Structure stability and microwave dielectric properties of double perovskite ceramics – Ba2Mg1−xCaxWO6 (0.0 ≤ x ≤ 0.15)

The structure stability of double perovskite ceramics – Ba₂Mg_1?xCa_xWO₆ (0.0 ≤ x ≤ 0.15) has been studied by X-ray powder diffraction (XRD), scanning electron microscopy (SEM) and Raman spectrometry in this paper. The microwave dielectric properties of the ceramics were studied with a network analyzer at the frequency of about 8–11 GHz. The results show that small amount of Ca substitution for Mg increases the Mg/CaO bond strength, and hence the stability of the double perovskite. But it cannot completely suppress the decomposition of Ba₂Mg_1?xCa_xWO₆ at high temperature. Although space group Fm?3m is adopted for all compositions, nonrandom distribution of Ca²⁺ and Mg²⁺ on 4b-site within the short range scale is observed due to their large cation size difference. Small level doping of Ca (x ≤ 0.1) increases the dielectric permittivity monotonically, but does not affect the Q × f value greatly. As expected, the substitution of Ca tuned the temperature coefficient of resonant frequency (τ_f value) from negative to positive value. Excellent combined microwave dielectric properties with ?_r = 20.8, Q × f = 120,729 GHz, and τ_f = 0 ppm/°C could be obtained for x = 0.1 composition. However the Q × f value degrades considerably when the sample was stored under ambient conditions for a long time.     

Phase evolution and chemical durability of Zr1-xNd xO2-x/2 (0 ≤ x ≤ 1) ceramics

A series of Zr_1-xNd _xO_2-x/2 (0 ≤ x ≤ 1) ceramics was prepared by solid-state reaction method. The effects of Nd content on the phase evolution were investigated. The chemical durability of resulting waste forms was also examined. The results show that the ceramics with x < 0.1 show monoclinic and cubic zirconia phase, with 0.2 ≤ x < 0.4 exhibit a single cubic phase, with 0.4 ≤ x ≤ 0.6 exhibit a single pyrochlore phase, with 0.6 < x < 0.8 exhibit a single cubic phase and remain cubic phases and hexagonal Nd₂O₃ when 0.8 ≤ x ≤ 1. The unit cell parameters of the Nd-doped zirconia samples increase as the Nd content increases. Moreover, the normalized element release rates of Nd element in Nd-doped zirconia ceramics firstly decrease with leaching time and almost no change after 21 days (∼0⁻⁶ g m⁻² d⁻¹), demonstrating its good chemical durability.     

Frequency and temperature dependent electrical properties of Ni0.7Zn0.3CrxFe2−xO4 (0 ≤ x ≤ 0.5)

Series of the ferrite samples with a chemical formula Ni_0.7Zn_0.3Cr_xFe_2?xO₄ (x = 0.0–0.5) were prepared by a sol–gel auto-combustion method and annealed at 600 °C for 4 h. The prepared samples have the cubic spinel structure with no impurity phase. As the Cr³⁺ content x increases, the unit cell dimensions decrease with an increase in Cr³⁺ content x. The crystallite size is decreases from 37 nm to 21 nm as the Cr³⁺ content increases from x = 0.0 to 0.5. Resistivity increases whereas dielectric constant decreases with an increase in Cr³⁺ content x. Maxima in the dielectric loss tangent versus frequency appear when the frequency of the hopping charge carriers coincides with the frequency of the applied alternating field. Dielectric constant and dielectric loss tangent increases with increase in temperature. Saturation magnetization of sintered samples showed higher values as compared to as-prepared sample. Curie temperature deduced from AC susceptibility data decreases with increasing x.     

Thermal expansion and thermal conductivity of SmxZr1−xO2−x/2 (0.1 ≤ x ≤ 0.5) ceramics

A study was conducted of the effect of additions of samarium oxide on the thermal expansion and thermal conductivity of zirconium oxide for thermal barrier coatings. Sm_xZr_1?xO_2?x/2 (0.1 ≤ x ≤ 0.5) ceramic powders synthesized with a chemical-coprecipitation and calcination method were sintered at 1873 K for 15 h. Structures of the synthesized powders and sintered ceramics were identified by X-ray diffractometer. The morphologies of ceramic powders were observed by transmission electron microscope. The thermal expansion coefficients and thermal diffusion coefficients of Sm_xZr_1?xO_2?x/2 ceramics were studied with a high-temperature dilatometer and a laser flash diffusivity technique from room temperature to 1673 K. The thermal conductivity was calculated from thermal diffusivity, density and specific heat of bulk ceramics. Sm_0.1Zr_0.9O_1.95 ceramics consists of both monoclinic and tetragonal structures. However, Sm_0.2Zr_0.8O_1.9 and Sm_0.3Zr_0.7O_1.85 ceramics only exhibit a defect fluorite structure. Sm_0.4Zr_0.6O_1.8 and Sm_0.5Zr_0.5O_1.75 ceramics have a pyrochlore-type lattice. With the increase of Sm₂O₃ content, the linear thermal expansion of Sm_xZr_1?xO_2?x/2 ceramics increases except for Sm_0.1Zr_0.9O_1.95. The thermal conductivities of Sm_xZr_1?xO_2?x/2 ceramics ranged from 1.41 at 873 K to 1.86 W m^?1 K^?1 at room temperature in a test temperature range of room temperature to 1673 K, and the results can be explained by phonon scattering mechanism.     

Structure and microwave dielectric characteristics of Sr2[Ti1−x(Al0.5Nb0.5)x]O4 (x ≤ 0.50) ceramics

Sr₂[Ti_1−x(Al_0.5Nb_0.5)_x]O₄ (x = 0, 0.10, 0.25, 0.30, 0.5) ceramics were synthesized by a standard solid-state reaction process. Sr₂[Ti_1−x(Al_0.5Nb_0.5)_x]O₄ solid solutions with tetragonal Ruddlesdon-Popper (R-P) structure in space group I4/mmm were obtained within x ≤ 0.50, and only minor amount (1-2 wt%) of Sr₃Ti₂O₇ secondary phase was detected for the compositions x ≥ 0.25. The temperature coefficient of resonant frequency τ_f of Sr₂[Ti_1−x(Al_0.5Nb_0.5)_x]O₄ ceramics was significantly improved from 132 to 14 ppm/°C correlated with the increase in degree of covalency (%) with increasing x. The dielectric constant ɛ_r decreased linearly with increasing x, while high Qf value was maintained though it decreased firstly. The variation tendency of Qf value was dependent on the trend of packing fraction combined with the microstructure. Good combination of microwave dielectric properties was achieved for x = 0.50: ɛ_r = 25.1, Qf = 77 580 GHz, τ_f = 14 ppm/°C. The present ceramics could be expected as new candidates of ultra-high Q microwave dielectric materials without noble element such as Ta.     

New high Q microwave dielectric ceramics with rock salt structures: (1 − x)Li2TiO3 + xMgO system (0 ≤ x ≤ 0.5)

The structural evolution and microwave dielectric properties of (1 ? x)Li₂TiO₃ + xMgO system (0 ≤ x ≤ 0.5) have been investigated in this paper. The ordering degree decreased with the increase of MgO content. The microcracks and cleavage on (0 0 1) due to the weak Li–O bonds disappeared with the increase of MgO content. The dielectric constant and temperature coefficient of resonant frequency decreased with the increase of MgO content. The Q × f value increased with x up to x = 0.2 and then decreases with the further increase of x. An excellent combined microwave dielectric properties could be obtained when x = 0.24, ?_r = 19.2, Q × f = 106,226 GHz and τ_f = 3.56 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.     

Lattice structure and microwave dielectric properties of La[Al1−x(Mg0.5Ti0.5)x]O3 (x = 0-0.2)-based ceramics

La[Al_1−x(Mg_0.5Ti_0.5)_x]O₃ (LAMT, x = 0-0.2) ceramics were synthesized by the conventional solid-state reaction method and formed a solid solution. The pure solid solutions were recorded by X-ray diffraction (XRD) in every range. Relative permittivity (ε_r) and structural stability were greatly affected because the Al³⁺ site was replaced by [Mg_0.5Ti_0.5]³⁺. The total ionic polarizability gradually increased with x, and ε_r gradually increased. The trend of τ_f is due to the change in structural stability. The variation in Q × f value increased firstly and then decreased due to the change in the symmetric stretching mode of Al/MgTi–O. The optimum microwave dielectric properties of LAMT were obtained at x of 0.1 after sintering at 1650°C for 5 hours, and ε_r = 24.9, Q × f = 79 956 GHz, and τ_f = −33 ppm/°C. The CaTiO₃ have a large positive τ_f (+800 ppm/°C), thus, the τ_f achieved near zero when CaTiO₃ and LAMT (x = 0.1) ceramics were mixed with a certain molar mass, and the optimum microwave dielectric properties of 0.65CaTiO₃–0.35LaAl_0.9(Mg_0.5Ti_0.5)_0.1O₃ were as follows: ε_r = 44.6, Q × f = 32 057 GHz, and τ_f = +2 ppm/°C.     

Preparation and microwave dielectric properties of BaLi1+xF3+x (x = 0–0.01) ceramics

BaLi_1+xF_3+x (x = 0–0.01) were successfully mechanosynthesized by a simple ball-milling process. The effects of excessive LiF and sintering method and/or annealing atmosphere on its sintering behavior, microstructure, and microwave dielectric properties have been investigated in this paper. The mechanosynthesized powder can be densified with relative densities of ∼95 % after sintering at 750–800 °C/2 h in N₂. The obtained ceramics exhibit excellent optimized microwave dielectric properties with ε_r of ∼11.46 ± 0.06, Q×f values of 83175 ± 1839 GHz and τ_f of ∼ − 70 ± 3 ppm/°C at the x = 0.006 composition. Its Q×f value could be improved to 94603 ± 2037 GHz) by post-annealing in N₂ after post annealing at 700 °C/2 h. The Q×f value could be further improved to (120,098 ± 2344 GHz) by hot-pressed sintering (HPS). Sintering in the ambient atmosphere or O₂ leads to lower Q×f values than those of the counterparts sintered in N₂ due to the introduction of F-vacancies by oxidation_, while little variation in ε_r andτ_f.     

Synthesis and negative thermal expansion properties of solid solutions Yb2−xLaxW3O12 (0 ≤ x ≤ 2)

A new series of rare earth solid solutions Yb_2?xLa_xW₃O₁₂ were successfully synthesized by the solid-state method. Effects of substituted ion lanthanum on the microstructures and thermal expansion properties in the resulting Yb_2?xLa_xW₃O₁₂ ceramics were investigated by X-ray diffraction (XRD), thermogravimetric analyzer (TGA), field emission scanning electron microscope (FESEM) and thermal mechanical analyzer (TMA). Results indicate that the structural phase transition of the Yb_2?xLa_xW₃O₁₂ changes from orthorhombic to monoclinic with increasing substituted content of lanthanum. The pure phases can form in the composition range of 0 ≤ x < 0.5 with orthorhombic structure and 1.5 < x ≤ 2 with monoclinic one. High lanthanum content leads to a low hygroscopicity of Yb_2?xLa_xW₃O₁₂. Negative thermal coefficients of the Yb_2?xLa_xW₃O₁₂ (0 ≤ x ≤ 2) also vary from ?7.78 × 10^?6 K^?1 to 2.06 × 10^?6 K^?1 with increasing substituted content of lanthanum.     

Crystal structure,densification, and microwave dielectric properties of Li3Mg2(Nb(1−x)Mox)O6+x/2 (0 ≤ x ≤ 0.08) ceramics

A novel system Li₃Mg₂(Nb_(1−x)Mo_x)O_6+x/2 (0 ≤ x ≤ 0.08) microwave dielectric ceramics were fabricated by the solid-state method. The charge compensation of Mo⁶⁺ ions substitution for Nb⁵⁺ ions was performed by introducing oxygen ions. The X-ray diffraction patterns and Rietveld refinements indicated Li₃Mg₂(Nb_(1−x)Mo_x)O_6+x/2 ceramics with single phase and orthorhombic structure. Micro-structure and density confirmed that the grain of Li₃Mg₂(Nb_(1-x)Mo_x)O_6+x/2 ceramics grew well. In addition, the permittivity of Li₃Mg₂(Nb_(1−x)Mo_x)O_6+x/2 ceramics with the same trend as density decreased slightly with increasing Mo⁶⁺ ions content. However, the Q*f and τ_f were obviously improved with an appropriate amount of Mo⁶⁺ ions. When x ≤ 0.04, the Q*f was closely related to the bond valence of samples, while when x ≥ 0.06, the Q*f was closely related to the density of samples. The variations of τ_f and oxygen octahedral distortion were the opposite. In conclusions, the Li₃Mg₂(Nb_0.98Mo_0.02)O_6.01 ceramic sintered at 1200°C for 6 hours exhibited outstanding properties: ε_r ~ 15.18, Q*f ~ 116 266 GHz, τ_f ~ −15.71 ppm/^oC.     

Impact of Mg-Zr substitution on the magnetic and microwave absorption properties of BaFe12-2xMgxZrxO19 (0.25 ≤ x ≤ 1.5)

In this study, magnesium-zirconium–substituted M-type barium hexaferrites BaFe_12-2xMg+_xZr_xO₁₉ (BFMZO, 0.25 ≤ x ≤ 1.5) nanoparticles were successfully synthesized by sol-gel autocombustion technique. On one hand, the effects of Mg-Zr substitution concentration on the magnetic features of doped magnetic nanoparticles were investigated which showed that increasing the doping concentration causes the saturation magnetization to decrease. On the other hand, the influence of the different layer thicknesses (2, 3, and 4 mm) of BFMZO on the microwave absorption was investigated in X-band frequencies (8-12 GHz). Absorption results showed that increasing the film thickness from 2 to 3 mm causes microwave absorption to increase. Moreover, the morphological study reveals that aggregation percentage decreased when the substitution concentration increased. Therefore, size, magnetic, and absorption properties are tunable by substitution concentration.     

Novel scheelite-type [Ca0.55(Nd1-xBix)0.3]MoO4 (0.2 ≤ x ≤ 0.95) microwave dielectric ceramics with low sintering temperature

Novel scheelite-type [Ca_0.55(Nd_1-xBi_x)_0.3]MoO₄ (0.2 ≤ x ≤ 0.95) ceramics were prepared using the solid-state reaction method. According to the X-ray diffraction data, a solid solution was formed in 0.2 ≤ x ≤ 0.95 and all the samples belong to pure scheelite phase with the tetragonal structure. As revealed by Raman spectroscopy, the number of vibrational modes decreased with the increase in x value, which further indicated that Bi³⁺ ions occupied A-site of scheelite structure. As the x value increased, the sintering temperature decreased from 740°C to 660°C; the permittivity increased from 12.6 to 20.3; the Qf value first decreased slightly and gradually remained stable. Based on the infrared reflectivity spectrum analysis, the calculated permittivity derived from the fitted data shared the same trend with the measured value. The [Ca_0.55(Nd_0.05Bi_0.95)_0.3]MoO₄ ceramic sintered at 660 °C attained a near-zero value temperature coefficient ~τ_f (−7.1 ppm/°C) and showed excellent microwave dielectric properties with a ɛ_r ~ 20.3 and a Qf ~ 33 860 GHz, making this system a promising candidate in the ultralow temperature cofired ceramic (ULTCC) technology.     

Phase composition,crystal structure and microwave dielectric properties of Mg2−xCuxSiO4 ceramics

In this work, the Mg_2-xCu_xSiO₄(x = 0–0.40) microwave dielectric ceramics were prepared using solid-state reaction method. Compared with the Mg₂SiO₄ sample, the Cu-substituted Mg samples could be sintered at a lower temperature. The Mg_2?xCu_xSiO₄ ceramics exhibit the composite phases of Mg₂SiO₄ and a small quantity of MgSiO₃. The Cu²⁺ ion presented a solid solution with the Mg₂SiO₄ phase and preferentially occupy Mg(1) site. The distortion of MgO₆ octahedron was modified by Cu²⁺ ions, resulting in a positive change in the temperature coefficient of resonance frequency (τ_f) values. Excellent microwave dielectric properties of ε_r = 6.35, high Qf of ～ 188,500 GHz and near zero τ_f = ?2.0 ppm/°C were achieved at x = 0.08 under sintering at 1250 °C for 4 h. Thus, the fabricated ceramics were considered as possible candidates for millimeter-wave device applications.     

Li2+xZrO3Fx (0 ≤ x ≤1.25): A new high-Q × f and temperature-stable microwave dielectric ceramic system for LTCC applications

Here we report a new high-Q × f and temperature-stable oxyfluoride microwave dielectric ceramic system of Li_2+xZrO₃F_x (0 ≤ x ≤ 1.25) sintered at low temperatures (i.e., ≤950°C). The sintering characteristics, phase assemblage, microstructures, and microwave dielectric properties (MDPs) of the Li_2+xZrO₃F_x specimens were studied. The chemical bond theory calculations were employed to analyze the compositional dependence of the MDPs in the Li_2+xZrO₃F_x ceramic system. The optimal MDPs of ε_r = 15.8, Q × f = 65 100 GHz, and τ_f = 1.2 ppm/°C were achieved in the sample with x = 1. Besides, the ceramic samples exhibited high chemical compatibility with Ag electrodes. Therefore, the novel ceramic system of Li_2+xZrO₃F_x is confirmed to be a promising candidate as a low-temperature co-fired ceramic material.     

Crystal structure and mixed ionic–electronic conductivity of La1−xCaxMnO3 (0 ≤ x ≤ 0.8) produced by mechanosynthesis

The aim of this work was to study the relationship between the crystalline structure, the mixed ionic–electronic conductivity and the calcium content in calcium-doped lanthanum manganites (CLM, La_1?xCa_xMnO₃) synthesized by reactive ball milling. Mechanosynthesis was employed to produce nanocrystalline CLM with varying calcium content (x = 0–0.8 in increments of 0.1). Powders of Mn₂O₃, La₂O₃ and CaO mixed in the stoichiometric ratio were used as raw materials. The mechanosynthesis was carried out using a high-energy shaker mixer/mill. X-ray powder diffraction and Rietveld refinement were used to determine the crystalline structure as a function of calcium content. The four-point probe resistivity test was used to measure the electrical resistivity of the compacted and sintered powders using a DC milli-ohm meter. The results showed that the substitution of the La³⁺ ion by the Ca²⁺ ion during mechanosynthesis only changed the lattice parameters but not the orthorhombic Pnma structure. The mixed ionic–electronic conductivity increased with the Ca²⁺ content. The best conductivity was observed for the composition of La_0.2Ca_0.8MnO₃.     

Phase structure,band gap and microwave dielectric properties of Ba8Ti3Nb4−xSbxO24 ceramics

High dielectric constant and low loss ceramics in the Ba₈Ti₃Nb_4?xSb_xO₂₄ (x=0–2) system were prepared by conventional solid-state ceramic route. As x increased from 0 to 1.5, a single phase with hexagonal 8H perovskite structure was formed and the band gap values increased from 3.38 to 3.47 eV. However, the Sb₂O₃ secondary phase was detected as the x reached 2. The optimum sintering temperature was reduced from 1460 to 1380 °C, the quality factors (Q×f) were effectively enhanced from 22,900 to 38,000 GHz and τ_f was significantly lowered from 110 ppm/°C to 2 ppm/°C, whereas the dielectric constant decreased from 49 to 35. A good combined microwave dielectric properties with ε_r=37.5, Q×f=38,000 GHz, τ_f=15 ppm/°C were obtained for x=1.5.     

Phase transitions and microwave dielectric behaviors of the (Bi1−xLi0.5xY0.5x)(V1−xMox)O4 ceramics

Microwave dielectric ceramics with intrinsic low sintering temperatures are potential candidates for low temperature co-fired ceramics technology. In the present work, the (Li_0.5Y_0.5)MoO₄ ceramic with tetragonal scheelite structures was selected to improve microwave dielectric properties of BiVO₄ ceramics. As proved by X-ray diffraction (XRD) results, scheelite structured solid-solution ceramics were formed with x value ≤0.1 in the (Bi_1−xLi_0.5xY_0.5x)(V_1−xMo_x)O₄. In situ XRD results further confirmed that the addition of (Li_0.5Y_0.5)MoO₄ also lowered transition temperature from distorted monoclinic to tetragonal scheelite structure. When x value increased further, zircon phase was detected by XRD. Room and high-temperature Raman spectra also supported the XRD results. Differences of thermal expansion coefficients of both monoclinic and tetragonal scheelite phases lead to an abnormality at phase transition temperature. Good microwave dielectric properties with permittivity above 70 and Qf (Q = quality factor = 1/dielectric loss and f = frequency) value above 8000 GHz were obtained in the (Bi_1−xLi_0.5xY_0.5x)(V_1−xMo_x)O₄ solid-solution ceramics with x value ≤0.1 sintered below 800°C. However, permittivity peak values at phase transition temperatures lead to large positive or negative temperature coefficient of resonant frequency, and this needs to be modified via composite technologies in the future.     

Structure and microwave dielectric properties of Ba1−xSrxMg2V2O8 ceramics

The Ba_1−xSr_xMg₂V₂O₈ (0≤x≤0.4) microwave dielectric ceramics were fabricated by a standard solid-state reaction method. The formation of a continuous solid solution within the whole composition range was identified. The ceramic samples could be well densified in the temperature range of 885–975 °C in air for 4 h. The permittivity ε_r was found to increase with increasing ionic polarizabilities. The Q×f values were believed to be closely related with packing fraction and grain refinement. The Sr²⁺ substitution contributed to a monotonous increase of the A-site bond valence, such that the τ_f value experienced a considerable variation from negative to positive values. The optimum microwave dielectric properties of an ε_r of 13.3, a high Qxf of 86,640 GHz (9.6 Hz) and a near-zero τ_f of −6 ppm/°C could be yielded in the x=0.15 sample when sintered at 915 °C for 4 h.     

Low temperature sintering and microwave dielectric properties of (Mg3 − xZnx)(VO4)2 ceramics

This paper describes the effects of Zn substitution for Mg on the microwave dielectric properties of (Mg_3 − xZn_x)(VO₄)₂ ceramics. As for the XRPD patterns of (Mg_3 − xZn_x)(VO₄)₂ ceramics sintered at the sintering temperature of 750 °C, no secondary phase was detected over the whole composition range. However, in the case of the sample sintered at 850 °C, the Zn₄V₂O₉ and Zn₂V₂O₇ compounds were identified by using XRPD; this result was attributed to the decomposition of Zn₃(VO₄)₂ phase. From crystal structure analysis, it was found that the atomic distances of M(1)O (M = Mg and Zn) and M(2)O in MO₆ octahedra increased, though that of VO in VO₄ tetrahedron decreased. Moreover, the slight tilting of M(2)O₆ octahedron was observed by the Zn substitution. As for the covalency of cation–oxygen bond, the covalency of MO bond in M(1)O₆ and M(2)O₆ octahedra decreased because of the increase in the atomic distance of MO, whereas that of VO increased with increasing the Zn addition. However, as a result, the slight decrease in the covalency of cation–oxygen bond was recognized because the variation in the covalency of MO bond is predominant in this crystal structure. The dielectric constants of the samples range from 4.4 to 11.1. The decrease in the covalency may be related to the difference in the dielectric constant of each composition. The maximum Q · f value of bulk densities is effected by varying the chemical composition of (Mg_3 − xZn_x)(VO₄)₂ ceramics and it shifts toward lower sintering temperature with an increase in x within the temperature region of 800–1050 °C. The temperature coefficient of resonant frequency (τ_f) of the samples decreased with increasing of Zn, and then a variation in τ_f value was attributed to the tilting of M(2)O₆ octahedron caused by Zn substitution for Mg.