Investigation of Resistivity and Permittivity for (Ba,Pb)TiO3 PTCR Ceramics

A scheme to examine quantitatively the interdependence between the measured resistance and permittivity data for semiconducting (Ba,Pb)TiO₃ samples having Curie points above 300°C was developed based on the Schottky-type potential barrier model. Specifically, the nonvanishing spontaneous polarization in the ferroelectric state was considered in terms of a useful parameter to explain the low resistivity below the Curie point. The resistivity derived from the measured permittivity shows a consistent temperature dependence with the dc measured one, i.e., the positive temperature coefficient of resistance (PTCR) characteristics. It is also observed that more satisfactory agreement can be achieved when the acceptor states are assumed to be distributed over a certain energy interval. The values of acceptor-state densities thus obtained are found to be in excellent agreement with those extracted from the slope in the Arrhenius plots of resistivity vs l/( T ε_m), where T is the absolute temperature and ε_m the dielectric constant. The validity of the present methodology is justified by obedience to the Curie–Weiss law for the calculated bulk dielectric constant.     

Structure and Properties of (Ba,Ca) TiO3 Ceramics Prepared Using (Ba,Ca)TiO3 Ceramics I, Crystallographic and Microstructural Studies

Ba_1–xCa_xTiO₃ powders have been prepared using a novel route involving solid-state reaction in a mixture of Ba_1–xCa_xCO₃ and TiO₂. The Ba_1–xCa_xCO₃ precursors used in this method were prepared by a chemical coprecipitation route to ensure a uniform supply of Ba and Ca ions during thermochemical reaction with TiO₂. The compositional homogeneity of Ba_1–xCa_xTiO₃ powder prepared by such a semiwet route is compared with those prepared by the conventional dry route, involving thermochemical reaction in a mixture of BaCO₃, CaCO₃, and TiO₂, using principles of X-ray line broadening. It is shown that the powders obtained by the semiwet route possess better compositional homogeneity, over a length scale of 1800 Å corresponding to the coherently scattering domain size, than those prepared by the conventional dry route. Microstructural studies have revealed grain sizes of the order of 1 μm and several micrometers, respectively, for ceramics prepared by the semiwet and conventional dry routes. The solid solubility limit of Ca in Ba_1–xCa_xTiO₃ ceramics fired at 1300°C is 16 mol% for samples prepared by the semiwet route while conventionally processed ceramics had a Ca solid Solubility limit of 12 mol% at the same temperature.     

Pressure and Temperature Dependencies of the Direct-Current Resistance of Semiconducting (Ba, Sr)TiO3 and (Ba, Pb)TiO3

The direct-current resistance of semiconducting compositions in the (Ba, Sr)TiO₃ and (Ba, Pb)TiO₃ systems has been measured under hydrostatic pressures from 0 to 35 MPa, and temperatures from 20° to 135°C. The temperature dependence of the hydrostatic piezoresistance coefficients is presented. Results are discussed in terms of barrier layer sensitivity to mechanical stress.     

Studies in the System (Ba, Ca, Pb)TiO3

The weight loss, dye absorption, crystalline phase or phases, dielectric constant, dissipation factor, and temperature variation of dielectric constant were determined for various bodies in the system (Ba, Ca, Pb)TiO₃ fired in an air atmosphere at temperatures from 800?° to 1400°C. The per cent of PbO loss is proportional to e^−B/T, where B is a constant and T is the absolute temperature. It is possible to fire most bodies in this system to zero (visual) dye absorption, but the sensitivity of the dissipation factor to moisture shows that some bodies are not well fired in the electrical sense. The electrical properties correlate well with the crystalline constitution. The two-phase region of the barium-calcium titanate binary extends into the ternary to about 35 mole %, lead titanate.     

Dislocation Loop Formation in Nonstoichiometric (Ba,Ca)TiO3 and BaTiO3 Ceramics

Dislocation loops observed in nonstoichiometric and stoichiometric (Ba,Ca)TiO₃, and in stoichiometric BaTiO₃ sintered in a reducing atmosphere, were characterized by conventional transmission electron microscopy (TEM) under two-beam conditions and high-resolution TEM atomic structure analysis. Dislocation loops mostly lay on {100} planes with Burgers vectors of type 〈100〉. The dynamic behavior of these dislocation loops during the electron beam irradiation (EBI), however, was classified into two different types of dislocation loops: in A-site-excess (Ba,Ca)TiO₃, contrasts of dislocation loops faded completely away; in BaTiO₃ and B-site-excess (Ba,Ca)TiO₃, fine-line contrasts remained. Dislocation loops with Burgers vectors of type 1/2〈100〉 and the resultant crystallographic shear (CS) structure with a displacement vector of type 1/2〈110〉 after EBI were proposed to interpret residual line images. Disappearance of these line images in A-site-excess (Ba,Ca)TiO₃ strongly suggests preferential Ca ion site occupancy at the CS structure.     

Role of Liquid Phase in PTCR Characteristics of (Ba0.7Sr0.3)TiO3 Ceramics

The role of liquid phase in the enhancement of the PTCR (positive temperature coefficient of resistance) effect in (Ba_0.7Sr_0.3)TiO₃ (BST) with the addition of AST (4Al₂O₃· 9SiO₂· 3TiO₂) is investigated in this paper. The AST–BST samples were characterized with optical microscopy, transmission electron microscopy, energy-dispersive spectroscopy, and impedance spectroscopy. Microscopic observations showed that slower cooling might facilitate the precipitation of the (Ba,Sr)TiO₃ phase from the liquid phase on matrix grains since the amount of liquid phase was reduced with a decreasing cooling rate. Impedance spectroscopy indicated that this variation accompanied the change in the intrinsic properties of grain boundaries, which could not be explained by well-known oxidation effects. With the aid of a brick-layer model and high-resolution transmission electron microscopy (HRTEM), it appeared that the change in electrical characteristics of grain boundaries with decreasing cooling rate originated from the precipitation of (Ba,Sr)TiO₃. Finally, the effect of precipitated (Ba,Sr)TiO₃ on the PTCR characteristics is discussed in terms of the acceptor-state density and the polarization state at grain boundaries.     

Effect of Sintering Aids on Microstructures and PTCR Characteristics of (Sr0.2Ba0.8)TiO3 Ceramics

The effects of liquid-phase sintering aids on the microstructures and PTCR characteristics of (Sr_0.2Ba_0.8)TiO₃ materials have been studied. The grain size of sintered materials monotonically decreases with increasing content of Al₂O₃–SiO₂–TiO₂ (AST). The ultimate PTCR properties with ρ_ht/ρ_rt as great as 10^5.61 are obtained for fine-grain (10-μm) samples, which contain 12.5 mol% AST and were sintered at 1350°C for 1.5 h. The quantity of liquid phase formed due to eutectic reaction between AST and (Sr,Ba)TiO₃ is presumably the prime factor in determining the grain size of samples. The grains grow rapidly at the sintering temperature in the first stage until the liquid phase residing at the grain boundaries reaches certain critical thickness such that the liquid–solid interfacial energy dominates the mechanism of grain growth.     

Structure and Properties of (Ba,Ca)TiO3 Ceramics Prepared Using (Ba,Ca)CO3 Precursors: II, Diffuse Phase Transition Behavior

Ferroelectric phase transition in (Ba,Ca)TiO₃ ceramics has been investigated using dielectric measurements. It is shown that samples prepared using (Ba,Ca)CO₃, precursors exhibit diffuse phase transition (DPT) while those prepared by the conventional route show BaTiO₃-type sharp transition. The diffuseness of the phase transition is found to increase with increasing calcium content. The critical exponent for the dielectric stiffness (1/ε') departs significantly from the mean field value of unity and is shown to increase from 1.21 to 1.86 with increasing calcium content. Arguments are advanced to show that the DPT behavior in these ceramics is inexplicable in terms of either the internal stress model due to the absence of 90° domains in fine-grain ceramics or the compositional inhomogeneity model. It is proposed that DPT behavidr is intrinsic to the system and is intimately linked with the appearance of polar phase in the critical regime whose width is shown to increase with increasing Ca content.     

Electromechanical Properties of Some Pb (Mg1/3Nb2/3–PbTiO3–(Ba,Sr)TiO3 Ceramics: I

Compositional variation within the Pb(Mg_1/3Nb_2/3) O₃–PbTiO₃–(Ba, Sr)TiO₃ (hereafter PMN–PT–BT,ST) ternary (6.4% PT% 14.1%, 1.25% BT,ST% 2.5%) results in major changes in induced strain and hysteresis. For the 1.25% BT family, the increase in strain correlates with an increase in T _max, while the dielectric loss is uncorrelated with hysteresis and strain. In addition, weak field aging (which is not reset by application of field) shows little effect on strain and hysteresis for drive fields of > 0.2 MV/m. The vary narrow polarization-fields loops (virgin curvesnearly indistinguishable from subsequent cycles) show that weak-field permittivity is a good approximation to the high-field permittivity. is a good approximation to the high-field Permittivity. Although these data clarify the frequency ( T _max is linearly dependent on the logarithm of the frequency) effect on weak-field dielectric behavior, they do not directly address the question of meaningful extrapolation of high-field strain with frequency. In particular, the question remains as to whether the high-field permittivity and strain are frequency dependent. In future papers we will address this question by a combination of measurement techniques as functions of frequency.     

Crystal Structure and Ferroelectric Properties of (Bi0.5Na0.5)TiO3–Ba(Zr0.05Ti0.95)O3 Piezoelectric Ceramics

The crystal structure and ferroelectric properties of (1− x )(Bi_0.5Na_0.5)TiO₃– x Ba(Zr_0.05Ti_0.95)O₃ (BNBZT x, x ≤12%) lead-free piezoelectric ceramics were studied. The distance between the centers of cations and anions ( d _c–a) as well as the lattice parameters was carefully investigated by Rietveld refinement on X-ray diffraction patterns. It was found that the crystal phase was determined by the amount of Ba(Zr_0.05Ti_0.95)O₃ added, whereas the pure rhombohedral and tetragonal phases are observed in compositions containing x ≤4 and x ≥8%, respectively. A rhombohedral–tetragonal morphotropic phase boundary (MPB) was found at around BNBZT6, which showed a maximum and minimum d _c–a at its rhombohedral and tetragonal phases, respectively. According to the present study, the ferroelectric properties show a strong dependence on their crystal phases. For the single-phase compositions, the remanent polarization ( P _r) generally increased with the value of d _c–a while their coercive fields ( E _c) were determined by their lattice parameters. Nevertheless, the behavior in P _r and E _c for MPB compositions is related to not only the lattice parameter but also the composed phases.     

(Bi1/2Na1/2)TiO3–Ba(Cu1/2W1/2)O3 Lead-Free Piezoelectric Ceramics

(Bi_1/2Na_1/2)TiO₃ with 0–6 mol% Ba(Cu_1/2W_1/2)O₃ (BNT-BCW), a new member of the BNT-based group, has been prepared following the conventional mixed oxide route. The compacted bodies were sintered at 1130°C for 2 h to get dense ceramics. The addition of BCW into BNT ceramics facilitated the poling process because of a reduction in leakage current. 0.995BNT·0.005BCW ceramics exhibit a relatively high piezoelectric constant ( d ₃₃= 80 × 10⁻¹² C/N) and a relatively low dielectric loss (tan δ= 1.5%). Increased amount of BCW was found to increase the dielectric constant and loss of BNT-BCW ceramics and to suppress the grain growth. During sintering, some BCW diffuses into the lattice of BNT to form a solid solution and some remains on the grain boundaries.     

Electromechanical Determination of the High-Field Phase Transition of Pb(Mg1/3Nb2/3)O3–PbTiO3–(Ba,Sr)TiO3 Relaxor Ferroelectrics

Ceramics in the (1 – x )[(1 – y )Pb(Mg_1/3Nb_2/3)O₃· y PbTiO₃] · x MeTiO₃ system, where Me is Sr or Ba, exhibit very large electrostrictive strains at reasonable drive fields. However, the optimum use temperature and frequency vary with the particular composition used. As relaxor ceramics, each composition has a broad transition from electrostrictive to partially piezoelectric behavior. The transition temperature ( T _t) can be roughly determined from strain or polarization properties; however, it can be more quantitatively determined from the effective electro-mechanical Q . A plot of induced transverse strain/induced polarization squared (effective Q ₁₂) as a function of temperature shows a sharp and unmistakable change in slope—this defines T _t. The slope of induced transverse strain/polarization (effective g₃₁) also shows a change in slope at T _t, although this is more gradual than that of effective Q . The indicated T _t correlates with those found from measurement of strain and polarization.     

Preparation of Full-Dense Pb(Zr,Ti)O3 Ceramics by Aerosol Deposition

Full-dense fine-grained bulk Pb(Zr,Ti)O₃ (PZT) ceramics with a thicknesses of 300 μm were successfully obtained by aerosol deposition (AD) employing the starting powder subjected to an adequate pretreatment. It was found that formation of internal pores during the postdeposition firing treatment takes place in two different mechanisms on different scales. Residual carbons contained in the as-deposited PZT ceramics are responsible for the formation of extra-large pores, inducing severe distortion to the shape of the sample. On the other hand, trapped agglomerates in the as-deposited PZT ceramics are responsible for the formation of intermediate pores. The revealed mechanisms are discussed with a focus on the positive/negative correlation between the pretreatment procedure of starting powders and the formation of internal pores.     

Effect of Simultaneous Addition of BiFeO3 and Ba(Cu0.5W0.5)O3 on Lowering of Sintering Temperature of Pb(Zr,Ti)O3 Ceramics

Sintering of 0.5-wt%-MnO₂-added Pb(Zr_0.53Ti_0.47)O₃ ceramics progresses at 935°C for 50 min by the addition of complex oxides of perovskite-type crystal structure, BiFeO₃ and Ba(Cu_0.5W_0.5)O₃. In order to elucidate the low-temperature sintering mechanism of Pb(Zr,Ti)O₃ ceramics, the shrinkage and the evolution of the microstructure of a compacted body during heating were studied. It has been shown that the densification process was separated into the following three stages: the rearrangement of grains, the grain boundary diffusion of atoms, and then grain growth. Also, microstructural and elemental analyses of the ceramics revealed the existence of an amorphous phase at the grain boundaries predominantly composed of lead and copper oxides. Consequently, this process can be facilitated by the occurrence of a transient liquid phase corresponding to the above amorphous phase.     

Infrared Reflection of Ba(Mg1/3Ta2/3)O3 Ceramics

The dielectric function of the ordered Ba(Mg_1/3Ta_2/3)O₃ ceramics was investigated by the infrared reflectance spectra taken over the 50–4000-cm⁻¹ range. The detailed crystal structure of the specimen was examined by the Rietveld method. The space group of trigonal D _3d³ and the degree of long-range order of 0.97 for Mg and Ta atomic arrangement were confirmed. The reflectance spectra were analyzed on the basis of the four-parameter semiquantum model assuming 16 infrared active vibrational modes allowed for the related D _3d³ structure. The lowest-frequency optical mode was found at 60 cm⁻¹, which can be assumed to involve the motions of the heavy TaO₆ octahedra.     

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.     

Low-Temperature Hydrothermal Synthesis of Phase-Pure (Ba,Sr)TiO3 Perovskite using EDTA

A thermodynamic model was developed to describe the stability of (Ba,Sr)TiO₃ (BST) solid solutions in the Ba–Sr–Ti–K–(EDTA)–H₂O (EDTA = ethylenediaminetetraacetic acid) system. Phase diagrams were computed to identify the range of conditions suitable for making phase-pure BST. Hydrothermal experiments were performed to validate the thermodynamic model. The model was found to be more useful when an ideal solid solution was used to estimate the energetics for the BST phase instead of experimental thermodynamic data. In addition, EDTA was found to promote stable conditions for BST formation. When attempting to prepare Ba_0.50Sr_0.50TiO₃ without EDTA, BaTiO₃-rich and SrTiO₃-rich phases precipitated separately, at 70°–160°C. However, in the presence of EDTA, a phase-pure Ba _0.55Sr_0.45TiO₃ solid solution was obtained at 90°–120°C. EDTA is effective because it prevents phase heterogeneities from forming and equalizes the adsorption affinity of strontium and barium species.