8 GHz) were obtained.     

Fabrication of lead-free piezoelectric (Bi<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>)TiO<Subscript>3</Subscript>–BaTiO<Subscript>3</Subscript> ceramics using electrophoretic deposition

Electrophoretic deposition (EPD) process has certain advantages such as it can be applied for a mass production and also can be combined with magnetic crystal alignment technique. In this work, we prepared lead-free 85(Bi_0.5Na_0.5)TiO₃–15BaTiO₃ (85BNT–15BT) piezoelectric ceramics by conventional uniaxial pressing and EPD process. Various conditions were optimized such as suspension media, applied electrical field, and deposition time in order to yield dense green ceramics of 85BNT–15BT composition using EPD process. 85BNT–15BT ceramics prepared using EPD process revealed the Curie temperature of about 250 °C, coercive field of about 30 kV/cm, and piezoelectric constant (d ₃₃) of 75 pC/N. The EPD-processed samples exhibited structural and electrical properties similar to that of the conventionally processed one suggesting the successful fabrication of 85BNT–15BT piezoelectric ceramics by EPD method without composition deviation. This study lays a foundation on the fabrication of Bi-based lead-free piezoelectric ceramics by an alternative route other than the conventionally practiced solid-state reaction method maintaining the similar chemical composition, moreover, leaving a large space to explore more in the future.     

Crystal structure and properties of BaTiO<Subscript>3</Subscript>–(Bi<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>)TiO<Subscript>3</Subscript> ceramic system

(1 − x)BaTiO₃–x(Bi_0.5Na_0.5)TiO₃ (x ranged from 0.01 to 0.96) ceramics were fabricated by the conventional ceramic technique. The crystal structure, as well as dielectric and piezoelectric properties of the ceramics were studied. All the ceramics formed single-phase solid solutions with perovskite structure after sintering in air at 1150–1250 °C for 2–4 h. The crystal structure and microstructure varied gradually with the increase of (Bi_0.5Na_0.5)TiO₃ (BNT) content. The Curie temperature, T _c, shifted monotonously to high temperature as BNT increased. The ceramics with 20–90 mol% BNT had relatively low and stable dielectric loss characteristics. The piezoelectric constant, d ₃₃, enhanced with the increase of BNT content through a maximum value in a composition of 93 mol% BNT and then tended to decrease. The maximum value, 148 pC/N, of piezoelectric constant d ₃₃ together with the electromechanical coupling factors, k _t, 19.8% and k _p, 15.8%, were obtained when BNT was 93 mol%.     

Sintering behavior and microwave dielectric properties of Y<Subscript>2</Subscript>O<Subscript>3</Subscript>–ZnO doped (Zr<Subscript>0.8</Subscript>Sn<Subscript>0.2</Subscript>)TiO<Subscript>4</Subscript> ceramics

(Zr_0.8Sn_0.2)TiO₄ (ZST) ceramics were fabricated via conventional solid-state reaction method. Sintering behavior, phase composition, microstructure and microwave dielectric properties of Y₂O₃–ZnO doped ZST ceramics were investigated. Only a single ZST phase was identified by X-ray diffraction patterns. The variation tendencies of dielectric constants as well as Q × f values were in accordance with the bulk densities. The appropriate Y₂O₃ and ZnO additions could not only efficiently lower the sintering temperature to 1240 °C, but also noticeably improve the densification and microwave dielectric properties of ZST ceramics. But excessive additives deteriorated the microstructures and comprehensive properties of samples. A dielectric constant ε _r of 39.73, a Q × f value of 48,545 GHz (at 5.5 GHz), and a τ _f value of ?2.13 ppm/°C were obtained for 1 wt% ZnO doped ZST ceramics with 0.5 wt% Y₂O₃ addition sintered at 1240 °C.     

Effect of excess Pb on microstructures and electrical properties of 0.67Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>–0.33PbTiO<Subscript>3</Subscript> ceramics

0.67Pb(Mg_1/3Nb_2/3)O₃–0.33PbTiO₃ (PMNT) ceramics were fabricated by using their powders synthesized through a sol–gel process. Excess Pb(CH₃COO)₂·3H₂O (0, 2, 5, 10 or 15 mol%) was added to the starting materials to study the effect of excess Pb on the microstructures, ferroelectric and dielectric properties of the PMNT ceramics. All the X-ray diffraction peaks can be indexed using perovskite-type PMNT for the ceramics prepared with excess Pb, while the PMNT ceramics with no excess Pb contain a little pyrochlore phase. The PMNT ceramics prepared with 2 mol% excess Pb are dense and uniform and composed of grains ranging from 3 to 7 μm. They exhibit the largest remnant polarization (P _r = 32.1 μC/cm²) and the highest peak dielectric constant (ε _max = 12,725). When more than 2 mol% excess Pb added, the electrical properties of the PMNT ceramics decreased with increasing excess Pb. Too much excess Pb (over 10 mol%) resulted in abnormal grain growth (>20 μm), large pores and residual PbO in amorphous state in PMNT ceramics, and they impaired the ferroelectric and dielectric properties of PMNT ceramics greatly.     

Dielectric and piezoelectric properties of Bi<Subscript>0·5</Subscript>(Na<Subscript>0·82</Subscript>K<Subscript>0·18</Subscript>)<Subscript>0·5</Subscript> TiO<Subscript>3</Subscript>-LiSbO<Subscript>3</Subscript> lead-free piezoelectric ceramics

The (1−x)Bi_0·5(Na_0·82K_0·18)_0·5TiO_3−x LiSbO₃ (x = 0−0·03) lead-free piezoelectric ceramics were fabricated by a conventional solid-state reaction method and the effect of LiSbO₃ addition on microstructure and electrical properties of the ceramics was investigated. The results of XRD measurement show that Li⁺ and Sb⁵⁺ diffuse into the Bi_0·5(Na_0·82K_0·18)_0·5TiO₃ lattices to form a solid solution with a pure perovskite structure. The LiSbO₃ addition has no remarkable effect on the crystal structure. However, a significant change in grain size took place. Simultaneously, with increasing amount of LiSbO₃, the temperature for a antiferroelectric to paraelectric phase transition clearly increases. The piezoelectric constant d ₃₃ and the electromechanical coupling factor k _p show an obvious improvement by adding small amount of LiSbO₃, which shows optimum values of d ₃₃ = 175 pC/N and k _p = 0·36 at x = 0·01.     

Good thermal stability and improved piezoelectric properties of (K<Subscript>0.5</Subscript>Na<Subscript>0.5</Subscript>)NbO<Subscript>3</Subscript>–Bi(Mg<Subscript>0.75</Subscript>W<Subscript>0.25</Subscript>)O<Subscript>3</Subscript> solid solutions

In this paper, (1 ? x)(K_0.5Na_0.5)NbO₃–xBi(Mg_0.75W_0.25)O₃ (x = 0–0.015) lead-free dielectric ceramics were investigated. XRD analysis certified that the Bi(Mg_0.75W_0.25)O₃ has diffused into (K_0.5Na_0.5)NbO₃ to fabricate a new solid solution. The addition of Bi(Mg_0.75W_0.25)O₃ depressed the orthorhombic–tetragonal phase transition temperature from 210 to 176 °C and tetragonal–pseudocubic phase transition temperature (Curie point) from 419 to 400 °C. As x = 0.005, the ceramics exhibited high relative permittivity (ε ~ 1325), low dielectric loss (tan δ < 2.9%) tan δ stability (Δε/ε_168°C ≤ ±15%) in the temperature range of 168 ~ 369 °C. Especially, the ceramics also showed optimized piezoelectric constant (d ₃₃ = 122 pC N^?1) and remnant polarization (P_r = 32.57 μC cm^–2). These results indicated that the BMW added ceramics have potential applications in ferroelectric and thermal stability devices.     

Synthesis and piezoelectric properties of (Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>)<Subscript>0.94</Subscript>Ba<Subscript>0.06</Subscript>TiO<Subscript>3</Subscript> ceramics prepared by sol–gel auto-combustion method

In this study, NaNO₃, Bi(NO₃)₃·5H₂O, Ba(NO₃)₂, Ti(OC₄H₉)₄ and citric acid were successfully introduced to fabricate lead-free piezoelectric (Na_0.5Bi_0.5)_0.94Ba_0.06TiO₃ [NBBT] nanopartical powders by a novel modified sol–gel auto-combustion method. The resultant products were characterized by the X-ray diffraction analysis and transmission electron microscope method. (Na_0.5Bi_0.5)_0.94Ba_0.06TiO₃ + Mn(NO₃)₂ [NBBTM] can be sintered by the traditional solid-state reaction, and the effects of NBBT doped different amounts of Mn(NO₃)₂ at various sintering temperatures upon phase formation, microstructure as well as piezoelectric properties were further studied. The experimental results show that it was helpful to control their chemical ingredients and microstructure to prepare nanocrystalline single phase NBBT powders. Where is the X-ray diffraction result of the corresponding ceramics to prove the existence of the mixing between rhombohedral and tetragonal phases at the MPB compositions. Doping 0.015 mol% Mn(NO₃)₂ into NBBT at 1,090 °C, piezoelectric constant (d ₃₃) and relative dielectric constant (ε_r) reach the superior value of 159pC/N and 1,304, respectively, and dielectric loss (tan δ) and electromechanical coupling factor (K _t) are 2.5% and 65%, respectively.     

Enhanced microwave dielectric properties of Ba<Subscript>0.40</Subscript>Sr<Subscript>0.60</Subscript>TiO<Subscript>3</Subscript>–Zr<Subscript>0.80</Subscript>Sn<Subscript>0.20</Subscript>TiO<Subscript>4</Subscript> composite ceramics

The (1−x) Ba_0.40Sr_0.60TiO₃ (BST)−xZr_0.80Sn_0.20TiO₄ (ZST) composite ceramics with x = 10, 20, 30, and 40 wt% were fabricated by conventional solid-state reaction method. With increasing of ZST content, the dielectric constant of composite ceramics was decreased and dielectric loss increases. The effect of ZnO addition to 70 wt% BST–30 wt% ZST composition on the microstructure and dielectric properties was investigated. The improvements in dielectric constant, dielectric loss, and microwave dielectric properties of composite ceramics can be achieved by ZnO addition. The sample with 98 wt% (70 wt% BST–30 wt% ZST)–2 wt%ZnO composition exhibits promising dielectric properties, with dielectric constant, loss tangent and tunability at 4 kV/mm, of 125, 0.0016 and 12%, at 10 kHz and room temperature. At ~2 GHz, it possesses a dielectric constant of 101 and a Q factor of 187, which makes it a good candidate for tunable microwave device applications.     

Aging and thermal stability of [001]<Subscript>c</Subscript>- and [111]<Subscript>c</Subscript>-poled 0.63Pb(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript>–0.37PbTiO<Subscript>3</Subscript> single crystals

The aging characteristics and thermal stability of [001]_c- and [111]_c-poled tetragonal 0.63Pb(Mg_1/3Nb_2/3)O₃–0.37PbTiO₃ single crystals have been studied. For [001]_c-poled crystal, the d₃₃, \(\varepsilon _{{33}}^{T}\), k_t, and k₃₃ increase slightly during the aging process due to the gradual depolarization of the single-domain state. On the contrary, the electromechanical properties of [111]_c-poled crystal decrease quickly with the aging time due to the growth and combination of micro-domains. The temperature-dependent electromechanical properties indicate that the [111]_c-poled multi-domain crystal is more stable than [001]_c-poled single-domain crystal. In addition, the second poling can effectively enhance the piezoelectric constant d₃₃ of the [111]_c-oriented multi-domain crystals from 1032 pC/N after the first poling to 1247 pC/N.     

The crossover of (Ba<Subscript>1−x</Subscript>Ca<Subscript>x</Subscript>)(Ti<Subscript>0.9</Subscript>Sn<Subscript>0.1</Subscript>)O<Subscript>3</Subscript> piezoelectric ceramics from single-phase to composite with studying the structural and dielectric properties

Lead-free (Ba_1?xCa_x)(Ti_0.9Sn_0.1)O₃ perovskite ceramics (x?=?0.02–0.5) (BCTS) were synthesized using the solid-state reaction technique. X-ray diffraction was used to identify the formed phases of the prepared compositions. The morphology of ceramics has been studied using a scanning electron microscope equipped with an energy dispersive spectrometer. Field emission scanning electron microscope was used to examine the morphology of sensing film calcined powder. The crossover from BCTS single-phase (x?=?0.02) to BCTS composite(x?=?0.5) was obtained via coexistence of both (x?=?0.3) of Ca addition. The composite powder was sintered at higher temperature rather than the single-phase powder. The calcined powder sensing film was prepared by the screen-printing technique as humidity sensors. Thereafter, DC resistance measurements were performed in the presence of relative humidity RH at room temperature. All the compositions exhibited a poor sensitivity toward the humidity sensing in the range of 0–98% RH. The compositions 0.02 and 0.06 have shown orthorhombic–tetragonal phase transition (T_O?T) below the room temperature, while the other compositions have shown a pure tetragonal phase. The highest value of permittivity at Curie temperature (ε?=?29241 at 100 Hz) and piezoelectric coefficient (d₃₃?=?495 pC/N) at room temperature were obtained at Ca?=?0.06 due to present polymorphic phase transition. The effect of frequency on the dielectric constant and dielectric loss at room temperature were investigated. All the prepared compositions exhibited small values of dielectric loss from 50 Hz up to 100 KHz, which indicates a good reliability for electronic applications such as capacitors or memory devices.     

Preparation,structure and microwave dielectric properties of 3MgO–Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–3TiO<Subscript>2</Subscript> ceramics

3MgO–Al₂O₃–3TiO₂ (MAT) ceramics were prepared by a conventional solid-state reaction method. The crystal structure, sintering behavior and microwave dielectric properties of ceramics were investigated using X-ray diffraction, scanning electron microscopy and network analyzer. MAT ceramics contained the coexistence of three phases, including MgAl₂O₄, MgTiO₃ and MgTi₂O₅. The ceramics sintered at 1350 °C for 4 h presented excellent comprehensive performances with relative permittivity (ε _r ) of 15.4, quality factor (Q × f) of 91,000 GHz and temperature coefficient of resonant frequency (τ _f ) about ?55.1 ppm/°C.