Polar Directions of the 90° and 180° Ferroelectric Domains in Tetragonal Barium Titanate Determined by Electron-Backscatter Diffraction

Ferroelectric domains induced in pressureless-sintered BaTiO₃ ceramics by the cubic to tetragonal phase transformation at Curie point T _C≈130°C have been analyzed using electron-backscatter diffraction (EBSD) equipped with the scanning electron microscope. The EBSD technique with built-in automatic indexing algorithms enabling the differentiation of the {110} family, and the measurement of the twin obliquity has permitted unambiguous assignment of the fourfold c -axis and twofold a -axes from Kikuchi patterns obtained from the twin domains. Both the 90° and 180° domains with mutually perpendicular and parallel polar directions thus determined are consistent with those deduced by the traditional techniques whereby the polar directions were resolved morphologically from the configuration of domains, and from differential etching rate along the a - and c -axis of the tetragonal phase. The successful demonstration of domain identification using EBSD has confirmed that the traditional techniques relying on differential etching rate are suitable for the purpose.     

Axial Thermal Expansion of TetragonaI ZrO, Between 1150° and 1700°C

The lattice constants for three samples of tetragonal ZrO₂ were measured in a high-temperature X-ray diffractometer in the range 1150° to 1700°C in an ambient air atmosphere. The unrefined lattice constants were the same for these materials only after each had been previously heat-treated at 1550° to 1750°C in an ambient air atmosphere. The thermal expansions of the two axes are linear and are given by: a value, A = 3.588₂+ 4.50 X 10+(T) , within 0.001₃ A; and c value, A = 5.188₂+ 7.57 × 10⁻⁵(T), within 0.002₂ A, where T is in °C for the range 1150° to 1700°C. The lattice constant values are a = 3.639₉ A and c = 5.275₈ A at 1150°C and a = 3.678₂ A and c = 5.339₇ A at 1700°C.     

Microstructural Evolution in a ZrO2 Wt% Y2O3 Ceramic

Several unusual microstructural features, i.e., 90° tetragonal ZrO₂ twins containing antiphase domain boundaries, tetragonal ZrO₂ precipitates in a colony morphology, and precipitate-free zones at the perimeter of cubic ZrO₂ grains containing fine tetragonal ZrO₂ precipitates, were observed in a single ZrO₂-12 wt% Y₂O₂ ceramic annealed at 1550°, 1400°, and 1250°C, respectively. The type of phase transformation responsible for each microstructural feature is described.     

Stable and Metastable Phase Relationships in the System ZrO2–ErO1.5

Stable and metastable phase relationships in the system ZrO₂–ErO_1.5 were investigated using homogeneous samples prepared by rapid quenching of melts and by arc melting. The rapidly quenched samples were annealed in air for 48 h at 1690°C or for 8 months at 1315°C. Two tetragonal phases ( t - and t '-phases) were observed after quenching samples heated at 1690°C to a room temperature, whereas one t -phase and cubic ( c -) phase were found in those treated at 1315°C. Since the t '-phase is obtained through a diffusionless transformation during cooling from a high-temperature c -phase, t - and c -phases can coexist at high temperature. The t - and c -phases field spans from 4 to 10 mol% ErO_1.5 at 1690°C and from 3 to 15 mol% ErO_1.5 at 1315°C. The equilibrium temperature T ^t-m ₀ between the t - and monoclinic ( m -) phases estimated from A_s and M_s temperatures decreased with increasing ErO_1.5 contents.     

Raman Scattering Study of Cubic–Tetragonal Phase Transition in Zr1−xCexO2 Solid Solution

A structural phase transition between the cubic (space group, Fm 3 m) and tetragonal (space group, P 4₂ /nmc) phases in a zirconia–ceria solid solution (Zr_1−xCe_xO₂) has been observed by Raman spectroscopy. The cubic–tetragonal ( c–t" ) phase boundary in compositionally homogeneous samples exists at a composition X₀ (0.8 < X₀ < 0.9) at room temperature, where t " is defined as a tetragonal phase whose axial ratio c/a equals unity. The axial ratio c/a decreases with an increase of ceria concentration and becomes 1 at a composition X'₀ (0.65 < X'₀ < 0.7) at room temperature. The sample with a composition between X₀ and X'₀ is t " ZrO₂. By Raman scattering measurements at high temperatures, the tetragonal ( t" ) → cubic and cubic → tetragonal phase transitions occur above 400°C in Zr_0.2 Ce_0.8O₂ solid solution.     

Anisotropic Thermal Expansion of Tetragonal Zirconia Polycrystals

Thermal expansion coefficients (α _a and α _c ) in two crystallographic axes ( a and c ) of the tetragonal phase are measured at 25°–1200°C in ZrO₂–M₂O₃ (M = Sc, In, Yb) and in ZrO₂–YTaO₄. The difference between these two thermal expansion coefficients, α _c –α _a , decreases with M₂O₃ or YTaO₄ composition even though the tetragonality ( c/a ) behaves differently in these two systems. The locus of α _c =α _a represents a maximum tetragonality for the tetragonal phase, but not the phase boundary for the cubic phase. The relationships among thermal expansion, temperature, and composition are discussed.     

Structure–Property Relationships of BaTi1−2yGayNbyO3 (0≤y≤0.35) Ceramics

BaTi_{1−2 y} Ga _y Nb _y O₃ (BTGN) (0≤ y ≤0.35) powders were synthesized at 1300°C by the conventional solid-state method. Room temperature x-ray diffraction patterns for y ≤0.025 and 0.05≤ y ≤0.30 can be indexed as the tetragonal ( P 4 mm ) and cubic ( Pm     m ) polymorphs of BaTiO₃, respectively, whereas y =0.35 consists of a mixture of the cubic polymorph of BaTiO₃ and an 8H hexagonal-type perovskite ( P 6₃/ mcm ) isostructural with Ba₈Ti₃Nb₄O₂₄. Scanning electron microscopy shows the microstructures of BTGN ceramics ( y ≤0.30) sintered at 1500°C to consist of fine grains (1–3 μm) within a narrow grain size and shape distribution. Room temperature transmission electron microscopy for y ≤0.08 reveals core–shell structures and (111) twins in some grains; however, their relative volume decreases with y . Energy dispersive spectroscopy reveals the cores to be Ga and Nb deficient with respect to y . For y >0.08 there is no evidence of core–shell structures, however, some grains have a high density of dislocations, consistent with chemical inhomogeneity. BTGN ceramics exhibit a diverse range of dielectric behavior in the temperature range 120–450 K and can be subdivided into two groups. 0.025≤ y ≤0.15 display modest ferroelectric relaxor-type behavior, with high room temperature permittivity, ɛ₂₅', (>300 at 10 kHz), whereas 0.25≤ y ≤0.30 are temperature and frequency stable dielectrics with ɛ₂₅'<100 that resonate at microwave frequencies with modest quality factors, Q × f , ∼3720 GHz (at ∼5 GHz) for y =0.30.     

Etched Structures Dependent on Sidewise Motion of 180° Domains in BaTiO3

Sidewise motion of 180° domains in BaTiO₃ single crystals during electrical poling with a wet electrode technique results in etch pit patterns strikingly similar to dislocation patterns in other crystals. The etching behavior of the pits is also consistent with that of small 180° domains in this material. Very small inclusions are also revealed in a poled and etched crystal as small round 180° domains representing regions which could not be reversed by the electric field. It is suggested that dislocations in tetragonal BaTiO₃, may also be revealed in this manner. The origin of the small circular 180° domains is revealed by a photomicrograph of the "hanging up" of a moving 180° domain wall as it encounters defects during sidewise motion through the crystal. Based on this photomicrograph a wall energy calculation was made for the 180'domain in a BaTiO₃ single crystal in which the sidewise motion of the wall is treated as a surface tension phenomenon. Good agreement with the accepted value of 1.4 ergs per cm² was obtained if a correction was made for the potential drop through the material of lower dielectric constant used in the poling process.     

Zirconia-Related Phases in the Zirconia/Titanium Diffusion Couple After Annealing at 1100°–1550°C

A diffusion couple of 3 mol% Y₂O₃–ZrO₂ and titanium was isothermally annealed in argon at temperatures between 1100° and 1550°C. The phases and microstructure in the ceramic side were investigated using scanning electron microscopy and transmission electron microscopy, both attached to an energy-dispersive spectrometer. After annealing at 1100°C/6 h, zirconia grains did not grow conspicuously and evolved only traces of oxygen, resulting in t -ZrO_{2− x} but not α-Zr. At temperatures above 1300°C, a significant amount of oxygen evolved from zirconia, reducing the O/Zr ratio, such that α-Zr was excluded from t -ZrO_{2− x} during cooling, yielding a higher O/Zr ratio (≈2). When held at 1550°C/6 h, zirconia grains grew rapidly. The α-Zr was segregated on grain boundaries during cooling by the exsolution of zirconium from ZrO_{2− x} , while twinned t '-ZrO_{2− x} or lenticular t -ZrO_{2− x} , which was embedded in ordered c- ZrO_{2− x} , was found. The ordered c -ZrO_{2− x} was identified by the     {113} superlattice reflections of its electron diffraction patterns.     

A β-Phase Based Superstructure in Bi2O3 Doped with PbF2

A new phase was prepared from Bi₂O₃·15 mol% PbF₂ by heating it at 700°C and then quenching to room temperature. The crystal structure (tetragonal, a =0.765 and c = 1.77 nm, P4₂/nmc) is related to that of the β-phase of Bi₂O₃ by a supercell which is 3 times larger in the c direction.     

Hydration in the System Ca2SiO4–Ca3(PO4)2 at 90°C

Compositions along the Ca₂SiO₄–Ca₃(PO₄)₂ join were hydrated at 90°C. Mixtures containing 15, 38, 50, 80, and 100 mol% Ca₃(PO₄)₂ were fired at 1500°C, forming nagelschmidtite + a ¹-CaSiO₄, A -phase and silicocarnotite and a -Ca₃(PO₄)₂, respectively. Hydration of these produces hydroxylapatite regardless of composition. Calcium silicate hydrate gel is produced when Ca₂SiO₄≠ 0 and portlandite when Ca₂SiO₄ is >50%. Relative hydration reactivities are a -Ca₃(PO₄)₂ > nagelschmidtite > α ¹-Ca₂SiO₄ > A -phase > silicocarnotite. Hydration in the presence of silica or lime influences the amount of portlandite produced. Hydration in NaOH solution produces 14-A tobermorite rather than calcium silicate hydrate gel.     

Low-Temperature Phase Equilibria by the Flux Method and the Metastable–Stable Phase Diagram in the ZrO2–CeO2 System

Low-temperature phase equilibria ranging from 1000° to 1200°C in the ZrO₂–CeO₂ system were investigated by annealing compositionally homogeneous ZrO₂–CeO₂ solid solutions in a Na₂B₂O₇.1 NaF flux. The 5 mol% CeO₂ samples decomposed into monoclinic ( m ) and tetragonal ( t ) phases during annealing at 1100°2 and 1120°C, and the t -phase transformed diffusionlessly into monoclinic ( m ') symmetry during quenching. A eutectoid reaction, t → ( m + c ), was confirmed to occur at 1055°± 10°C, where the equilibrium compositions of the t -, m -, and c -phases were 11.2 ± 2.8, 0.9 ± 0.9, and 84 ± 1 mol% CeO₂, respectively. The equilibrium phase boundaries were almost independent of the annealing time and/or the flux:sample ratio, which indicates that the flux accelerates the reaction rate withouts affecting the equilibration. The previous data are discussed using metastable–stable phase diagrams. The discrepancies of the low-temperature phase diagram in the literature are attributable to either regarding the metastable phase boundaries as stable ones or ignoring the sluggish kinetics.     

〈111〉 Rotation Twins in an Orthorhombic LaGaO3 Perovskite

Phase-transformation-induced twins in pressureless-sintered lanthanum gallate (LaGaO₃) ceramics have been analyzed using transmission electron microscopy. Twins are induced by solid-state phase transformation upon cooling from rhombohedral ( r , R 3 c ) to orthorhombic ( o , Pnma ) symmetry at 145°C. Domains with a 150°–60°–150° configuration were frequently detected when viewed along [210]. This observation representing the co-existence of the {121} and {123} twins is suggested by analyzing corresponding selected area diffraction patterns across the domain boundaries. The former, with the twin plane lying on {121}, is the reflection type whose twin variants are related by mirror plane symmetry. The latter, although its nature was confirmed by tilting experiments along an unsplit row of reflections, exhibits characteristic crystallographic orientation relationships that are distinctive from those of the {121} twins. The twin laws represented in the matrix form are also derived accordingly from corresponding orientation relationships. Crystallographic analysis indicates that these domains commonly possess an orientation relationship that can be described by the twofold rotation axis about 〈111〉 lost upon the rhombohedral→orthorhombic phase transition. They are therefore the 180° parallel-rotation twin, with the twin axis 〈111〉 lying in {123}. Twins generated by the r → o phase transition between crystals of non-group–subgroup relations are discussed in terms of an intermediate metastable cubic phase of the lowest common supergroup symmetry.     

Revised Phase Diagram of the System ZrO2-CeO2 Below 1400°C

The phase diagram of the system ZrO₂-CeO₂ was rein-vestigated using hydrothermal techniques. Cubic, tetragonal, and monoclinic solid solutions are present in this system. The tetragonal solid solution decomposes to monoclinic and cubic solid solutions by a eutectoid reaction at 1050°50°C. The solubility limits of the tetragonal and cubic solid solutions are about 18 and 70 mol% CeO₂, respectively, at 1400°C, and about 16 and 80 mol% CeO₂, respectively, at 1200°C. Solubility limits of the monoclinic and cubic solid solutions are about 1.5 and 88 mol% CeO₂ at 1000°C, and 1.5 and 98 mol% CeO₂ at 800°C, respectively. The compound Ce₂Zr₃O₁₀ is not found in this system.     

Influence of Non-Stoichiometry on the Structure and Properties of Ba(Zn1/3Nb2/3)O3 Microwave Dielectrics: I. Substitution of Ba3W2O9

A narrow region of Zn-vacancy-containing cubic perovskites was formed in the (1− x )Ba₃(ZnNb₂)O₉−( x )Ba₃W₂O₉ system up to 2 mol% substitution ( x =0.02). The introduction of cation vacancies enhanced the stability of the 1:2 B-site ordered form of the structure, Ba(Zn_{1− x} □ _x )_1/3(Nb_{1− x} W _x )_2/3O₃, which underwent an order–disorder transition at 1410°C, ∼35° higher than pure Ba(Zn_1/3Nb_2/3)O₃. The Zn vacancies also accelerated the kinetics of the ordering reaction, and samples with x =0.006 comprised large ordered domains with a high lattice distortion ( c/a =1.226) after a 12 h anneal at 1300°C. The tungstate-containing solid solutions can be sintered to a high density at 1390°C, and the resultant ordered ceramics exhibit some of the highest microwave dielectric Q factors ( Q × f =1 18 000 at 8 GHz) reported for a niobate-based perovskite.     

Microstructure and Dielectric Characteristics of (PbxBa0.5−xSr0.5)TiO3 Ceramics

Microstructural and dielectric properties of the Pb _x Ba _0.5__x —Sr_0.5TiO₃ system have been studied. It is found that this system forms a solid solution in the entire composition range (0.0≤ x ≤0.5) and is cubic for the x = 0, 0.1, and 0.2 compositions and tetragonal for other compositions. Measurements of the dielectric constant as a function of temperature reveal that this material is ferroelectric at room temperature for the x > 0.2 compositions and has a broad paraelectric-ferroelectric transition region. No shift in the dielectric maxima was noted; however, there is a slight spread in the dielectric constant with frequency for the x = 0.4 composition. A quantitative model to mathematically analyze the effect of composition fluctuations on the dielectric broadening for a ternary system is presented. Transmission electron microscopic studies reveal the presence of 90° ferroelectric domains oriented along the {01     } planes for the x = 0.3 and 0.4 compositions.     

On the Microstructures Resulting from the Diffusionless Cubic→Tetragonal Transformation in ZrO2-Y2O3 Alloys

A diffusionless cubic (c)→metastable tetragonal (t') phase transformation occurs in certain alloys in the ZrO₂-Y₂O₃ system on quenching from elevated temperatures. Microstructural features due to this phase transformation, principally anti-phase domain boundaries (APB's) and mechanical accommodation twins, have been characterized using transmission electron microscopy. Certain differences between our interpretation and those of other workers are discussed.     

Optical, Electron Microscopic, and X-ray Topographic Studies of Ferroic Domains in Barium Titanate Crystals Grown from High-Temperature Solution

BaTiO₃ single crystals were grown by the top-seeded solution growth (TSSG) technique and the spatial domain configurations in the tetragonal crystals were observed by using a polarizing microscope, SEM, TEM, and X-ray topography. The 90° domain boundaries were stopped, forming wedge shapes, by another 90° boundary. All of the straight lamellar boundaries in the observed domain patterns, even in the herringbone structure, can be interpreted as head-to-tail 90° walls. The irregular overlapped boundary can be observed by using a polarizing microscope and X-ray topography. It looks as if the lamellar domains are penetrating one another because the wedge-shaped lamellar domains are spatially overlapped at those boundaries. After thinning and polishing {001} crystal plates, some 90° a–c boundaries disappear and a -domains become predominant.     

Metastable Phase Selection and Partitioning in ZrO2—MgO Processed from Liquid Precursors

Aqueous mixtures of either zirconium acetate or zirconium nitrate and magnesium nitrate were dried and subsequently pyrolyzed at fast heating rates (upquenching) to form metastable crystalline phases of ZrO₂ with various degrees of MgO supersaturation. The crystallization temperature was determined to be 380°C for the zirconium acetate, and 270°C for the zirconium nitrate at a heating rate of 5°C/min. The crystalline structures were characterized as a function of MgO content and thermal history for specimens containing 0 to 30 mol% MgO. Upquenching to 900°C, where monoclinic ( m ) ZrO₂ and MgO are the equilibrium phases, yielded single-phase tetragonal ( t ) ZrO₂ (<8 mol% MgO), single-phase cubic ( c ) ZrO₂ (9 to 17 mol% MgO), and two-phase c -ZrO₂+ MgO structures (>17 mol% MgO). The composition for which T ₀( t/c ) = 900°C was estimated as 9 ± 1 mol% MgO. Compositions crystallizing as metastable t -ZrO₂ (<8 mol% MgO) partitioned at higher temperatures and/or longer times into two-phase mixtures, following the general sequence t → t + m → m + MgO. Similarly, compositions forming metastable c -ZrO₂ (10 to 30 mol% MgO) partitioned in the following sequence: c → c + t + MgO → t + MgO → t + m + Mgo → m + Mgo. The initial phase selection and subsequent partitioning sequence are discussed in light of phase hierarchies predicted from thermodynamic concepts and kinetic constraints which are introduced by the solute partitioning required to achieve equilibrium.     

Grinding-Induced Texture in Ferroelastic Tetragonal Zirconia

Ceria- and yttria-doped tetragonal polycrystalline zirconia ceramics were ground at temperatures as high as 1100°C. X-ray diffraction revealed that the intensity ratio I ₍₀₀₂₎/ I ₍₂₀₀₎ increased (to as high as ∼4.5) compared with that from the as-sintered surfaces (∼0.55). The enhancement in I ₍₀₀₂₎/ I ₍₂₀₀₎ at temperatures well above the m → t transition temperature shows that it is not related to transformation, reversible or otherwise, but can be explained by ferroelastic domain switching.