ZnBO-doped (Ba, Sr)TiO3 ceramics for the low-temperature sintering process

ZnBO-doped (Ba, Sr)TiO₃ ceramics were investigated for low-temperature co-fired ceramics (LTCCs) applications. Until now, B₂O₃ and Li₂CO₃ dopants have been commonly employed as the low-temperature sintering aids. In this paper, we suggest ZnBO as an alternative dopant to the B₂O₃ and Li₂CO₃. To reduce the sintering temperature of (Ba, Sr)TiO₃, we have added 1–5 wt.% of ZnBO to (Ba, Sr)TiO₃. ZnBO-doped (Ba, Sr)TiO₃ ceramics were respectively sintered from 750 to 1350 °C by 50 °C to confirm the sintering temperature with different dopant contents. By adding 5 wt.% of ZnBO to the (Ba, Sr)TiO₃ ceramics, the sintering temperature of (Ba, Sr)TiO₃ ceramics can be reduced to 1100 °C. From the XRD analysis, ZnBO-doped (Ba, Sr)TiO₃ has no pyro phase. By adding ZnBO dopants to (Ba, Sr)TiO₃ ceramics, both of relative dielectric permittivity and loss tangent were decreased. From the frequency dispersion of dielectric properties, the relative dielectric permittivity and loss tangent of 5 wt.% ZnBO-doped (Ba, Sr)TiO₃ were 1180 and 3.3 × 10⁻³, while those of BST were 1585 and 4.8 × 10⁻³, respectively.     

Low Dielectric Loss and Good Dielectric Thermal Stability of xNd(Zn1/2Ti1/2)O3–(1−x)Ba0.6Sr0.4TiO3 Thin Films Fabricated by Sol–Gel Method

xNd(Zn_1/2Ti_1/2)O₃–(1?x)Ba_0.6Sr_0.4TiO₃ (xNZT–BST) thin films were fabricated on Pt/Ti/SiO₂/Si substrates by sol–gel method with x = 0, 3%, 6%, and 10%. The structures, surface morphology, dielectric and ferroelectric properties, and thermal stability of xNZT–BST thin films were investigated as a function of NZT content. It was observed that the introduction of NZT into BST decreased grain size, dielectric constant, ferroelectricity, tunability, and significantly improved dielectric loss and dielectric thermal stability. The corresponding reasons were discussed. The 10%NZT–BST thin film exhibited the least dielectric loss of 0.005 and the lowest temperature coefficient of permittivity (TCP) of 3.2 × 10^?3/°C. In addition, the figure of merit (FOM) of xNZT–BST (x = 3%, 6%, and 10%) films was higher than that of pure BST film. Our results showed that the introduction of appropriate NZT into BST could modify the dielectric quality of BST thin films with good thermal stability. Especially for the 3%NZT–BST thin film, it showed the highest FOM of 33.58 for its appropriate tunability of 32.87% and low dielectric loss of 0.0098.     

Effects of vacancy defects caused by non-stoichiometric ratio on dielectric properties of ABO3 perovskite (Ba0.5Sr0.5)xTiO3 ceramics

Non-stoichiometric Ba_0.5Sr_0.5TiO₃ (BST50) ceramics with varying A/B ratios, namely (Ba + Sr)/Ti, were prepared by a conventional solid-state reaction approach. The effects of vacancy defects caused by varying the A/B ratio on the structure and dielectric properties of BST50 ceramics were systematically investigated. A remarkable change in grain size was found when the A/B ratio was increased, which led to apparent variations in the dielectric properties of the BST50 ceramics. The Curie temperature (T_c) and dielectric permittivity peak (ε_max) increased first and then decreased with increasing A/B ratio, and reached the maximum at A/B = 1. Simultaneously, the dielectric diffusion parameter of BST50 ceramics was studied by the Lorenz-type formula. All samples exhibited diffusion phase transition behavior, and T_c was frequency independence. When A/B < 1, the Q value remained at a high level; in contrast, when A/B > 1, the Q value was significantly reduced. For this BST50 system, high tunability of 24.95% (at 30 kV/cm), low dielectric loss of 0.0017 (at 10 kHz), and high figure of merit (FOM) of 147 were achieved simultaneously at A/B = 1.01.     

Phase content and dielectrical properties of sintered BaSrTiO ceramics prepared by a high temperature hydrothermal technique

Ba_xSr_1−xTiO₃ ceramic powders with varying barium content were prepared by a high temperature hydrothermal technique and sintered at 1300 °C for 1–8 h. Their dielectrical, phase and structural properties were investigated. It was computed from the XRD spectra that the samples with a small amount of strontium, no more than 10% of the initial Ba:Sr share, had a single phase structure with x = 0.77–0.79 and Curie point T_c = 37–53 °C. Samples with a higher initial Sr ratio developed a two-phase structure and two Curie points. T_c(x) dependence showed that all the experimental data followed a linear trend and were close to the values obtained from the conventional solid state technique, while the dielectric constant was almost one order of magnitude smaller.     

Preparation of La1?x Sr x CoO3 Oxide Electrode Material and its Influence on the Structure and Dielectric Performance of the Supported Ba1?x Sr x TiO3 Thin Films

Using the sol–gel method, La_1−x Sr _x CoO₃ (LSCO) electrode films were first fabricated on the Si (100) substrates, followed by the growth of Ba_1−x Sr _x TiO₃ (BST) thin films on the LSCO electrode film. The crystal structure and surface morphology of these films were characterized by XRD and SEM. The effects of Sr-doping and annealing temperature on the structure and electric resistivity of the LSCO films and the dielectric properties of the BST films were studied. Results show that the La_0.5Sr_0.5CoO₃ electrode annealed at 750 °C has the lowest electric resistivity, 1.1 × 10⁻³Ω cm. The relative permittivity of the La_0.5Sr_0.5CoO₃-supported BST films first increases and then decreases with Sr-doping. The relative permittivity of the BST film decreases while the dielectric loss increases with frequency. Among the studied BST films, Ba_0.5Sr_0.5TiO₃ has the largest relative permittivity and the smallest dielectric loss (95 and 0.1, respectively) when the frequency is 1 kHz.     

Microstructure,colossal permittivity,and humidity sensitivity of (Na,Nb) co-doped rutile TiO2 ceramics

(Na_0.25Nb_0.75)_xTi_1−xO₂ (NNTO) ceramics (x = 0, 0.005, 0.01, 0.02, and 0.05) were prepared by the conventional solid-state reaction. The microstructure, dielectric, and humidity sensitivity of the ceramics were systematically investigated. Results showed that all ceramics exhibit pure rutile TiO₂ phase with dense microstructures. Co-doping of (Na, Nb) can effectively improve the microstructure homogeneity of the ceramics. When the doping level x ≥ 0.01, the co-doped samples show colossal permittivity higher than 10⁴ and dielectric loss tangent lower than 0.38. This dielectric behavior features the merit of both frequency and temperature stability in the range of 10²-10⁶ Hz and 100-300 K, respectively. The co-doped ceramics were found to be sensitive to the environment moisture. The humidity sensitivity incurs a Maxwell-Wagner relaxation near room temperature, which further enhances the dielectric permittivity. Excellent humidity sensitive properties of sensitivity to be 102.6 pF/%RH, response/recovery time to be 115/20 seconds, as well as good repeatability, were achieved in the sample with the doping level x = 0.05. This work underscores that the room temperature dielectric properties of doubly doped TiO₂ system depends strongly on the environmental condition and suggests that the (Na + Nb) co-doped TiO₂ ceramics might be promising humidity sensing materials.     

Systematic investigation of the annealing temperature and composition effects on the dielectric properties of sol–gel BaxSr1−xTiO3 thin films

In this work, Ba_xSr_1?xTiO₃ sol–gel thin films (x = 0.7, 0.5 and 0.3) deposited on Pt/Si substrate and post-annealed at different temperatures have been investigated. A systematic study of the structure, microstructure and dielectric properties has been achieved for each composition. To our knowledge, for the first time, a systematic effect of post-deposition annealing temperature and composition is reported. For each Ba/Sr ratio, higher annealing temperature leads to crystallinity improvement and to grain growth. A shift of the ferroelectric to paraelectric transition toward the bulk Curie temperature with the increase of the annealing temperature is shown. These results are correlated with the increase of the permittivity, tunability and dielectric losses measured on MIM capacitors at low frequency. Moreover, the high frequency results, between 800 MHz and 30 GHz, are in very good agreement with low frequency measurements, and show a huge tunability up to 80% under 600 kV/cm.     

Lead-free high-temperature dielectrics with wide temperature stability range induced from BiFeO3-BaTiO3-based system

Lead-free BNSTNZ ((Bi,Na,Ba,Sr)(Ti,Nb,Zr)O₃)-modi?ed BF35BT (0.65BiFeO₃-0.35BaTiO₃) dielectrics were investigated by conventional solid-state reaction method. Dielectric permittivity of BFBT-BNSTNZ ceramics was suppressed through addition of BNSTNZ content, while dielectric temperature stability range was expanded from 105 °C to 412 °C as BNSTNZ content increases from 0.025 to 0.1, due to the ferroelectric-relaxor phase transition. In particular, x = 0.10 exhibits the widest stability temperature range from 88 °C to 500 °C having small variation of (Δε_m/ε_{m 150 °C} ≤ 15%) with high dielectric permittivity (> 1000) and low dielectric loss (tan? ≤ 0.1) in temperature range from 50 °C to 250 °C. Moreover, high room temperature energy storage density (W_store) of 0.75 and 0.57 J/cm³ with energy storage efficiency (?) of 57% and 78% for x = 0.03 and x = 0.10, respectively, was achieved. These results indicate that BFBT-BNSTNZ can be a promising system for high-temperature dielectric and energy storage applications.     

Good dielectric performance and broadband dielectric polarization in Ag,Nb co-doped TiO2

Due to the demand of miniaturization and integration for ceramic capacitors in electronic components market, TiO₂-based ceramics with colossal permittivity has become a research hotspot in recent years. In this work, we report that Ag⁺/Nb⁵⁺ co-doped (Ag_1/4Nb_3/4)_xTi_1−xO₂ (ANTOx) ceramics with colossal permittivity over a wide frequency and temperature range were successfully prepared by a traditional solid–state method. Notably, compositions of ANTO0.005 and ANTO0.01 respectively exhibit both low dielectric loss (0.040 and 0.050 at 1 kHz), high dielectric permittivity (9.2 × 10³ and 1.6 × 10⁴ at 1 kHz), and good thermal stability, which satisfy the requirements for the temperature range of application of X9R and X8R ceramic capacitors, respectively. The origin of the dielectric behavior was attributed to five dielectric relaxation phenomena, i.e., localized carriers' hopping, electron–pinned defect–dipoles, interfacial polarization, and oxygen vacancies ionization and diffusion, as suggested by dielectric temperature spectra and valence state analysis via XPS; wherein, electron-pinned defect–dipoles and internal barrier layer capacitance are believed to be the main causes for the giant dielectric permittivity in ANTOx ceramics.     

Zirconium Incorporation into CaTiO3 Perovskite Prepared from Xerogels and Implication for the Fate of (Ca,Sr)TiO3 Nuclear Waste Ceramics

CaTiO₃ perovskite has been proposed as a ceramic waste form for immobilization of ⁹⁰Sr. Nonradioactive coprecipitated xerogel powders with nominal atomic ratios of Ca:Zr:Ti = 0.75:0.25:1.00 were synthesized to mimic the fate of (Ca_0.75⁹⁰Sr_0.25)TiO₃ solid solution after complete decay of the Sr and its intermediate product Y to stable Zr when an excess B⁴⁺ (Ti and ⁹⁰Zr) cations will present. Ca:Ti = 1.00:1.00 samples were used as a reference. The powders were heated to various conditions to explore the thermodynamic stability of its oxides. The heated Ca:Zr:Ti = 0.75:0.25:1.00 samples formed a major orthorhombic Ca(Zr_1?xTi_x)O₃ perovskite phase. The Ti/(Ti + Zr) ratio of the perovskite preserves its nominal ratio at 600°C. The Zr rejects from the Ca(Zr_1?xTi_x)O₃ with further increasing the temperature, following the formation of Ca–Ti–Zr–O secondary phases. This study indicates a tendency of the Zr to segregate from an original (Ca,Sr)TiO₃ waste form when the stoichiometry is controlled by the conversion of Sr to Zr (in normal oxidation states).     

Nanocrystalline Barium Strontium Titanate Ceramics Synthesized via the “Organosol” Route and Spark Plasma Sintering

Dense nanocrystalline barium strontium titanate Ba_0.6Sr_0.4TiO₃ (BST) ceramics with an average grain size around 40 nm and very small dispersion were obtained by spark plasma sintering at 950°C and 1050°C starting from nonagglomerated nanopowders (~20 nm). The powders were synthesized by a modified “Organosol” process. X‐ray diffraction (XRD) and dielectric measurements in the temperature range 173–313 K were used to investigate the evolution of crystal structure and the ferroelectric to paraelectric phase transformation behavior for the sintered BST ceramics with different grain sizes. The Curie temperature T_C decreases, whereas the phase transition becomes diffuse for the particle size decreasing from about 190 to 40 nm with matching XRD and permittivity data. Even the ceramics with an average grain size as small as 40 nm show the transition into the ferroelectric state. The dielectric permittivity ε shows relatively good thermal stability over a wide temperature range. The dielectric losses are smaller than 2%–4% in the frequency range of 100 Hz–1 MHz and temperature interval 160–320 K. A decrease in the dielectric permittivity in nanocrystalline ceramics was observed compared to submicrometer‐sized ceramics.     

Stability of High‐Temperature Dielectric Properties for (1 − x)Ba0.8Ca0.2TiO3–xBi(Mg0.5Ti0.5)O3 Ceramics

Ceramics in the solid solution system, (1 ? x)Ba_0.8Ca_0.2TiO₃–xBi(Mg_0.5Ti_0.5)O₃, were prepared by a conventional mixed oxide route. Single‐phase perovskite‐type X‐ray diffraction patterns were observed for compositions x < 0.6. A change from tetragonal to single‐phase cubic X‐ray patterns occurred at x ≥ 0.1. Dielectric measurements indicated relaxor behavior for x ≥ 0.1. Increasing the Bi(Mg_0.5Ti_0.5)O₃ content improved the temperature sensitivity of relative permittivity ?_r at high temperatures. At x = 0.5, a near‐plateau relative permittivity, 835 ± 40, extended across the temperature range, 65°C–550°C; the permittivity increased at x = 0.6 to 2170 ± 100 for temperatures 160°C–400°C (1 kHz). The corresponding loss tangent, tanδ, was ≤0.025 for temperatures between 100°C and 430°C for composition x = 0.5; at x = 0.6, losses increased sharply at >300°C. Comparisons of dielectric properties with other materials proposed for high‐temperature capacitor applications suggest that (1 ? x)Ba_0.8Ca_0.2TiO₃–xBi(Mg_0.5Ti_0.5)O₃ ceramics are a promising base material for further development.     

Effect of A-site substitutions on energy storage properties of BaTiO3-BiScO3 weakly coupled relaxor ferroelectrics

Weakly coupled relaxors based on compositions (1-x) BaTiO₃-xBiMeO₃, where Me is a metal ion, have attracted attention as potential candidates for high-temperature high-energy density capacitors. However, the necessary Bi content is typically high with x = 0.3-0.4. In order to reduce problems associated with compatibility for base metal electrodes and due to additional problems due to Bi volatility, it is desirable to lower the Bi content in the overall composition for these materials. Here, we have explored a possible way to reduce BiMeO₃ content through additional A-site substitutions viz. Ca and Sn. The relaxor nature and energy storage properties of Sn-modified (Ba,Ca)(Ti)O₃-BiScO₃ ceramics were determined from their dielectric and ferroelectric behaviors. The material showed attractive properties in terms of a frequency-independent (200 Hz-1 MHz) dielectric response from room temperature to 200°C, extremely low loss and high-energy storage efficiency. The structural phenomena underlying the functional properties of Sn-modified (Ba,Ca)TiO₃-BiScO₃ are characterized from temperature-dependent X-ray diffraction and pair distribution function analysis. In broader terms, the study illustrates the potential for tailoring relaxor behavior in Pb-free ferroelectrics by combining phenomena, such as quantum fluctuations and lone pair stereochemical effect associated with different solid-solution substitutions.     

Intrinsic correlation between structure,vibration spectrum and microwave dielectric properties of ferroelectric-dielectric composite ceramics

A novel series of (1-x)Ba_0.45Sr_0.55TiO₃-xMgGa₂O₄ (x = 0, 10, 30, 50, 70 wt%) ceramics was prepared by a solid-state method to investigate the relationship between their dielectric properties and ion diffusion, composition effect, and lattice vibration. XRD refinement and DFT calculations of Ba_0.45Sr_0.55TiO₃ (BST45) revealed that the substitution of Ga³⁺ and Mg²⁺, both of which have small polarizability for Ti⁴⁺, reached the saturation state at x = 10 wt%, thus decreasing the quality factor (Q value). In contrast, the addition of MgGa₂O₄ (MG) with x > 10 wt% significantly reduced the relative permittivity and improved the Q value owing to the compositional effect. The vibration spectra (Raman and FT-IR) confirmed that the Q value initially decreased owing to ion diffusion at x < 10 wt% and then increased with increasing MG content according to the composition effect. Therefore, the Q value was remarkably improved in the Ba_0.45Sr_0.55TiO₃-MgGa₂O₄ composites, with good tunability and low relative permittivity.     

Influence of stoichiometry on the dielectric and ferroelectric properties of the tunable (Ba,Sr)TiO3 ceramics investigated by First Order Reversal Curves method

The changes induced by the different stoichiometries in Ba_0.9Sr_0.1TiO₃ solid solutions, with (Ba,Sr)/Ti = 1 and (Ba,Sr)/Ti > 1, on the dielectric, ferroelectric and ac tunability characteristics are investigated. A small difference in the (Ba,Sr)/Ti ratio causes a shift of the Curie and Curie–Weiss temperatures of 16 and 19 °C, respectively, but does not change the diffuse character of the phase transitions. The FORC method is used for describing the local switching properties and the ac tunability characteristics. Irrespective of the stoichiometry, no clear separation between the reversible and irreversible contributions to the polarization are visible on the FORC diagrams. The maximum of the FORC distribution is located in almost the same position, at low fields, meaning that small fields are necessary to switch the majority of the dipolar units of these systems. The diagram obtained for the solid solutions with (Ba,Sr)/Ti = 1 shrinks towards smaller coercivities in comparison with the Ba-rich samples, due to the smaller Curie temperature, making it closer to the ferro–para phase transition. The tunability determined in the FORC experiment depends not only on the actual field, but also on the reversal field. A dependence of the FORC susceptibility on the two maxima corresponding to the reversal field was found for the stoichiometric samples, while one single maximum at low reversal fields is characteristic of the Ba-rich samples. These results are interpreted in relationship to domain wall mobility, which is higher for the ferroelectric sample, close to its ferro–para phase transition.     

Effects of A1/A2‐Sites Occupancy upon Ferroelectric Transition in (SrxBa1−x)Nb2O6 Tungsten Bronze Ceramics

The dielectric and ferroelectric characteristics of (Sr_xBa_1?x)Nb₂O₆ unfilled tungsten bronze ceramics have been investigated together with the structure. The dielectric and ferroelectric characteristics of the present ceramics vary significantly with x, and the A1/A2‐sites occupancy has been determined as the primary parameter governing this variation tendency. Ba ions tend to occupy A2‐sites, Sr ions tend to occupy A1‐sites, and one A1‐site is empty. When the ratio of Sr/Ba is close to 1:4 (where four A2‐sites are just occupied by Ba ions, and one A1‐site is occupied by Sr ion while another A1‐site is empty), the normal ferroelectric transition is observed with one anomaly in the tanδ–T curve (x = 0.25). When the ratio of Sr/Ba is far away from 1:4, the typical relaxor behavior is indicated together with three anomalies in the tanδ–T curve (x = 0.75). The incommensurate oxygen octahedral tilting and A‐site random distribution are considered to be the structure origins for the relaxor ferroelectricity and low temperature dielectric relaxations.     

Microstructure and dielectric properties of Ba0.6Sr0.4TiO3-MgAl2O4 composite ceramics

(1 − x)Ba_0.6Sr_0.4TiO₃-xMgAl₂O₄(x = 25, 30, 35 and 40 wt%) composite ceramics were prepared by conventional solid-state reaction method. The microstructures, dielectric properties and tunability of the composites have been investigated. The XRD patterns analysis reveals two crystalline phases, a cubic perovskite structure Ba_0.6Sr_0.4TiO₃ (BST) and a spinel structure MgAl₂O₄ (MA). SEM observations show that the BST grains slightly dwindle and agglomerate with increasing amounts of MA. A dielectric peak with very strong frequency dispersion is observed at higher MA content, and the Curie temperature shifts to a higher temperature with increasing MA content. The ceramic sample with 30 wt% MA has the optimized properties: the dielectric constant is 1503, the dielectric loss is 0.003 at 10 kHz and 25 °C, the tunability is 23.63% under a dc electric field of 1.0 kV/mm, which is suitable for ferroelectric phase shifter.     

Influence of Se and Te substitutions at Tl-site of Tl(Ba,Sr)CaCu2O7 superconductor on the AC susceptibility and electrical properties

The Sr and Ba bearing Tl-1212 phase, Tl(Ba,Sr)CaCu₂O₇ is an interesting superconductor. The Sr only bearing TlSr₂CaCu₂O₇ is not easily prepared in the superconducting form. The Ba only bearing TlBa₂CaCu₂O₇ on the other hand does not show improvement in the transition temperature with elemental substitution. In this work the influence of multivalent Se (non-metal) and Te (metalloid) substitutions at the Tl-site of Tl_1-xM_x(Ba,Sr)CaCu₂O₇ (M = Se or Te) superconductors for x = 0–0.6 was studied. The samples were prepared via the conventional solid-state reaction method. XRD patterns showed a single Tl-1212 phase for x = 0 and 0.1 Se substituted samples. The critical current density at the peak temperature, T_p of the imaginary (χ”) part of the AC susceptibility (χ = χ’ +χ”), J_c-inter(T_p) for all samples was between 15 and 21 A cm⁻². The highest superconducting transition temperature was shown by the x = 0.3 Se-substituted sample (T_c-onset = 104 K, T_c-zero = 89 K, T_cχ’ = 104 K and T_p = 80 K). Te suppressed the superconductivity of Tl-1212 phase. The order of highest transition temperatures are as follows: Tl_1-xTe_x(Ba,Sr)CaCu₂O₇<Tl(Ba,Sr)CaCu₂O₇<Tl_1-xSe_x(Ba,Sr)CaCu₂O₇. This work showed that Se was better than Te in improving the transition temperature and flux pinning of the Tl-1212 phase. The roles of ionic radius of Se and Te on the superconductivity of Tl(Ba,Sr)CaCu₂O₇ are discussed in this paper.     

Structural and dielectric behavior of yNi1 ? xCdxFe2O4 + (1 ? y)Ba0.8Sr0.2TiO3 magnetoelectric composites prepared through SHS route

The structural and dielectric properties of SHS-produced yNi_{1 − x} Cd _x Fe₂O₄ + (1 − y)Ba_0.8Sr_0.2TiO₃ (x = 0.2, 0.4, 0.6; y = 15, 30, 45%) magnetoelectric composites were characterized by XRD, SEM, and resistivity/dielectric measurements. SEM images reveal that SHS reaction can produce two pure phases simultaneously. The grown Cd-substituted nickel ferrite grains were well dispersed in a BST matrix. A decrease in resistivity with temperature shows the semiconducting nature of synthesized samples. The dielectric results demonstrated an attractive response of dielectric constant to frequency and temperature. The Curie temperature of about 480°C was observed in the Ni_0.4Cd_0.6Fe₂O₄ + Ba_0.8Sr_0.2TiO₃ composite.     

Low‐Temperature Sintering and Microwave Dielectric Properties of ZnNb2O6–TiO2 Ceramics with BaCu(B2O5) Additions

The influence of BaCu(B₂O₅) (BCB) on densification, phases, microstructure and microwave dielectric properties of ZnNb₂O₆–xTiO₂ (x = 1.70–1.90) composite ceramics have been investigated. Undoped ZnNb₂O₆–1.8TiO₂ ceramics sintered at 1200°C exhibit temperature coefficient of resonant frequency (τ_f) ~9.25 ppm/°C. When BaCu(B₂O₅) was added, the sintering temperature of the ZnNb₂O₆–1.8TiO₂ composite ceramics was effectively reduced to 950°C. The results indicated that the permittivity and Q × f were dependent on the sintering temperature and the amounts of BaCu(B₂O₅). Addition of 3.0 wt% BaCu(B₂O₅) in ZnNb₂O₆–1.8TiO₂ ceramics sintered at 950°C showed excellent dielectric properties of ε_r = 40.9, Q × f = 12,200 GHz (f = 5.015 GHz) and τ_f = +0.3 ppm/°C.