Comprehensive Linkage of Defect and Phase Equilibria Through Ferroelectric Transition Behavior in BaTiO3-Based Dielectrics: Part 2. Defect Modeling Under Low Oxygen Partial Pressure Conditions

Defect and phase equilibria have been investigated through the ferroelectric phase transition behavior of pure and equilibrated nonstoichiometric BaTiO₃ powders. The paraelectric–ferroelectric phase transition temperature ( T _{C – T} ) was found to vary systematically with materials fabricated with different Ba/Ti ratio ( g ^*) and under various oxygen partial pressure (     ) conditions. ¹ The solubility regime, as determined through the T _{C – T} variation, decreased with decreasing     . ² Determining the solubility limits and equilibrating the defect reactions at the solubility limits provide a direct approach to calculate the defect formation energies and provide data to test a new defect model for concurrent defect reactions of partial Schottky and reduction defects. A refined approach introduces a balanced equilibrium between the oxygen vacancy concentrations controlled by the partial Schottky and reduction reactions. In the limiting ambient cases the approach gives the expected results, and also fully explains the solubility trends under low     's. Universally, the theory supports all the experimental data over different temperatures and     's.     

Solid-State Preparation of BaTiO3-Based Dielectrics, Using Ultrafine Raw Materials

BaTiO₃ and Ba(Ti,Zr)O₃ dielectric powders have been prepared from submicrometer BaCO₃, TiO₂, and ZrO₂. By use of submicrometer BaCO₃ the intermediate formation of Ba₂TiO₄ second phase can be widely suppressed. Monophase perovskites of BaTiO₃ were already formed at 900°C and Ba(Ti,Zr)O₃ at 1050°C. Aggregates of very small subgrains could be easily disintegrated to particle sizes <0.5 μm.     

Phase Equilibria in the System BaTiO3–SrTiO3

Phase equilibria in the binary system BaTiO₃–SrTiO₃ were studied above 1200°C. This system is characterized by a complete series of solid solutions with a minimum at 2.5 mole % SrTiO₃ and 1585°C. The hexagonal BaTiO₃ phase is suppressed to a region extending no farther than 0.5% SrTiO₃ at 1600°C. No immiscibility gap was found.     

Phase Equilibria in the System BaTiO3—CaTiO3

The system BaTiO₃–CaTiO₃ was investigated from room temperature to 1900°C. by several different techniques. The system is characterized by extensive solid solution with a minimum at 18 wt.% CaTiO₃. The extent of solid solution decreases rapidly with temperature from a maximum of approximately 30 wt.% in each end member at 1595°C. The temperature of the cubic-hexagonal inversion in BaTiO₃ is raised very rapidly with additions of CaTiO₃. The tetragonal-cubic inversion in BaTiO₃ is lowered slightly to a minimum of 105°C. by the additions of CaTiO₃. Within a wide composition region crystals of cubic BaTiO₃ solid solution may be grown directly from the melt, and at the minimum from a melt of the same composition.     

Fatigue Crack Growth for BaTiO3 Ferroelectric Single Crystals Under Cyclic Electric Loading

Electrically induced fatigue crack growth is an important degradation mechanism for ferroelectric devices. Reliability concerns for ferroelectric devices place stringent demands for ferroelectric materials. In situ observation of electrically induced fatigue crack growth was carried out for ferroelectric single crystals under alternating electric field. Electrically induced fatigue crack growth was observed both below and above the coercive field. Crack closure and open behavior were observed together with 90° ferroelectric domain switching during the electric cycling. The crack propagation behavior is a repeated process of continuous but small increments followed by a sudden increase in the crack length. It was suggested that the electric boundary condition along the crack face, from its mouth to its tip, is a variation from the impermeable to the permeable state. The gradual attainment of an impermeable crack tip after an incubation period of field cycling causes the observed jump in crack propagation.     

The Solid Solubility of Holmium in BaTiO3 Under Reducing Conditions

The solid solubility of Ho³⁺ in BaTiO₃ fired under the reducing conditions of a nitrogen atmosphere containing 10% of hydrogen was studied by quantitative electron-probe microanalysis using wavelength-dispersive spectroscopy. The solubility was found to depend mainly on the starting composition. In the TiO₂-rich samples, the solubility of the Ho³⁺ donors at the Ba lattice sites was measured to be ∼4 mol% Ho_Ba (Ba_0.96Ho_0.04TiO_3−δ at 1400°C), which is much higher than after sintering in air. In the BaO-rich compositions, the solubility of the Ho³⁺ acceptors at the Ti sites (solubility limit     at 1500°C) decreased compared with that in air. Like with sintering in air, under reducing conditions, the highest solubility of holmium in BaTiO₃ was determined when it was incorporated at both lattice sites (solubility limit     ).     

Effect of the Phase Transformation on the Fracture Behavior of BaTiO3

The fracture energy of BaTiO₃ increased with increasing grain size at 25°C in the ferroelectric 4 mm symmetry state and remained constant at 150°C in the paraelectric m 3 m state. In general, observed flaw sizes agreed with those predicted from fracture mechanics equations. The fracture energy measurements combined with previously reported strength measurements were analyzed in terms of fracture mechanics principles to determine the effect of internal stresses on fracture. The analysis showed that the effect of internal stress on fracture for a given flaw size can be determined from a combination of fracture energy and strength measurements at two temperatures. The increase in fracture energy with grain size in the ferroelectric state is attributed to ferroelastic twin formation and wall motion.     

Factors Limiting Equilibrium in Fabricating a Simple Ferroelectric Oxide: BaTiO3

This paper demonstrates a number of features that can contribute to BaTiO₃ being perturbed from an equilibrium condition. The BaTiO₃ synthesis study was conducted with a modified citrate process, but the kinetic aspects limiting the equilibrium state are believed to be general to any processing route. The equilibrium conditions can be determined through a detailed analysis of the paraelectric–ferroelectric phase transition data measured by differential scanning calorimeter. Broadened and multiple latent heat peaks are found indicating a distribution of slightly different ferroelectric transition temperatures for nonequilibrated BaTiO₃ materials. A number of factors have been found that limit the equilibrium conditions, and these include time at formation conditions of temperature and oxygen partial pressure, a second phase BaCO₃, and the rapid nucleation of a BaTi₂O₅ phase on quenching to room temperature from temperatures in and around 1250°C. All of these nonequilibrium factors that occurs at high temperature lead to the ferroelectric phase transition having multiple phase transitions, owing to regions of the BaTiO₃ having different partial Schottky concentrations.     

High-Temperature Dielectrics in the BiScO3–BaTiO3–(K1/2Bi1/2)TiO3 Ternary System

Perovskite solid solution in the (1− x )[0.4BiScO₃–0.6BaTiO₃]+ x (K_1/2Bi_1/2)TiO₃ [BSBT–KBT x ] system was synthesized using conventional sintering and hot-isostatic pressing. Dielectric properties of BSBT ceramics with different dopant levels of KBT were characterized as a function of temperature and frequency for potential use of high-temperature capacitors. The BSBT ceramics with KBT exhibited high dielectric permittivities (ɛ_r) (>1700 at RT) and low dielectric loss over the temperature range from 100° to 300°C, with flat temperature coefficients of permittivity (TCɛs). In addition, BSBT ceramics with increasing KBT were observed to possess dielectric relaxation characteristics at temperatures (>RT) as observed in lead-based relaxors. Furthermore, high energy densities, being on the order of 4.0 J/cm³ at 220 kV/cm was observed for the BSBT–KBT20 ceramics from the electric-field polarization behavior.     

Phase Equilibria in the System La2O3—Iron Oxide in Air

Phase equilibria data are presented for compositions in the system La₂O₃-iron oxide in air. Liquidus and solidus curves were obtained by the quenching method in the iron-rich portion of the system. The remainder of the diagram was determined using a strip-furnace technique. Two compounds have been found, the ortho-rhombic perovskite LaFeO₃ and a compound with the magnetoplumbite structure corresponding to a composition LaFe₁₂O₁₉. LaFeO₃ was determined to melt congruently at about 1890°C. whereas LaFe₁₂O₁₉ has both a stability minimum and maximum at 1380° and 1421°C., respectively. The iron-rich portion of the system is essentially ternary whereas the remainder can be considered to be a simple binary. Liquid compositions have been determined and are plotted in terms of the ternary system La₂O₃-Fe₂O₃-FeO.     

Influence of Cation Order on the Electric Field-Induced Phase Transition in Pb(Mg1/3Nb2/3)O3-Based Relaxor Ferroelectrics

The effect of cation ordering on an electric field-induced relaxor to normal ferroelectric phase transition in Pb(Mg_1/3Nb_2/3)O₃ (PMN)-based ceramics was investigated. Both A-site La doping and B-site Sc doping were found to enhance the chemical ordering in these relaxor ceramics. However, the enhanced chemical orderings showed different impacts on the dielectric and ferroelectric properties in these perovskite materials. The 5% La doping was observed to shift the dielectric maximum temperature ( T _max) to a significantly lower temperature and suppress the electric field-induced transition to a ferroelectric phase. In contrast, the 5% and 10% Sc doping showed little effect on T _max but strengthened the ferroelectric coupling. The difference is discussed on the basis of cation size and charge imbalance. An electric field-temperature phase diagram is also proposed for the 0.90PMN–0.10Pb(Sc_1/2Nb_1/2)O₃ based on its history dependence of the electric field-induced phase transition.     

Phase Transition and Physical Characteristics of Nanograined BaTiO3 Ceramics Synthesized from Surface-Coated Nanopowders

Nanograined BaTiO₃ ceramics prepared from 40-nm-size BaTiO₃ nanopowders exhibited the cubic as well as the tetragonal phase, while nanograined BaTiO₃ ceramics prepared from BaTiO₃ nanopowders coated with Mn had only the tetragonal phase. The dielectric constant of the latter was 10 times larger than that of the former; the latter exhibited PTCR behavior with a resistivity jump ratio of about 5.0 × 10⁴. These physical properties of the BaTiO₃ ceramics appeared to be significantly affected by the strain near grain boundaries; such strain resulted in a phase transition from the cubic to the tetragonal phase in the nanograined BaTiO₃ ceramics, even though the grain size was about 40 nm.     

Role of Liquid Phase in Achieving a Fine Microstructure and Diffusive Phase Transition of MgO-Doped BaTiO3

Two types of glass compositions, with MgO and CaO modifiers, respectively, were used to promote l`iquid-phase sintering of 2 mol% MgO–BaTiO₃ at 1280°C in reducing atmosphere ( p O₂=10⁻⁹ atm). By combining the observations of the grain size of about 1 μm for both specimens and the diffusive phase transition only when MgO modifier was used, it has been interpreted that an appropriate solubility of BaTiO₃ is necessary to yield the fine and composite microstructures via a dissolution–reprecipitation process. Further, a reasonable dopant provision to BaTiO₃ has been shown to be required to achieve the diffusive phase transitions.     

Oxygen Displacement through the Ferroelectric Phase Transition of Barium Titanate—High-Temperature 17O NMR

Perovskite-structured BaTiO₃ undergoes a ferroelectric tetragonal-to-cubic phase transition at 130°C. High-temperature ¹⁷O MAS and static NMR line shapes and relaxation times were examined to elucidate the nature of the anion motions associated with the transition. ¹⁷O MAS spectra show a gradual shift of the two oxygen peaks toward one another with increasing temperature, and a sudden collapse to one peak at the transition, which is consistent with its first-order character. ¹⁷O T _I data are relatively imprecise below the transition, but appear to decrease above it, indicating an increase in low-frequency motions, suggesting a dynamically averaged high-temperature phase.     

Phase Diagram of the Bi4Ti3O12–BaTiO3–(Na1/2Bi1/2)TiO3 System

The phases formed in the ternary system (Na_1/2Bi_1/2)TiO₃–Bi₄Ti₃O₁₂–BaTiO₃ (NBT–BTO–BT) were studied at 1150°C in air. A very accurate picture of the ternary phase diagram was obtained examining almost 90 different compositions, exploiting low-angle XRD analyses to study the layer compounds. New compounds with five perovskite blocks ( m =5) were discovered deep in the phase diagram. No compounds with m >5 were found. It was also established that pure perovskite compounds can be obtained only at compositions very close to the NBT–BT line. The relationships between the phases is discussed and it is hypothesized that the number of perovskite blocks in the system is determined by charged sites being created by the progressive substitution of Bi³⁺ in the A site of the perovskite blocks of BTO with the A cations of the perovskite end-member.     

Phase Equilibria in the System Iron Oxide—Cr2O3– SiO2 in Air

Phase equilibrium data, obtained by the quenching technique, are presented for the liquidus temperature region of the system iron oxide-Cr₂O₃-SiO₂ in air, which represents an O₂ isobaric section (p_o2= 0.21 atm.) through the quaternary system Fe-Cr-Si-O at a total pressure of 1 atm. The diagram is dominated by a large area of coexistence of two immiscible liquids, and high liquids temperatures prevail throughout most of the system. Possible applications to refractory problems are indicated.     

Phase Transition and Ferroelectric Characteristics of Pb[(Mg1/3Nb2/3)1-xTix]O3 Ceramics Modified with La(Mg2/3Nb1/3)O3

The effects of 0–5 mol% addition of La(Mg_2/3Nb_1/3)O₃ (LMN) on the phase transition and ferroelectric behaviors of Pb[(Mg_1/3Nb_2/3)_1-xTi_x]O₃ (PMNT) ceramics with compositions near the morphotropic phase boundary (MPB) were studied. An evolution of structure from rhombohedral to tetragonal was found with increasing PbTiO₃ (PT) content across the MPB (at ∼32.5 mol% PT), and a coexistence of both rhombohedral and tetragonal phases was also found at the MPB. The dual-phase field extended toward the lower PT content side of the MPB, and, moreover, the rhombohedrality or tetragonality was reduced, especially for the compositions near the MPB, by the addition of La in PMNT. The ferroelectric transition was found to change from normal to diffuse as the La content increased and the compositions became more rhombohedral. In accordance with the structural evolution, the change of remanent polarization ( P _r) and coercive field ( E _c) also became gradually indistinct, and both P _r and E _c were reduced. For compositions near the MPB, both PMNT and La-modified PMNT had a similar electromechanical factor ( k _p) in a range around 0.55–0.60, but the mechanical quality factor ( Q _m) was significantly reduced for the La-modified PMNT. The piezoelectric coefficient ( d ₃₃), however, was largely improved with increasing La content in PMNT of compositions at MPB. A high value of d ₃₃∼ 815 pC/N was obtained for the 5-mol%-La-modified ceramics, but it was associated with a low value of Q _m.