Contribution of Structure to Temperature Dependence of Resonant Frequency in the (1 −x)La(Zn1/2Ti1/2)O3·xATiO3 (A = Ca, Sr) System

The crystal structure and microwave dielectric properties of the (1 − x ) La(Zn_1/2Ti_1/2)O₃· x SrTiO₃ and (1 − x )La(Zn_1/2Ti_1/2)O₃· x CaTiO₃ system were investigated. X-ray powder diffraction showed that cation ordering disappeared at x > 0.3 for both systems. However, infrared spectra demonstrated that short-range cation ordering could exist at x = 0.4. Permittivity and the temperature coefficient of the resonant frequency (τ_f) of both systems exhibited nonmonotonic variations with composition. Both systems exhibited a τ_f of zero at the same composition of x = 0.5 although the τ_f of SrTiO₃ was about two times larger than that of CaTiO₃. The behavior of the permittivity and τ_f were described by the tilting of oxygen octahedra and cation ordering. The relation between τ_f and cation ordering of La(Zn_1/2Ti_1/2)O₃ was discussed in conjunction with the experimental results on metal halides. It is suggested that cation ordering induced a negative τ_f and suppressed the increase of permittivity for compositions between x = 0 to x = 0.5 for (1 − x )La(Zn_1/2Ti_1/2)O₃· x SrTiO₃ and (1 − x )La(Zn_1/2Ti_1/2)O₃· x CaTiO₃ systems.     

Characteristics of High-Q Microwave Dielectric Ceramics Nd(Co1/2Ti1/2)O3 With CuO Addition

We report the microwave dielectric properties and the microstructures of Nd(Co_1/2Ti_1/2)O₃ ceramics prepared by the conventional solid-state route. The prepared Nd(Co_1/2Ti_1/2)O₃ exhibits a mixture of Co and Ti showing a 1:1 order in the B site. Lowering the sintering temperature (as low as 1260°C) and promoting the densification of Nd(Co_1/2Ti_1/2)O₃ ceramics could be effectively achieved by adding CuO (up to 0.75 wt%). At 1350°C, Nd(Co_1/2Ti_1/2)O₃ ceramics with 0.5 wt% CuO addition possess a dielectric constant (ɛ_r) of 27.6, a Q × f value of 165 000 GHz (at 9 GHz), and a temperature coefficient of resonant frequency (τ_f) of −20 ppm/°C. By comparing with pure Nd(Co_1/2Ti_1/2)O₃ ceramics, incorporating additional CuO helps to render a dielectric material with a higher dielectric constant, a smaller τ_f value, and a 20% dielectric loss reduction, which makes it a very promising candidate for applications requiring low microwave dielectric loss.     

Dielectric Properties of (1−x)CaTiO3–xCa(Zn1/3Nb2/3)O3 Ceramic System at Microwave Frequency

The microwave dielectric properties of the (1− x )CaTiO₃– x Ca(Zn_1/3Nb_2/3)O₃ ceramic system have been investigated. The ceramic samples sintered at 1300°–1450°C for 4 h in air exhibit orthorhombic pervoskite and form a complete solid solution for different x value. When the x value increased from 0.2 to 0.8, the permittivity ɛ_r decreased from 115 to 42, the unloaded quality factor Q × f increased from 5030 to 13 030 GHz, and the temperature coefficient τ_f decreased from 336 to −28 ppm/°C. When x =0.7, the best combination of dielectric properties, a near zero temperature coefficient of resonant frequency of τ_f∼−6 ppm/°C, Q × f ∼10 860 GHz and ɛ_r∼51 is obtained.     

Structure–Property Relations in xBaTiO3–(1−x)La(Mg1/2Ti1/2)O3 Solid Solutions

The microwave dielectric properties and microstructures of compounds in the solid solution series x BaTiO₃–(1− x )La(Mg_1/2Ti_1/2)O₃ (BTLMT) have been investigated. The structural phase transitions that occur as a function of x have been studied and are related to changes in the dielectric properties. For compounds where x ≤ 0.1, X-ray diffraction (XRD) showed evidence of 1:1 ordering between Mg and Ti cations. For x ≤ 0.3, XRD and electron diffraction revealed that compounds were tilted in both antiphase and in-phase. However, for 0.3 < x < 0.7, only antiphase tilting was present. The temperature coefficient of resonant frequency (τ_f) vs the relative permittivity (ɛ_r) was linear until x = 0.5 at which point in the solid solution the transition to a nontilted structure resulted in nonlinear behavior. τ_f values close to zero (−2 ppm/°C) were achieved at x = 0.5 (ɛ_r∼ 60), which had a quality factor ( Q · f _o) of 9600 GHz.     

Dielectric Properties of Ceramics in Ba (Co1/3 Nb2/3)O3–Ba(Zn1/3Nb2/3)O3 Solid Solution

The dielectric properties of the Ba (Co_1/3 Nb_2/3)O₃–Ba(Zn_1/3Nb_2/3)O₃ system were determined. Ba (Co_1/3 Nb_2/3)O₃–Ba(Zn_1/3Nb_2/3)O₃ has a complex perovskite structure, a high dielectric constant, a low dielectric loss, and a low temperature coefficient of the resonant frequency. A solid-solution ceramic with 0.7Ba (Co_1/3 Nb_2/3)O₃·0.3 Ba(Zn_1/3Nb_2/3)O₃ has a dielectric constant of K=33.5, Q=11000 at 6.5 GHz, and a temperature coefficient of the resonant frequency of τ_f=0 ppm/°C. The temperature coefficient of resonant frequency can be varied by changing the composition. The Q values of the ceramics can be increased by annealing in a nitrogen atmosphere. These ceramics can be used for resonant elements and stabilized oscillators.     

Adhesive-Bonded Ca(Mg1/3Nb2/3)O3/Ba(Zn1/3Nb2/3)O3 Layered Dielectric Resonators with Tunable Temperature Coefficient of Resonant Frequency

Ca(Mg_1/3Nb_2/3)O₃ and Ba(Zn_1/3Nb_2/3)O₃ ceramic cylinders with the same diameter were bonded by adhesive with low dielectric loss to yield the layered dielectric resonators, and the microwave dielectric characteristics were evaluated with TE_01δ mode. With increasing the Ba(Zn_1/3Nb_2/3)O₃ thickness fraction, the resonant frequency ( f ₀) decreased, while the effective dielectric constant (ɛ _{r ,eff}) and temperature coefficient of resonant frequency (τ _f ) increased. Good microwave dielectric characteristics were attained for the samples with the Ba(Zn_1/3Nb_2/3)O₃ thickness fraction of 0.5: ɛ _{r ,eff}=34.33, Q × f =57 930 GHz and τ _f =2.6 ppm/°C. Finite-element method was used to predict the microwave dielectric characteristics of the layered resonators and good agreements were attained between the experimental results and predicted ones. Also, both experiment and finite-element analysis indicated that the effects of the adhesive on f ₀, ɛ _{r ,eff}, and τ _f were slight, while that on Q × f value was significant.     

Crystal Structure and Microwave dielectric Properties of Ba(Zn1/3Ta2/3)O3–(Sr,Ba)(Ga1/2Ta1/2)O3 Ceramics

The microwave dielectric properties and crystal structure of Ba(Zn_1/3Ta_2/3)O₃– (Sr,Ba)(Ga_1/2Ta_1/2)O₃ ceramics were investigated in the present study. The Q value of Ba(Zn_1/3Ta_2/3)O₃ was improved by adding 5 mol% Sr(Ga_1/2Ta_1/2)O₃. The maximum Q value of Q × f = 162000 GHz was obtained at 0.95Ba(Zn_1/3Ta_2/3)O₃. 0.05Sr(Ga_1/2Ta_1/2)O₃. For this composition, a lattice super structure caused by hexagonal ordering was observed. A further improvement in the Q value was attained when some Sr was replaced with Ba, and 0.95Ba(Zn_1/3Ta_2/3)O₃· 0.05(Sr_0.25Ba_0.75)(Ga_1/2Ta_1/2)O₃ exhibited a maximum Q value such that Q × f = 210000 GHz. Despite the increased Q value with the replacement of Sr by Ba, the c/a value, which indicates the degree of lattice distortion, remained constant near 3/2. The Q value thus improved without lattice distortion in the system Ba(Zn_1/3Ta_2/3)O₃-(Sr,Ba)(Ga_1/2Ta_1/2)O₃, whereas the improvement of Q value increased with lattice distortion in the solid solution system with Ba(Zn_1/3Ta_2/3)O₃ as an end member.     

Dielectric Characteristics of Nd(Zn1/2Ti1/2)O3 Ceramics at Microwave Frequencies

The microwave dielectric properties and the microstructures of Nd(Zn_1/2Ti_1/2)O₃ (NZT) ceramics prepared by the conventional solid-state route have been studied. The prepared NZT exhibited a mixture of Zn and Ti showing 1:1 order in the B-site. The dielectric constant values (ɛ_r) saturated at 29.1–31.6. The quality factor ( Q × f ) values of 56 700–170 000 (at 8.5 GHz) can be obtained when the sintering temperatures are in the range of 1300°–1420°C. The temperature coefficient of resonant frequency τ_f was not sensitive to the sintering temperature. The ɛ _r value of 31.6, the Q × f value of 170 000 (at 8.5 GHz), and the τ_f value of −42 ppm/°C were obtained for NZT ceramics sintering at 1330°C for 4 h. For applications of high selective microwave ceramic resonators, filters, and antennas, NZT is proposed as a suitable material candidate.     

Microwave Dielectric Properties of (1−x)(Na1/2Nd1/2)TiO3−xLa(Mg1/2Ti1/2)O3 via Ordering and Far IR Reflectivity Spectra

Microwave dielectric properties of (1− x )(Na_1/2Nd_1/2)TiO₃(NNT)− x La(Mg_1/2Ti_1/2)O₃(LMT) system have been investigated with focus on structural ordering and far IR reflectivity spectra. A single perovskite phase was found to exist with various superlattice reflections over the entire compositional range. 1:1 ordering observed in the (111) reflection of X-ray diffraction patterns was found to progress significantly in the specimens above x =0.8. The ordering characteristics that presumably related to B-site Mg/Ti ordering were assumed to affect favorably the quality factor at microwave frequencies. The increase of the quality factor also could be explained in terms of the decrease of lattice anharmonicity with LMT by analysis of far IR reflectivity spectra. As expected from the values of pure NNT and LMT, the dielectric constant and the temperature coefficient of frequency tended to gradually decrease with increasing LMT content.     

Low-Loss Microwave Dielectrics Using Mg2(Ti1−xSnx)O4 (x=0.01–0.09) Solid Solution

Low-loss ceramics having the chemical formula Mg₂(Ti_{1− x} Sn _x )O₄ for x ranging from 0.01 to 0.09 have been prepared by the conventional mixed oxide route and their microwave dielectric properties have been investigated. X-ray powder diffraction patterns indicate the corundum-structured solid solutions for the prepared compounds. In addition, lattice parameters, which linearly increase from 8.4414 to 8.4441 Å with the rise of x from 0.01 to 0.09, also confirm the forming of solid solutions. By increasing x from 0.01 to 0.05, the Q × f of the specimen can be tremendously boosted from 173 000 GHz to a maximum 318 000 GHz. A fine combination of microwave dielectric properties (ɛ_r∼15.57, Q × f ∼318 000 GHz at 10.8 GHz, τ_f∼−45.1 ppm/°C) was achieved for Mg₂(Ti_0.95Sn_0.05)O₄ ceramics sintered at 1390°C for 4 h. Ilmenite-structured Mg(Ti_0.95Sn_0.05)O₃ (ɛ_r∼16.67, Q × f ∼275 000 GHz at 10.3 GHz, τ_f∼−53.2 ppm/°C) was detected as a second phase. The presence of the second phase, however, would cause no significant variation in the dielectric properties of the specimen, because the second phase properties are very similar to the primary phase. These unique properties, in particular, low ɛ_r and high Q × f , can be utilized as a very promising dielectric material for ultra-high-frequency applications.     

Compositional Dependence of Microwave Dielectric Properties in (1 −x)(Na1/2Nd1/2)TiO3−xNd(Mg1/2Ti1/2)O3 Ceramics

The compositional dependence of microwave dielectric properties has been investigated in the (1 − x )(Na_1/2Nd_1/2)TiO₃− x Nd(Mg_1/2Ti_1/2)O₃ (NNT-NMT) system. The addition of NMT results in significant improvement in the quality factor and the temperature coefficient of frequency, but gradually decreases the dielectric constant from ∼100 for pure NNT to ∼25 for pure NMT. The single perovskite phase is observed with various { hkl } superlattice reflections over the entire compositional range. The increasing tendency of peak splitting with increasing x at some perovskite reflections strongly suggests that the crystal structure of the system changes to lower symmetry structures. This is confirmed using infrared reflectivity spectra. The superlattice reflections related to structural deviation become more predominant as the composition reaches pure NMT. Particularly, {111} superlattice reflections are believed to be associated with the 1:1 cation ordering and responsible for the observed abrupt increase in quality factor at x > 0.7.     

Formation and Structural Characterization of 1:1 Ordered Perovskites in the Ba(Zn1/3Ta2/3)O3–BaZrO3 System

The phase stabilities in the(1−x)Ba(Zn_1/3Ta_2/3)O₃ (BZT)-xBaZrO₃(BZ)system have been investigated using samples prepared by the mixed oxide method. The substitution of Zr⁴⁺destabilizes the 1:2 cation ordering in BZT and pro-motes the formation of a cubic, 1:1 ordered structure with a doubled perovskite repeat. The homogeneity range of the 1:1 phase extends from x = 0.04 to approximately x = 0.25; substitutions beyond this range stabilize a disordered perovskite. The limits of stability of the 1:1 ordering coin-cide with compositions previously found to exhibit anoma-lies in their dielectric loss. The range of homogeneity is consistent with a "random layer" model for the 1:1 ordered "Ba{β';_1/2β^1/2}O₃" structure. In this model the B× positions are assumed to be occupied exclusively by Ta⁵⁺, and the b× sites by a random distribution of Zn₂₊, Zr₄₊, and the remaining Ta 5+ cations. The validity of the model, where the ordered solid solutions can be represented by Ba{[Zn_{2− y /3}Ta_{(1−2 y )/3}Zr y ]_1/2[Ta]_1/2}O₃(y =2x)was con-firmed by Rietveld refinements conducted using data col-lected with a synchrotron X-ray source.     

Titanium Incorporation in Zn2TiO4 Spinel Ceramics

Compositions in the Zn₂TiO₄+ x TiO₂ system ( x = 0–0.43) were synthesized via the solid-state reaction route, using high-purity (≥99.99%) metal-oxide powders. The incorporation of titanium, in the form of TiO₂, in Zn₂TiO₄ spinel ceramics was investigated by analyzing the crystal structure and measuring the dielectric properties. The results of the crystal structure analyses suggested that TiO₂ levels of x ≤ 0.33 could be incorporated into the Zn₂TiO₄ spinel at temperatures of T > 945°C, whereas the solid solubility of titanium in Zn₂TiO₄ decreased for T < 945°C. When x ≥ 0.28, the Zn₂Ti₃O₈ phase formed in the Zn₂TiO₄ grain interior while cooling after heat treatment. Measurement of the microwave dielectric properties also supported the conclusion that the solubility limit of titanium in Zn₂TiO₄ was close to x = 0.33, as determined through analysis of the crystal structure.     

Cation Ordering Transformations in the Ba(Zn1/3Nb2/3)O3-La(Zn2/3Nb1/3)O3 System

Single-phase perovskites were formed in the (1−_x)Ba(Zn_1/3Nb_2/3)O₃-( _x )La(Zn_2/3Nb_1/3)O₃ system for compositions with 0.0≤ x ≤0.6. Although the stability of the trigonal "1:2" ordered structure of the Ba(Zn_1/3Nb_2/3)O₃ end member is very limited (0.0≤ x ≤0.05), low levels of lanthanum induce a transformation to a cubic, "1:1" ordered structure that has a broad range of homogeneity (0.05≤ x ≤0.6). Samples with x > 0.6 were comprised of La₃NbO₇, ZnO, and a perovskite with x = 0.6. The cubic 1:1 phases were fully ordered and no evidence was found for a compositionally segregated microstructure. These observations could not be reconciled in terms of a "space-charge" model; rather, they supported a charge-balanced, "random-site" structure for the 1:1 cation-ordered Ba(β_1/2'β_1/2")O₃ phases.     

Influence of Non-Stoichiometry on the Structure and Properties of Ba(Zn1/3Nb2/3)O3 Microwave Dielectrics: I. Substitution of Ba3W2O9

A narrow region of Zn-vacancy-containing cubic perovskites was formed in the (1− x )Ba₃(ZnNb₂)O₉−( x )Ba₃W₂O₉ system up to 2 mol% substitution ( x =0.02). The introduction of cation vacancies enhanced the stability of the 1:2 B-site ordered form of the structure, Ba(Zn_{1− x} □ _x )_1/3(Nb_{1− x} W _x )_2/3O₃, which underwent an order–disorder transition at 1410°C, ∼35° higher than pure Ba(Zn_1/3Nb_2/3)O₃. The Zn vacancies also accelerated the kinetics of the ordering reaction, and samples with x =0.006 comprised large ordered domains with a high lattice distortion ( c/a =1.226) after a 12 h anneal at 1300°C. The tungstate-containing solid solutions can be sintered to a high density at 1390°C, and the resultant ordered ceramics exhibit some of the highest microwave dielectric Q factors ( Q × f =1 18 000 at 8 GHz) reported for a niobate-based perovskite.     

Perovskite Phase Formation in the Relaxor System [Pb(Fe1/2Nb1/2)O3]1-x–[Pb(Zn1/3Nb2/3)O3]x

Phase formation and dielectric properties of the compositions in the system [Pb(Fe_1/2Nb_1/2)O₃]₁_ _x –[Pb(Zn_1/3Nb_2/3)O₃] _x were investigated as possible materials for multilayer ceramic capacitors. The formation of the phase with perovskite structure and dielectric properties of ceramics at room temperature in the entire composition range are presented. The undesirable pyrochlore phase can be suppressed up to x = 0.6 by adopting calcination of B-site oxides, followed by reaction with PbO. Compositions in the single-phase range can be sintered at less than 1000°C.     

Effects of Stacking Scheme on Microwave Dielectric Characteristics of Ca(Mg1/3Nb2/3)O3–Ba(Zn1/3Nb2/3)O3 Layered Dielectric Resonators

Ca(Mg_1/3Nb_2/3)O₃ (CMN) and Ba(Zn_1/3Nb_2/3)O₃ (BZN) ceramic disks were stacked with three stacking schemes, designated as CMN/BZN, CMN/BZN/CMN, and BZN/CMN/BZN, to yield layered dielectric resonators, and the microwave dielectric characteristics were evaluated with the TE_01δ mode. Both experiments and finite element analysis showed that the microwave dielectric characteristics of the layered resonator were determined not only by the volume fraction of BZN but also by the stacking scheme. For each stacking scheme, a good combination of microwave dielectric characteristics with an effective dielectric constant of 34.33–34.52, a Q × f value of 58 800–62 080 GHz, and a near-zero temperature coefficient of resonant frequency could be achieved by adjusting the volume fraction of BZN. The effects of the stacking scheme on the microwave dielectric characteristics of the temperature-stable layered resonator were discussed by combining finite element analysis and dielectric composite models.     

Microscopic Calculation of Dielectric Loss at Microwave Frequencies for Complex Perovskite Ba(Zn1/3Ta2/3)O3

The dielectric loss tangent at microwave frequencies for the complex perovskite Ba(Zn_1/3Ta_2/3)O₃ was calculated with respect to the degree of structural disorder on B sites. Starting out from the equations of ion motion, dielectric loss was expressed in terms of the pair-correlation functions corresponding to the ordering of Zn and Ta ions on B sites. The characteristic length included in the pair-correlation functions corresponds to the average size of the region containing disorder in ion arrangements on B sites; thus the relation between the structural disorder on the B site and the dielectric loss tangent at microwave frequencies was clarified theoretically. The numerical results show that the microwave loss tangent values change their power from – 3 to – 6 with increasing degree of order on the B site, which agrees well with the experimental observations. Results obtained here confirm the physical origin of the microwave loss of complex perovskite Ba(Zn_1/3Ta_2/3)O₃.     

Perovskite Formation and Dielectric Characteristics of Pb(Zn1/3Ta2/3)O3 with PbTiO3 Substitution

Perovskite developments in the Pb(Zn_1/3Ta_2/3)O₃–PbTiO₃ system were explored. Formation yields and lattice parameters of the perovskite were determined from X-ray diffractometry results. Weak-field low-frequency dielectric properties of the system ceramics were investigated, followed by microstructure examination. Perovskite started to develop in Pb(Zn_1/3Ta_2/3)O₃ after the introduction of 30 mol% PbTiO₃, whereas complete stabilization was accomplished at 60% substitution. Dielectric relaxation behavior was not substantial across the entire composition range, whereas phase transition modes changed from diffuse to sharp with increased PbTiO₃ fraction.     

Crossover of Ba(Ti,Y)O3 Solid Solutions to Ba3Ti2YO8.5–BaTiO3 Composites and their Dielectric Properties

Ceramic samples with the nominal composition (1− x ) BaTiO₃+ x Ba₃Ti₂YO_8.5 ( x =0−0.535) were prepared by the mixed oxide method. X-ray diffraction (XRD) analysis shows that the materials are of single phase with a cubic symmetry as x ≤0.16. The compositions of the solid solutions ( x ≤0.16) can be expressed equivalently as Ba(Ti_{1− y} Y _y )O_3−δ ( y ≤0.122, y = x /(1+2 x )). For x >0.16, the materials are diphasic composites consisting of Ba(Ti_{1− y} Y _y )O₃ ( y =0.122) and Ba₃Ti₂YO_8.5. The microstructure observation by scanning electron microscopy supports the XRD result. The dielectric behavior and phase transitions of the solid solutions ( x ≤0.16) vary with different Y concentrations. The dielectric constant of the composites ( x >0.16) follows approximately the Lichteneker relation in a wide temperature range.