Effects of Postdensification Annealing upon Microstructures and Microwave Dielectric Characteristics in Ba((Co0.6−x/2Zn0.4−x/2Mgx)1/3Nb2/3)O3 Ceramics

Effects of postdensification annealing upon microstructures and microwave dielectric characteristics in Ba((Co_0.6?x/2Zn_0.4?x/2Mg_x)_1/3Nb_2/3)O₃ (x = 0, 0.1, 0.2, and 0.3) complex perovskite ceramics have been investigated. Long‐time annealing at temperatures below the order–disorder transition temperature enhances the cation ordering degree and promotes the ordering domain growth. The most significant improvement of Qf value is obtained together with the suppressed temperature coefficient of resonant frequency in the samples annealed at 1400°C for 12 h, while the dielectric constant decreases slightly. The Qf value of ceramics annealed at 1400°C mainly attributes to the enhanced cation ordering degree, because their low‐energy domain boundaries are not detrimental to the Qf value. As the annealing temperature increases close to the transition temperature, coarse ordering domains with high‐energy boundaries are formed, and then the Qf value steadily decreases because of the inferior domain structure, even the cation ordering degree increases. The microwave dielectric characteristics of Ba((Co_0.6?x/2Zn_0.4?x/2Mg_x)_1/3Nb_2/3)O₃ ceramics are affected by the common function of ordering degree and domain structure. The best combination of microwave dielectric characteristics is obtained in the composition of x = 0.3 after annealing at 1400°C for 12 h: ε_r = 33.2, Qf = 117 200 GHz, and τ_f = 8.6 ppm/°C.     

Abnormal variation of microwave dielectric properties in A/B site co-substituted (Ca1−0.3xLa0.2x)[(Mg1/3Ta2/3)1−xTix]O3 complex perovskite ceramics

A/B site co-substituted (Ca_1?0.3xLa_0.2x)[(Mg_1/3Ta_2/3)_1?xTi_x]O₃ ceramics (0.1 ≤ x ≤ 0.5) were prepared by solid state reaction and the structures, microstructures and dielectric properties were investigated. B site 1:2 cation ordering and oxygen octahedra tilting lead to monoclinic symmetry with space group P2₁/c for x = 0.1. For x above 0.1, the ordering was destroyed and the crystal structure became orthorhombic with space group Pbnm. The B site 1:2 cation ordering tended to be destroyed to form 1:1 ordering by the A site La³⁺ substitution. The dielectric constant increased linearly with increasing content of Ti⁴⁺ as the increasing second Jahn–Teller distortion enhanced the B site cation rattling. The temperature coefficient of resonant frequency and Qf values showed abnormal variations, which were refined to be caused by the increasing A site cation vacancy and diffused distribution of small size ordering domains respectively. Good combination of microwave dielectric properties was obtained at x = 0.5, where ?_r = 48, Qf = 21,000 GHz and τ_f = 2.2 ppm/°C.     

Effects of Mg Substitution on Order/disorder Transition,Microstructure, and Microwave Dielectric Characteristics of Ba((Co0.6Zn0.4)1/3Nb2/3)O3 Complex Perovskite Ceramics

Effects of Mg substitution on order/disorder transition, microstructure, and microwave dielectric characteristics of Ba((Co_0.6Zn_0.4)_1/3Nb_2/3)O₃ complex perovskite ceramics have been investigated. The ordered complex perovskite solid solutions are obtained in Ba((Co_0.6?x/2Zn_0.4?x/2Mg_x)_1/3Nb_2/3)O₃ ceramics (x = 0, 0.1, 0.2, and 0.3), and the ordering degree in the as‐sintered dense ceramics increases with increasing Mg‐substitution amount. The significantly improved Qf value is obtained in the present ceramics with increasing x, whereas the dielectric constant decreases slightly together with some increase of temperature coefficient of resonant frequency. The best combination of microwave dielectric characteristics is obtained in the composition of x = 0.3: ε_r = 33.7, Qf = 93 800 GHz, and τ_f = 9.6 ppm/°C. In the Mg‐substituted compositions, clear domain boundaries are obtained and the domain size increases as x increases, the highest Qf value is obtained when the domain size is about 40–60 nm in the ceramics with x = 0.3. The increased ordering degree and the fine ordering domain structure are considered to primarily contribute to the significant increase of Qf value in the Mg‐substituted Ba((Co_0.6Zn_0.4)_1/3Nb_2/3)O₃ complex perovskite ceramics.     

Impedance spectroscopy,B-site cation ordering and structure–property relations of (1 − x) La[Al0.9(Mg0.5Ti0.5)0.1]O3–x CaTiO3 ceramics for 5G dielectric waveguide filters

Dense (1 ? x) La[Al_0.9(Mg_0.5Ti_0.5)_0.1]O₃–x CaTiO₃ ceramics were synthesized via solid-state reaction. The crystal structure and microwave dielectric properties of the ceramics were systematically investigated. Rietveld refinement revealed that when x ≤ 0.2, the ceramics had a rhombohedral structure with an R-3c space group. When x ≥ 0.5, the ceramics had an orthorhombic structure with a Pbnm space group. Selected area electron diffraction and Raman spectroscopy analyses proved that the microwave dielectric ceramics had a B-site order, which accounted for the great improvement in microwave dielectric properties. The content of oxygen vacancies was identified through X-ray photoelectron spectroscopy, and the change rule of Q × f was closely related to oxygen vacancy content. The perturbation of A-site cations had an important influence on dielectric constant. Specifically, with the increase in Ti⁴⁺ content, the perturbation effect of the A-site cations was enhanced and dielectric constant increased. When x = 0.65, the temperature coefficient of resonant frequency of the (1 ? x) La[Al_0.9(Mg_0.5Ti_0.5)_0.1]O₃–x CaTiO₃ microwave dielectric ceramics was near zero. The optimal microwave dielectric properties of 0.35LaAl_0.9(Mg_0.5Ti_0.5)_0.1O₃–0.65CaTiO₃ were ε_r = 44.6, Q × f = 32,057 GHz, and τ_f = +2 ppm/°C.     

Enhancement of structural and microwave properties of Zn2+ ion-substituted Li2MgSiO4 ceramics for LTCC applications

In this study, Zn²⁺-substituted Li₂MgSiO₄ ceramics (Li₂(Mg_1-xZn_x)SiO₄, x = 0.00, 0.05, 0.10, 0.15, and 0.20) were synthesized using a traditional solid-state method. A fixed amount of LiF sintering aid (1.5 wt%) was added to the ceramics for decreasing the sintering temperature and adjusting their microwave dielectric properties. X-ray diffraction (XRD) results revealed no secondary phases, and scanning electron microscopy (SEM) data suggest that the Zn²⁺ ion substitution increased the size and uniformity of the grains, thereby affecting the densification of the prepared ceramics. The maximum bulk density (2.94 g/cm³) was found in a Zn²⁺ ion-substituted ceramic with x = 0.10 at a relative density of 94.2% (compared with the XRD theoretical density). Excellent microwave dielectric properties (ε_r = 6.28, Q × f = 50400 GHz, and τ_f = ?145 ppm/°C) can also be obtained at this zirconium content. We believe that the developed ceramics are promising for use as antenna substrates or transmit/receive modules in low-temperature co-firing ceramic applications.     

Effects of Magnesium–Tungsten co-substitution on crystal structure and microwave dielectric properties of CaTi1-x(Mg1/2W1/2)xO3 ceramics

CaTi_1-x (Mg_1/2W_1/2)_xO₃ (x = 0, 0.02, 0.04, 0.06, 0.08) dielectric ceramics were synthesized via the traditional solid-state reaction method. Crystal structure and microwave dielectric properties of CaTi_1-x (Mg_1/2W_1/2)_xO₃ system were systematically investigated based on chemistry bond theory (P–V-L theory) for the first time. The pure perovskite phase was obtained for all doped samples, as confirmed through the XRD and Rietveld refinement results. The lattice characteristics were closely related to the microwave dielectric properties. The bond ionicity, lattice energy, and bond energy affected the dielectric constant, quality factor, and temperature stability of the ceramic material. Through the use of (Mg_1/2W_1/2)⁴⁺ doped on B-site, the CaTi_1-x (Mg_1/2W_1/2)_xO₃ system can maintain a high dielectric constant (ε_r > 100) while effectively reducing the τ_f value from 800 ppm/^°C to less than 300 ppm/^°C and improving the Q × f value to 9650 GHz (at 3.76 GHz).     

Structure and microwave dielectric properties of La(2−x)/3Nax(Mg1/2W1/2)O3

The structure evolution, sintering behavior and microwave dielectric properties of La_(2−x)/3Na_x(Mg_1/2W_1/2)O₃ (x = 0–0.5) were investigated in this paper. The X-ray diffraction (XRD) results show that all samples exhibit single phase, and the structure changed from orthorhombic when 0 ≤ x < 0.3 to monoclinic phase when 0.3 ≤ x ≤ 0.5. The size and ordering degree of A/B-site domains decrease with the increase in x value. The sintering temperature of the Na-doped samples increased compared to the pure La_2/3(Mg_1/2W_1/2)O₃ (LMW) due to the estimated decrease in the concentration of A-site vacancies. The addition of Na⁺ ion does not affect the dielectric permittivity greatly. The Q × f value decreases with the increase in x value, although the estimated concentration of A-site vacancies decreases with increasing x, which may be ascribed to the decrease of A/B-site ordering and domain size with the increase in x. The temperature coefficient of resonant frequency changed from negative values into positive values with the increase in x value.     

Effect of nonstoichiometry on the structure and microwave dielectric properties of Ba(Co1/3Nb2/3)O3 ceramics

The effect of B-site cation deficiency on the structure and microwave dielectric properties of Ba(Co_1/3Nb_2/3)O₃ (BCN) was investigated. Stoichiometric and co-deficient compositions based on Ba(Co_1/3−xNb_2/3)O₃ [x = 0.0, 0.01, 0.02, 0.03 and 0.04] were prepared using the conventional mixed oxide route. Small amounts of V₂O₅ (0.1 wt%) were added to promote densification. The dielectric loss is very sensitive to the composition; it was found that co-deficiency degraded the microwave dielectric properties. The stoichiometric formulation (x = 0) exhibited the best microwave properties. The improvements in the microwave dielectric properties were achieved by increasing the degree of 1:2 cation ordering. The highly ordered, stoichiometric BCN ceramics showed a relative permittivity (ɛ_r) of 32, quality factor (Q × f) of 66,500 GHz and a negative temperature coefficient of resonant frequency (τ_f) of −10 ppm/°C at 4 GHz.     

Crystal structure and microwave dielectric properties of Li2Mg0.6− xCoxZn0.4SiO4 ceramic for LTCC applications

In this work, Li₂Mg_0.6−xCo_xZn_0.4SiO₄ ceramics (x = 0–0.4) added with 3 wt% Li₂O–B₂O₃–Bi₂O₃–SiO₂ (LBBS) glass were synthesised using the solid-state reaction method. The effects of substituting Co²⁺ for Mg²⁺in Li₂Mg_0.6−xCo_xZn_0.4SiO₄ ceramics on crystal structure, microstructure, densification, crystallisation and microwave dielectric properties were investigated. X-ray diffraction patterns showed that monoclinic Li₂MgSiO₄, monoclinic Li₂ZnSiO₄ and orthorhombic Li₂CoSiO₄ formed finite solid solution in Li₂Mg_0.6−xCo_xZn_0.4SiO₄ ceramics. Clear grain boundaries were observed via scanning electron microscopy. The substitution of Co²⁺ for Mg²⁺ increased grain size, densification, crystallinity degree and dielectric constant; it also reduced the dielectric loss of the ceramics to a certain extent. The absolute values of τ_f were positively related to the crystallinity degree. Li₂Mg_0.55Co_0.05Zn_0.4SiO₄ ceramic added with 3 wt% LBBS and sintered at 900 °C exhibited considerable microwave dielectric properties of ε_r = 5.8, Q × f = 47,518 GHz and τ_f = −74.8 ppm/°C. Therefore, the ceramic is considered a candidate low-temperature co-fired ceramic material for substrate and filter applications.     

New Antiferroelectric Solid Solution of Pb(Mg1/2W1/2)O3–Pb(Zn1/2W1/2)O3 as Dielectric Ceramics

A new solid solution of (1?x)Pb(Mg_1/2W_1/2)O₃–xPb(Zn_1/2W_1/2)O₃ has been prepared in the form of ceramics by solid‐state reaction with composition x up to 30%. It is found that with the substitution of Zn²⁺ for Mg²⁺ on the B site of the of complex perovskite structure the antiferroelectric (AFE) Curie temperature T_C of PMW increases from 40°C (x = 0) to 67°C (x = 30%), indicating an enhancement of antiferroelectric order, whereas, at the same time, the phase transition becomes more diffuse due to a higher degree of chemical inhomogeneity. X‐ray diffraction analysis indicates that the crystal structure adopts an orthorhombic space group (Pmcn) with a decrease in lattice parameter a, but an increase in b and c as the Zn²⁺ concentration increases. The low dielectric constant (~ 10²), low dielectric loss (tanδ ≈ 10^?3), linear‐field‐induced polarization, and significantly high breakdown field (~ 125 kV/cm) at room temperature make this family of dielectric materials a promising candidate for ceramic insulators.     

Microwave dielectric properties and cation distributions of Zn1-3xAl2+2xO4 ceramics with defect structures

The spinel-structured Zn_1-3xAl_2+2xO₄ (x = 0–0.2) ceramics having defective structures were synthesized using the molten salt method, and their microwave dielectric properties and cation distributions were assessed. The ²⁷Al solid-state nuclear magnetic resonance spectra of these ceramics demonstrate that they have an intermediate spinel structure in which the tetrahedral site occupancy increases from 0.03 to 0.64 as x increases. Moreover, crystal structure refinements suggest that cation vacancies are located at octahedral sites for x = 0.1 and 0.2. Based on these data, the introduction of cation vacancies at octahedral sites appears to enhance the preferential occupation of tetrahedral sites by Al³⁺. The ε_r of these ceramics slightly decreased from 8.5 to 8.2 with increasing x, while the Q·f value increased significantly, from 127,532 to 202,468 GHz, upon the introduction of cation vacancies. An intermediate spinel structure with preferential occupancy of tetrahedral sites by trivalent cations exhibits an enhanced Q·f value.     

Optical and Microwave Dielectric Properties of Zn‐Doped MgAl2O4 Transparent Ceramics Fabricated by Spark Plasma Sintering

(Mg_1?xZn_x)Al₂O₄ transparent ceramics were fabricated by spark plasma sintering technique at 1325°C for 10 min. A small mount of Zn²⁺ addition to MgAl₂O₄ ceramics was very effective to the performance improvement, while further increase in Zn‐doped content would give rise to the optical transmittance deterioration. The optical and microwave dielectric properties of MgAl₂O₄ transparent ceramics were improved by Zn substitution for Mg. The in‐line transmittance of the (Mg_1?xZn_x)Al₂O₄ (x = 0.02) ceramics can be as high as 70% at λ = 550 nm and 86.5% at λ = 2000 nm, respectively. The dielectric constant ε_r of (Mg_1?xZn_x)Al₂O₄ just varied from 8.32 to 8.54, however, the Q × f value increased significantly up to a maximal value of 66,000 GHz at x = 0.02. Moreover, the τ_f of (Mg_1?xZn_x)Al₂O₄ transparent ceramics changed from ?74 to ?65.5 ppm/°C. With the increasing of Zn‐doped content, the average grain size and the porosity increased, which was the primary reason for the change in optical and microwave dielectric properties.     

Crystal structures and microwave dielectric properties of low-firing Ca5Zn4-xMgxV6O24 ceramics

Ca₅Zn_4-xMg_xV₆O₂₄ (x?=?0–3) microwave dielectric ceramics with low sintering temperature were synthesized via the conventional solid-state reaction. Effects of the substitution of Mg²⁺ for Zn²⁺ on crystal structures and microwave dielectric properties were investigated. XRD and Rietveld refinement showed the solid solution single phase formed when 0?≤?x?≤?2, but a few ZnO was observed when x?=?3. Meanwhile, the lattice parameters were found to decrease monotonously with Mg content increasing. The vibration modes of Raman were confirmed and the relationship with microwave dielectric properties was analyzed. Appropriate substitution of Mg²⁺ improved the packing fraction, the cation ordering degree, and the Y-site bond valence, contributing to high Q×f and low | τ_f |. However, the ε_r reduced with the increasing content of Mg²⁺ due to the decrease of ion polarizability. Finally, the best microwave dielectric properties were achieved at x?=?2 with ε_r =?11.0, Q?×?f?=?66,365?GHz (at 10.0?GHz), and τ_f =??80.4?ppm/°C.     

Structure Stability and Microwave Dielectric Properties of (1 − x) Ba(Mg1/2W1/2) O3 + xBa(Y2/3W1/3)O3 Ceramics

The structure stabilities of double perovskite ceramics‐ (1 ? x) Ba(Mg_1/2W_1/2)O₃ + xBa(Y_2/3W_1/3)O₃ (0.01 ≤ x ≤ 0.4) have been studied by X‐ray powder diffraction (XRD), scanning electron microscopy (SEM), and Raman spectrometry in this study. The microwave dielectric properties of the ceramics were studied with a network analyzer at the frequency of about 8–11 GHz. The results showed that all the compounds exhibited face‐centered cubic perovskite structure. Part of Y³⁺ and W⁶⁺ cations occupied 4a‐site and the remaining Y³⁺ and Mg²⁺ distributed over 4b‐site, respectively, and kept the B‐site ratio 1:1 ordered. Local ordering of Y³⁺/Mg²⁺ on 4b‐site and Y³⁺/W⁶⁺ cations on 4a‐site within the short‐range scale could be observed with increasing Y‐doping content. The decomposition of the double perovskite compound at high temperature was successfully suppressed by doping with Y on B‐site. However, Ba₂Y_0.667WO₆ impurity phase appeared when x > 0.1. The optimized dielectric permittivity increased with the increase in Y doping. The optimized Q × f value was remarkably improved with small amount of Y doping (x ≤ 0.02) and reached a maximum value of about 160 000 GHz at x = 0.02 composition. Further increasing in Y doping led to the decrease in Q × f value. All compositions exhibited negative τ_f values. The absolute value of τ_f decreased with increasing Y‐doping content. Excellent combined microwave dielectric properties with ε_r = 20, Q × f = 160 000 GHz, and τ_f = ?21 ppm/°C could be obtained for x = 0.02 composition.     

Broadband dielectric spectroscopy of PbMg1/3Nb2/3O3–PbSc1/2Nb1/2O3 ceramics

Broadband dielectric spectroscopy results of various ordered and disordered (1 ? x)Pb(Mg_1/3Nb_2/3)O₃–(x)Pb(Sc_1/2Nb_1/2)O₃ (PMN–PSN) ceramics are investigated in the temperature range from 80 K to 300 K and frequency range from 20 Hz to 2 THz. Dielectric dispersion is very broad and in the ferroelectrics case (x = 1, 0.95) consists of two parts: low-frequency part caused by ferroelectric domains and higher frequency part caused by soft mode. The relaxational soft mode exhibits pronounced softening close to phase transition temperature, as it is typical for order–disorder phase transitions. By substituting Sc³⁺ by Mg²⁺ in PMN–PSN ceramics relaxation slows down, and for relaxors (x = 0.2) the most probable relaxation frequency decreases on cooling according to Vogel–Fulcher law.     

High-Qf value and temperature stable Zn2+-Mn4+ cooperated modified cordierite-based microwave and millimeter-wave dielectric ceramics

Cordierite-based dielectric ceramics with a lower dielectric constant would have significant application potential as dielectric resonator and filter materials for future ultra-low-latency 5G/6G millimeter-wave and terahertz communication. In this article, the phase structure, microstructure and microwave dielectric properties of Mg₂Al_4–2x(Mn_0.5Zn_0.5)_2xSi₅O₁₈ (0 ≤ x ≤ 0.3) ceramics are studied by crystal structure refinement, scanning electron microscope (SEM), the theory of complex chemical bonds and infrared reflectance spectrum. Meanwhile, complex double-ions coordinated substitution and two-phase complex methods were used to improve its Q×f value and adjust its temperature coefficient. The Q×f values of Mg₂Al_4–2x(Mn_0.5Zn_0.5)_2xSi₅O₁₈ single-phase ceramics are increased from 45,000 GHz@14.7 GHz (x = 0) to 150,500 GHz@14.5 GHz (x = 0.15) by replacing Al³⁺ with Zn²⁺-Mn⁴⁺. The positive frequency temperature coefficient additive TiO₂ is used to prepare the temperature stable Mg₂Al_3.7(Mn_0.5Zn_0.5)_0.3Si₅O₁₈-ywt%TiO₂ composite ceramic. The composite ceramic of Mg₂Al_3.7(Mn_0.5Zn_0.5)_0.3Si₅O₁₈-ywt%TiO₂ (8.7 wt% ≤ y ≤ 10.6 wt%) presents the near-zero frequency temperature coefficient at 1225 °C sintering temperature: ε_r = 5.68, Q×f = 58,040 GHz, τ_f = ?3.1 ppm/°C (y = 8.7 wt%) and ε_r = 5.82, Q×f = 47,020 GHz, τ_f = +2.4 ppm/°C (y = 10.6 wt%). These findings demonstrate promising application prospects for 5 G and future microwave and millimeter-wave wireless communication technologies.     

Microwave Dielectric Properties and Thermally Stimulated Depolarization Currents of (1−x)Ba(Mg1/3Nb2/3)O3–xBaSnO3 Solid Solutions

Microwave dielectric ceramics of (1?x)Ba(Mg_1/3Nb_2/3)O₃‐xBaSnO₃ [(1?x)BMN‐xBS] with high quality factors was synthesized by the solid‐state reaction method. The effects of BaSnO₃ additions (x = 0–0.2) on the sinterability, crystal structures, microwave dielectric properties, and microwave dielectric loss mechanisms of BMN were investigated systematically. The degree of 1:2 cation ordering was decreased with increasing Sn content and eventually faded away as x ≥ 0.1, where the low‐temperature relaxations disappeared coincidently through the thermally stimulated depolarization current technique. It was supposed to be the short‐range misplacements of the B‐site cations within the long‐range ordered structure. Meanwhile, the high‐temperature relaxations associated with the in‐grain oxygen vacancies were found in all the title compounds. Though the concentrations of oxygen vacancies of 0.8BMN‐0.2BS were higher than BMN, high Q × f values could also be obtained even in the absence of 1:2 cation ordering. Specifically, the excellent characteristics like ε_r = 29.02, Q × f = 90 000 GHz and τ_f = 6.3 ppm/°C were achieved in the specimens of x = 0.2 sintered at 1450°C.     

Correlations between structure and microwave dielectric properties of Co doped MgMoO4 ceramics

Mg_1-xCo_xMoO₄ (x = 0.01–0.15) ceramics were prepared by traditional solid-state methods. The phase composition, crystalline structure, micromorphology, and microwave dielectric properties of Mg_1-xCo_xMoO₄ ceramics were comprehensively studied. Mg_1-xCo_xMoO₄ ceramics present monoclinic wolframite structures from x = 0.01 to x = 0.15 with Co occupying the Mg-site. With the addition of Co²⁺, ε_r of Mg_1-xCo_xMoO₄ ceramics increase. Q × f is maximal at 5 mol% Co²⁺ content. The Mg_0.95Co_0.05MoO₄ ceramic exhibits an optimal microwave dielectric property: ε_r = 7, Q × f = 59247 GHz, τ_f = −68 ppm/°C. The Q × f values increase by 20% compared with the pure MgMoO₄ ceramics (~49149 GHz). Doping Co²⁺ effectively promotes the densification of ceramics and increases ε_r and Q × f. However, when the Co content exceeds 5 mol%, the decreased packing fraction and disorder distribution of ions contribute to the increase in dielectric losses. The correlations between Co²⁺ substitution and wolframite structure have been discussed by Raman spectroscopy, FT-IR spectroscopy and Rietveld refinement.     

Improvement of microwave dielectric properties for Ba(Ni1/3Nb2/3)O3 ceramics by Zr-substitution

Effects of Zr-substitution on the structure, microstructure and microwave dielectric properties of Ba(Ni_1/3Nb_2/3)O₃ ceramics have been investigated. A small amount of Zr-substitution facilitates the densification of Ba(Ni_1/3Nb_2/3)O₃ ceramics. Within x≤0.05, the densification temperature decreases with increasing x in Ba[(Ni_1/3Nb_2/3)_1−xZr_x]O₃, while it turns to increase for x>0.05. With increasing x, the grains become more homogeneous and closely contacted, and significantly increase in size for x=0.15–0.20. The B-site cations 1:2 ordering is destroyed by Zr-substitution, and only stabilizes for x≤0.04. B-site cations 1:1 ordering starts to form in x=0.04, and the 1:1 ordering degree first increases and then decreases with increasing x. Qf value decreases slightly in x=0.01 and then increases monotonously with x increasing from 0.02 to 0.20. The destroyed 1:2 ordering structure is responsible for the decreased Qf value in x=0.01, while the improved grain configuration dominates the increase of Qf value for x=0.02–0.20. The dielectric constant ε_r increases monotonously with increasing x, due to the higher polarizability of Zr ion than the average value of Ni/Nb ions. The temperature coefficient of resonant frequency τ_f shifts from negative to positive through zero with increasing x, which is ascribed to the highly positive τ_f value of the end member BaZrO₃. The significant improvement of microwave dielectric properties has been achieved for x=0.10, higher ε_r, higher Qf as well as near zero τ_f value have been obtained: ε_r=31.8, Qf=36,100 GHz, τ_f=7.8 ppm/°C.     

The structure evolution and lattice energy of spinel-structured Li(Mg0.5Ti0.5)xGa5−xO8 microwave dielectric ceramics

The microwave dielectric properties of spinel-structured Li(Mg_0.5Ti_0.5)_xGa_5−xO₈ (0 ≤ x ≤ 1) ceramics were researched together with their microstructures. The X-ray diffraction and Raman spectroscopic revealed that an ordered spinel structure in 1: 3 B-site ordering with space group P4₃32 was formed in the composition range of 0 = x ≤ 0.25, and a disordered spinel with space group Fd-3m was formed in 0.5 = x ≤ 1. All the ceramics were compact with uniform grain, clear grain boundaries and high relative density (ρ_relative ≥ 95 %). With the substitution of [Mg_0.5Ti_0.5]³⁺ for Ga³⁺ increased, the dielectric constant (ε_r) increased from 10.48 to 11.28, which was related to the increased molar ionic polarizability (α_theo/V_m) and B-site bond ionicity. The temperature coefficient of the resonant frequency (τ_f) slightly increased from −66.27 ppm/°C to −61.45 ppm/°C, due to the decrease of B-site bond valence. The Q × f value firstly decreased from 125,400 GHz to 50,381 GHz and then increased to 85,360 GHz, which was affected by the intrinsic loss analyzed by lattice energy. The optimal microwave dielectric properties were obtained for LiMg_0.5Ti_0.5Ga₄O₈ ceramic (x = 1) sintered at 1260 °C with ε_r = 11.28, Q × f = 85,360 GHz and τ_f = −61.45 ppm/°C.