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.     

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.     

A Novel Temperature-Compensated Microwave Dielectric (1−x)(Mg0.95Ni0.05)TiO3−xCa0.6La0.8/3TiO3 Ceramics System

The microstructure and microwave dielectric properties of a (1− x )(Mg_0.95Ni_0.05)TiO₃− x Ca_0.6La_0.8/3TiO₃ ceramics system have been investigated. The system was prepared using a conventional solid-state ceramic route. In order to produce a temperature-stable material, Ca_0.6La_0.8/3TiO₃ was added for a near-zero temperature coefficient (τ_f). With partial replacement of Mg²⁺ by Ni²⁺, the dielectric properties of the (1− x )(Mg_0.95Ni_0.05)TiO₃− x Ca_0.6La_0.8/3TiO₃ ceramics can be promoted. The microwave dielectric properties are strongly correlated with the sintering temperature and the composition. An excellent Q × f value of 118,000 GHz can be obtained for the system with x =0.9 at 1325°C. For practical application, a dielectric constant (ɛ_r) of 24.61, a Q × f value of 102,000 GHz, and a temperature coefficient of resonant frequency (τ_f) of −3.6 ppm/°C for 0.85(Mg_0.95Ni_0.05)TiO₃−0.15Ca_0.6La_0.8/3TiO₃ at 1325°C are proposed. A parallel-coupled line band-pass filter is designed and simulated using the proposed dielectric to study its performance.     

Cation Ordering and Domain Boundaries in Ca[(Mg1/3Ta2/3)1−xTix]O3 Microwave Dielectric Ceramics

Cation ordering and domain boundaries in perovskite Ca[(Mg_1/3Ta_2/3)_{1− x} Ti _x ]O₃ ( x =0.1, 0.2, 0.3) microwave dielectric ceramics were investigated by high-resolution transmission electron microscopy (HRTEM) and Rietveld analysis. The variation of ordering structure with Ti substitution was revealed together with the formation mechanism of ordering domains. When x =0.1, the ceramics were composed of 1:2 and 1:1 ordered domains and a disordered matrix. The 1:2 cation ordering could still exist until x =0.2 but the 1:1 ordering disappeared. Neither 1:2 nor 1:1 cation ordering could exist at x =0.3. The space charge model was used to explain the cation ordering change from 1:2 to 1:1 and then to disorder. A comparison between the space charge model and random layer model was also conducted. HRTEM observations showed an antiphase boundary inclined to the (111) _c plane with a projected displacement vector in the 〈001〉 _c direction and ferroelastic domain boundaries parallel to the 〈100〉 _c direction.     

A-Site and B-Site Order in (Na1/2La1/2)(Mg1/3Nb2/3)O3 Perovskite

(Na_1/2La_1/2)(Mg_1/3Nb_2/3)O₃ undergoes a series of phase transitions that involve cation order on the A- and B-sites of the parent perovskite structure. At high temperatures both sites contain a random distribution of cations; below 1275°C a 〈111〉 layering of Mg and Nb leads to the formation of a 1:2 ordered structure with a monoclinic supercell. A second transition was observed at 925°C, where the Na and La cations order onto alternate A-site positions along the 〈001〉 direction of the parent subcell. By quenching samples from above 1275°C to preserve the disorder on the B-site, a fourth variant of this compound was obtained by inducing A-site order through a subsequent anneal at 900°C. Although the changes in structure do not produce significant alterations in the relative permittivity (ɛ_r∼ 35), they do have a significant effect on the value of the temperature coefficient of the capacitance.     

Dielectric and Piezoelectric Properties of the Morphotropic Phase Boundary Composition in the (0.8−x) Pb(Mg1/3Ta2/3)O3−0.2PbZrO3−xPbTiO3 Ternary System

Morphotropic phase boundary (MPB) compositions separating rhombohedral and tetragonal phases in the (1− x − y )Pb(Mg_1/3Ta_2/3)O₃– y PbZrO₃– x PbTiO₃ (PMT–PZ–PT100 x ) ternary solid solution system were characterized using X-ray diffraction and dielectric, piezoelectric properties. This work focused on compositions with a PZ content fixed at y =0.2, with an MPB composition found to be located at x =0.4. Piezoelectric coefficients and dielectric permittivity were found to be on the order of d ₃₃=580 pC/N and 4100, respectively. Acceptor modification using manganese was found to induce a "hardening" effect in 0.4PMT–0.2PZ–0.4PT, with decreased piezoelectric coefficients d ₃₃ and dielectric loss and increased mechanical quality factor Q . Piezoelectric coefficients d ₃₃, Q values, and dielectric loss were found to be 500 pC/N, 2000, and 0.4%, respectively, for 0.4PMT–0.2PZ–0.4PT with MnO₂ dopant levels around 0.5 wt%. The figure of merit (product of Q and d ₃₃) was found to be on the order of 1 × 10⁶, significantly higher when compared with other hard piezoelectric PZT materials. Specifically, the PMT–PZ–PT materials may be attractive candidates for high-power ultrasonic applications, particularly fine-scale components that require relating high permittivities.     

Microstructure and Microwave Dielectric Properties of (1−x)Ca(Mg1/3Ta2/3)O3/xCaTiO3 Ceramics

Dense (1− x )Ca(Mg_1/3Ta_2/3)O₃/ x CaTiO₃ ceramics (0.1≤ x ≤0.9) were prepared by a solid-state reaction process. The crystal structures and microstructures were characterized by X-ray diffraction, scanning electron microscopy, and transmission electron microscopy. Single-phase solid solutions were obtained in the entire composition range. Long-range 1:2 ordering of B-site cations and oxygen octahedra tilting lead to the monoclinic symmetry with space group P 2₁/ c for x =0.1. For x above 0.1, the long-range ordering was destroyed and the crystal structure became the orthorhombic with space group Pbnm . The microwave dielectric properties showed a strong dependence on the composition and microstructure. The dielectric constant and temperature coefficient of resonant frequency increased nonlinearly as the CaTiO₃ content increased while the Qf values decreased approximately linearly. Good combination of microwave dielectric properties was obtained at x =0.45, where ɛ_r=45.1, Qf =34 800 GHz, and τ_f=17.4 ppm/°C.     

Ordering Structure and Dielectric Properties of Undoped and La/Na-Doped Pb(Mg1/3Nb2/3)O3

Transmission electron microscopy was used to study the ordered domain structures in undoped and La/Na-doped Pb(Mg_1/3Nb_2/3)O₃ (PMN), where the compositions of the doped samples were specifically chosen so as to elucidate the ordering mechanism. The results showed that the Mg²⁺ ions and Nb⁵⁺ ions are short-range ordered on the B-site sublattice in undoped PMN, with a domain size of 2 to 5 nm. This short-range ordering gives rise to B-site composition fluctuations occurring on a nanometer scale, and it is this compositional inhomogeneity which is believed to be responsible for the diffuse phase transition behavior. Donor doping with La₂O₃ can compensate for the local charge imbalance resulting from the short-range order and thus enhances the degree of ordering. Acceptor doping with Na₂O, however, increases the charge effect, and hence ordering is suppressed. The effect of Na doping and La doping on the dielectric properties of PMN is also discussed.     

Structure and Dielectric Properties of the Ba(Mg1/3Nb2/3)O3-La(Mg2/3Nb1/3)O3 System

A complete range of perovskite solid solutions can be formed in the (1 − x )Ba(Mg_1/3Nb_2/3)O₃- x La(Mg_2/3Nb_1/3)O₃ (BMN-LMN) pseudobinary system. While pure BMN adopts a 1:2 cation ordered structure, 1:1 ordered phases are stabilized for 0.05 ≤ x ≤ 1.0. Dark-field TEM images indicate that the La-doped solid solutions are comprised of large 1:1 ordered domains and no evidence was found for a phase-separated structure. This observation coupled with the systematic variations in the intensities of the supercell reflections supports a charge-balanced "random-site" model for the 1:1 ordering. The substitution of La also induces a transformation from a negative to positive temperature coefficient of capacitance in the region 0.25 ≤ x ≤ 0.5.     

Structure Evolution from Pb(Mg1/3Nb2/3)O3 to La(Mg2/3Nb1/3)O3

The crystal structure of lanthanum-modified lead magnesium niobates having composition (Pb_{1− x} La _x ) (Mg_{(1+ x )/3}-Nb_{(2− x )/3})O₃ with X = 0 to 1 was investigated by X-ray powder diffraction. It was found that the fundamental reflections from perovskite structure remain in the whole range of composition. The superlattice reflections from the A(B'_1/2-B"_1/2)O₃ ordered structure are also well preserved for La content greater than 50 at.%; however, a series of extra peaks of mixing indices appears, with intensities gradually enhanced with the increase of La content. For the complete substitution of Pb by La, a splitting of some reflections can be observed in the diffraction pattern. The results indicate that the crystal structure evolves continuously with the La content, from disordered cubic perovskite of space group Pm 3 m for X = 0, to ordered cubic perovskite of space group Fm 3 m for X = 0.5, distorted cubic perovskite of space group Pa 3 for 0.5 < X < 0.9, and finally to a rhombohedral perovskite, possibly belonging to the space group R 3 , for X ≥ 0.9. In the evolution of structure, a linear reduction of the lattice constant of the perovskite cell from 4.048 to 3.964 Å was observed.     

Dielectric Properties and Relaxation in (1−x)BiScO3–xBa(Mg1/3Nb2/3)O3 Solid Solutions

The dielectric properties and frequency dispersion associated with a dielectric relaxation were evaluated within the perovskite (1− x )BiScO₃– x Ba(Mg_1/3Nb_2/3)O₃ solid solution systems (0.7 ≤ x ≤ 1). With increasing BiScO₃, the room-temperature dielectric permittivity at low frequency (100 Hz) increased up to 115 at x = 0.7, and a dielectric relaxation phenomenon was evident. Relaxation parameters were analyzed using several Arrhenius-type equations, and the microwave dielectric property measurement using rectangular wave-guide method enabled confirmation of the extrapolated value of the Arrhenius plot. The result of the microwave dielectric property measurement was also checked with J -function fitting based on the frequency-dependent Gaussian distribution of the associated dielectric loss data at low frequency.     

Relaxor Behavior of the 0.9BaTiO3–0.1La(Mg1/2Ti1/2)O3 Solid Solution

Low-frequency dielectric response of air- and oxygen-sintered ceramics with the composition 0.9BaTiO₃–0.1La(Mg_1/2Ti_1/2) O₃ (0.9BT–0.1LMT) has been studied in the temperature range of 12–550 K. In comparison with pure BT, in 0.9BT–0.1LMT the dielectric permittivity maximum is shifted by almost 300 K toward lower temperatures. Both real and imaginary parts of dielectric permittivity of the solid solution, in the range 12–150 K, show a strong frequency-dependent behavior, which is typical of relaxors. On the basis of the model of exponential cluster size distribution and the Cole–Cole equation, the degree of interaction between the polar clusters was estimated. It was shown that the oxygen vacancies arising during sintering at high temperatures did not affect noticeably the relaxor properties of the material. The role of heterovalent La³⁺/Ba²⁺ and Mg²⁺/Ti⁴⁺ substitutions in the relaxor behavior formation is discussed.     

Structural Studies of Ordering in the (Pb1-xBax)(Mg1/3Nb2/3)O3 Crystalline Solution Series

The ordered structures of the (Pb_{1- x} Ba _x )(Mg_1/3Nb_2/3)O₃crystalline solution series were investigated by selected area electron diffraction (SAED) and high-resolution electron microscopy (HREM). At low Ba contents (e.g., x < 0.40), the ordered structure was found to be isostructural with Pb(Mg_1/3Nb_2/3)O₃, with a doubled unit cell characterized by 1/3{111} superlattice reflections. At higher Ba contents (e.g., x > 0.60), the ordered structure was characterized by 1/3{111} superlattice reflections. For intermediate Ba contents (e.g., x - 0.60), diffuse scattering along the {111} between diffuse 1/2{111} and 1/3{111} reflections was observed. The ordering is attributed to the distribution of the B-site cations between multiple sublattices. Strong fluctuations in the B-site cation ratio between ordered and disordered regions are believed not to exist; however, the possibility of weak fluctuations is consistent with the observed lattice images.     

Dielectric Characteristics of Bi- and Ti-Substituted Pb(Mg1/3Nb2/3)O3

Pb[Mg_1/3Nb_2/3]O₃ was gradually substituted by Bi[Mg_2/3Nb_1/3]O₃ (BiMN) up to 30 mol%, with an overall modification by a constant fraction of PbTiO₃ (10 mol%). Monophasic perovskite powders could be prepared via the B-site precursor route. Ceramic samples of the system showed a typical relaxor behavior of frequency-dependent dielectric dispersion. Values of the maximum dielectric constant decreased substantially with increasing BiMN concentration, whereas corresponding temperatures changed only moderately.     

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.     

Nonstoichiometry and the Long-Range Cation Ordering in Crystals of (Na1/2Bi1/2) TiO3

Crystals of (Na_1/2Bi_1/2)TiO₃ have grown by the flux technique and the Czochralski method. Nonstoichiometry, twin configurations, and long-range cation ordering in the crystals have been investigated using X-ray diffraction and an optical polarizing microscope. It has been found that nonstoichiometry was induced in the crystal grown by the Czochralski method owing to the volatilization of Bi-rich phase during the crystal growth. This nonstoichiometry in the crystal resulted in less lattice distortion from cubic symmetry, a lower degree of cation ordering, and a larger domain width in twin configuration. Variations in twinning with temperature and isotropization have been investigated.     

B-Site Order–Disorder Transition in Pb(Mg1/3Nb2/3)O3–Pb(Mg1/2W1/2)O3 Triggered by Mechanical Activation

B-site cation order–disorder transition induced by mechanical activation was observed in Pb(Mg_1/3Nb_2/3)O₃–Pb(Mg_1/2W_1/2)O₃ (PMN–PMW) solid solution, which was examined using both XRD diffraction and Raman spectroscopic study. The order–disorder transition is composition dependent. Mechanical activation triggers the B-site disordering, which can be steadily recovered by thermal annealing at elevated temperature, i.e., at temperatures around 600°C. Raman spectroscopy demonstrated that there existed tiny ordered microdomains in 0.4PMN·0.6PMW subjected to up to 20 h of mechanical activation, although they cannot be shown by X-ray diffraction. This is a result of the equilibrium between the mechanical destruction and temperature-facilitated recovering at the collision points during mechanical activation. It is therefore unlikely that a complete disordering can be realized in PMN–PMW by mechanical activation. The disordering in PMN–PMW triggered by mechanical activation occurs simultaneously with the refinement in crystallite size at the initial stage of mechanical activation, suggesting that the fragmentation of crystallites is responsible for the order–disorder transition at least during the initial stage of mechanical activation.     

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.     

Spray Pyrolysis Synthesis and Dielectric Properties of Pb(Mg1/3Nb2/3)O3

Spray pyrolysis was used to synthesize lead magnesium niobate (PMN) by atomizing a mixture of nitrate aqueous solutions into a high-temperature furnace. This approach allows for instant removal of solvents and decomposition of metal–salts, thereby limiting phase segregation on a nanometer scale, and lowering the transformation temperature for pyrochlore-to-perovskite phase transition. As-synthesized particles were nanocrystalline pyrochlores, with an average crystallite size ∼22 nm. More than 96% perovskite phase was obtained when as-sprayed powders were subsequently calcined at 750°C for 4 h. Sintered PMN ceramics exhibited the typical frequency-dependent dielectric properties, with a peak value of dielectric constant of 18 000, and a transition temperature at −9.6°C at 100 Hz. A series of ceramics were prepared with varied grain sizes. Increasing the grain size increased the dielectric constant, probably due to the smaller fraction of the less-polarizable grain-boundary phases.