Dependence of Grain Growth and Grain-Boundary Structure on the Ba/Ti Ratio in BaTiO3

The grain-growth behavior and grain-boundary structure in titanium-excess BaTiO₃ depend on the amount of excess titanium at 1250° and 1300°3C. With excess titanium, abnormal grain growth (AGG) occurs and the grain boundaries are mostly flat or faceted with hill-and-valley shapes. With 0.5 at.% excess titanium, the large grains have flat {111} faces forming singular grain boundaries parallel to {111} double twins. With excess-titanium content between 0.1 and 0.3 at.%, the abnormal grains appear to have polyhedral shapes with {100} faces. These flat or faceted grain boundaries are expected to have singular structures, and hence AGG can occur by the step growth mechanism. When the excess-titanium content is decreased to 0, the grain boundaries become curved, indicating a rough atomic structure, and normal grain growth occurs.     

Transmission Electron Microscopy Microstructure of 0.95(Na0.5K0.5)NbO3–0.05BaTiO3 Ceramics

Microstructural characterizations using transmission electron microscopy on 0.95(Na_0.5K_0.5)NbO₃–0.05BaTiO₃ ceramics sintered at 1030°–1150°C for 2 h were carried out. The liquid phase was found at the triple junction of the grains in all specimens and abnormal grain growth occurred in the presence of the liquid phase. Abnormally grown grains whose shapes were cuboidal were well developed. Anisotropically faceted amorphous liquid phase pockets were observed inside the grain in a specimen sintered at 1060°C for 2 h. The interface between the grain and the liquid matrix was flat and some were identified to be {100} planes of the grains. A certain amount of liquid at the sintering temperature of 1060°C enhanced the abnormal grain growth and contributed to the improvement of the piezoelectric properties.     

Crystallographic Facetting in Sintered Barium Titanate

A commercial TiO₂-excess BaTiO₃ powder has been sintered and its microstructure analyzed for crystallographic facetting via both scanning and transmission electron microscopy (SEM and TEM). Facetted grain surfaces are developed initially from {111} at a low temperature of 1215°C, which are then altered to {111} and {100} at 1290°C in the presence of a grain-boundary liquid phase. The grain shape is also modified correspondingly from platelike to polygonal. Facetting of the intragranularly located residual pores in BaTiO₃ along the {141} planes further develops on the (quasi-)equilibrium shape after annealing at 1400°C for 100 h from the initially well-characterized {111}, {110}, and {100} in as-sintered samples sintered at the same temperature for 10 h. The Wulff plots derived from the residual pores in as-sintered and annealed samples are constructed for the 〈011〉 zone. Microstructural analysis also suggests that the shape of grains and intragranular residual pores is modified progressively upon annealing. The initial solid–vapor surface energy has become less anisotropic crystallographically. Abnormal grain growth in relation to the surface energy anisotropy is discussed.     

Distribution of Grain Boundaries in SrTiO3 as a Function of Five Macroscopic Parameters

Measurements of the grain boundary population as a function of misorientation and boundary plane orientation show that the distribution is inversely correlated to the sum of the energies of the surfaces comprising each boundary. The observed correlation suggests that the difference between the energy of a high-angle grain boundary and the two component surfaces is relatively constant as a function of misorientation. Two exceptions to this correlation were identified: low-misorientation-angle boundaries and the coherent twin boundary, where the (111) planes in the adjoining crystals are parallel to each other, but rotated by 60° around the [111] axis. In these cases, the high degree of coincidence across this interface probably lowers the boundary energy with respect to that of the component surfaces. For all other boundaries, the anisotropy of the population is accurately predicted by the surface energy anisotropy, and in general, boundaries display a preference for {100} orientations, the planes of minimum surface energy.     

Abnormal Grain Growth in Alumina with Anorthite Liquid and the Effect of MgO Addition

Abnormal grain growth (AGG) in alumina with anorthite liquid has been observed with varying anorthite and MgO contents, at 1620°C. When only anorthite is added to form a liquid matrix, the grain–liquid interfaces have either flat or hill-and-valley shapes indicating atomically flat (singular) structures. The large grains grow at accelerated rates to produce AGG structures with large grains elongated along their basal planes. This is consistent with the slow growth at low driving forces and accelerated growth above a critical driving force predicted by the two-dimensional nucleation theory of surface steps. With increasing temperature, the AGG rate increases. The number density of the abnormally large grains increases with increasing anorthite content. The addition of MgO causes some grain–liquid interfaces to become curved and hence atomically rough. The grains also become nearly equiaxed. With increasing MgO content the number density of the abnormally large grains increases until the grain growth resembles normal growth. This result is qualitatively consistent with the decreasing surface step free energy associated with partial interface roughening transition.     

The Effect of MgO Addition on Grain Growth in PMN–35PT

When Pb(Mg_1/2Nb_2/3)O₃–35PbTiO₃ (mol%) (PMN–35PT) is sintered at 1200°C after packing in PbZrO₃ powder, the grains show normal growth with time invariant normalized grain size distributions. If 0.5 wt% MgO is added to PMN–35PT, abnormal grain growth occurs with the large abnormal grains developing nearly cubic shapes. The interfaces between grains and PbO-rich liquid at grain triple junctions are flat, indicating that they are singular. Many central segments of the liquid films and possibly grain boundaries between the abnormal grains and the small neighboring grains are also flat along the {100} planes of the abnormal grains. The abnormal grain growth in the MgO-doped specimens is likely to be caused by the presence of these singular interfaces. Most of the large abnormal grains do not contain any Σ=3 penetration twin boundaries unlike the previous observations in PbO-excess PMN–35PT.     

Facet–Defacet Transition of Grain Boundaries in Alumina

Grain boundaries in pure alumina powder compacts sintered at 1400°C are smoothly curved, indicating that they have atomically rough structures. When these specimens are heat-treated at temperatures between 900° and 1100°C, a small fraction of the grain boundaries develop either hill-and-valley or kinked shapes with flat segments. Some of these flat boundary segments lie on the {011[Twomacr]} plane of one of the grain pairs. These grain boundaries thus appear to become singular at these temperatures. When a corundum crystal with a basal surface is sintered in alumina powder at 1400°C, all grain boundaries formed between the corundum basal surface and small grains, as well as those between the small grains, are smoothly curved, indicating their rough structure. When heat-treated at 900°C for 3 days, about 30% of the grain boundaries between the corundum basal surface and the small grains develop kinks with flat boundary segments, and some of these flat segments lie on the basal plane of the corundum. When heat-treated again at 1400°C, all grain boundaries are curved, indicating that they become reversibly rough. These observations show that at least some of the grain boundaries in alumina undergo roughening-singular transitions at temperatures between 900° and 1100°C.     

Singular Grain Boundaries in Alumina and Their Roughening Transition

The shapes and structures of grain boundaries formed between the basal (0001) surface of large alumina grains and randomly oriented small alumina grains are shown to depend on the additions of SiO₂, CaO, and MgO. If a sapphire crystal is sintered at 1620°C in contact with high-purity alumina powder, the grain boundaries formed between the (0001) sapphire surface and the small alumina grains are curved and do not show any hill-and-valley structure when observed under transmission electron microscopy (TEM). These observations indicate that the grain boundaries are atomically rough. When 100 ppm (by mole) of SiO₂ and 50 ppm of CaO are added, the (0001) surfaces of the single crystal and the elongated abnormal grains form flat grain boundaries with most of the fine matrix grains as observed at all scales including high-resolution TEM. These grain boundaries, which maintain their flat shape even at the triple junctions, are possible if and only if they are singular corresponding to cusps in the polar plots of the grain boundary energy as a function of the grain boundary normal. When MgO is added to the specimen containing SiO₂ and CaO, the flat (0001) grain boundaries become curved at all scales of observation, indicating that they are atomically rough. The grain boundaries between small matrix grains also become defaceted and hence atomically rough.     

Grain Boundaries in Titania-Doped α-Alumina with Anisotropic Microstructure

The microstructure of sol-gel-derived alpha-alumina (Al₂O₃) doped with 0.6 wt% titania, sintered at 1450°C for 1 h, consisted of thin platelets with (0001) faces in a matrix of equiaxed grains. Short facets at the edges of the platelets developed primarily parallel to the {10     2} planes, while some were parallel to the {11     3} planes; other edges showed irregular, curved boundaries. The basal surfaces of the platelets were coated with thin layers (0.5-6 nm) of an amorphous titanium-containing aluminosilicate phase, which also was present at triple points. No amorphous phase was found on the short faceted boundaries, on curved boundaries at platelet edges, or at grain boundaries of equiaxed, matrix grains. However, titanium enrichment was observed at all examined boundaries, suggesting that titanium segregation alone did not account for the development of anisotropic microstructure. Curved incursions on basal facets were associated with occasional particles of aluminum titanate (Al₂TiO₅).     

Effect of Magnesium Oxide Addition on Surface Roughening of Alumina Grains in Anorthite Liquid

Alumina sintered with 5 wt% anorthite at 1620°C for 48 h has grains with flat boundaries and a size distribution representing abnormal grain growth. TEM observations of the grain triple junctions show flat grain surfaces, some of which are the (0001), ([Onemacr]012), and (1[Onemacr]01) planes. HRTEM observations confirm these surfaces to be atomically flat and hence singular. When sintered further after embedding in MgO powder, the {0001} and { 01[Onemacr]2} planes remain flat, but curved surface segments also appear. These curved surface segments are confirmed to be atomically rough by HRTEM. They are connected to the flat segments with discontinuously changing slopes. Thus, when MgO is added, the singular and rough surface phases coexist.     

Singular Grain Boundaries in Alumina Doped with Silica

Pure Al₂O₃ powder compact sintered at 1400°C after adding 100 mol ppm of SiO₂ shows grain boundaries that are flat, even across the triple junctions. TEM observations show that these flat grain boundaries are parallel to the basal planes of the grains on one side. These flat grain boundaries must be singular. At such a low SiO₂ concentration and a low temperature, it is very unlikely that any liquid phase is present at these grain boundaries to cause such flat boundary shapes.     

Plasticity and Creep in Single Crystals of Zirconium Carbide

High-temperature deformation in ZrC single crystals was studied. Seeded crystals were grown by a direct rf-coupling floating-zone process. Yield stresses were measured from 1080° to 2000°C as a function of stress axis orientation. The Burgers vector was shown to be parallel to the 〈110〉 axes by transmission electron microscopy. Slip was observed on {100}, {110}, or {111} planes, depending on the orientation of the stress axis; it always occurred on the most favorably oriented slip system. The dependence of steady-state creep rate on the applied stress indicated that recovery occurred by a dislocation climb mechanism. Examination of the dislocation structure in deformed crystals by transmission electron microscopy supported this conclusion.     

ZnO with Additions of Fe2O3: Microstructure, Defects, and Fe Solubility

Zinc oxide (ZnO) crystals with additions of iron (III) oxide exhibit a characteristic inversion domain microstructure with domain boundaries on two different habit planes: parallel to {0001} basal planes and parallel to {2 1 1 5} pyramidal planes of ZnO. The structural inversion of the domains is proved by electron diffraction experiments. In the present transmission electron microscopy study, emphasis is placed on the early stages of domain formation in sintered polycrystalline material and in diffusion couples with single crystals of ZnO. For solute iron content >0.5 at.% of the cations, defects nucleate at the surface and in the interior of ZnO grains at >900°C. These primary defects propagate along the basal planes of ZnO and gradually widen in the positive c -axis direction of the ZnO host crystal. The widening along c is promoted by a second defect on {2 1 1 l } planes that moves away from the basal plane defect. The c -axis orientation in the ZnO region swept by the second defect is inverted, finally resulting in the inversion domain microstructure. A low iron content ≈0.1 at.% was measured in the inverted domains. Energy-filtered imaging and quantitative electron energy-loss spectroscopy show that the inversion domain boundaries (IDBs) parallel to the basal planes contain a full close-packed monolayer of iron whereas the pyramidal IDBs are occupied by iron with ≈2/3 of the content of the basal IDB. Based on experimental observations and arguments of structural chemistry, a mechanism is proposed explaining the nucleation and oriented growth of the inversion domains that are finally induced and driven by the trivalent iron ions at octahedral sites in the primary defects.     

Effect of Ba6Ti17O40/BaTiO3 Interface Structure on {111} Twin Formation and Abnormal Grain Growth in BaTiO3

A structural transition of Ba₆Ti₁₇O₄₀/BaTiO₃ interfaces from faceted to rough was induced by reducing oxygen partial pressure in the atmosphere. As the oxygen partial pressure decreased, the number densities of {111} twins and abnormal grain decreased. TEM observation showed that the twin formation was governed only by the faceting of the interface. Experimental evidence of {111} twin-assisted abnormal growth of faceted BaTiO₃ grains was also obtained.     

Formation Energies of Antiphase Boundaries in GaAs and GaP: An ab Initio Study

Electronic and structural properties of antiphase boundaries in group III-V semiconductor compounds have been receiving increased attention due to the potential to integration of optically-active III-V heterostructures on silicon or germanium substrates. The formation energies of {110}, {111}, {112}, and {113} antiphase boundaries in GaAs and GaP were studied theoretically using a full-potential linearized augmented plane-wave density-functional approach. Results of the study reveal that the stoichiometric {110} boundaries are the most energetically favorable in both compounds. The specific formation energy γ of the remaining antiphase boundaries increases in the order of γ_{113} ≈ γ_{112} < γ_{111}, which suggests {113} and {112} as possible planes for faceting and annihilation of antiphase boundaries in GaAs and GaP.     

Surface Roughening Transition and Coarsening of NbC Grains in Liquid Cobalt-Rich Matrix

When NbC–30 wt% Co powder compact is sintered at various temperatures where NbC grains (with small amounts of Co) coexist with a liquid Co–NbC matrix, the NbC grains undergo a surface roughening transition with temperature increase and the grain growth changes from abnormal to normal growth. When sintered at 1400°C, the grains are polyhedral with sharp edges (and corners) and grow abnormally because their singular surfaces move by nucleation of surface steps. When sintered at 1600°C, the edges become round, indicating the surface roughening transition. The grains still grow abnormally, but their number density is larger than that at 1400°C because of the smaller surface step free energy. When sintered at 1820°C, the grains are nearly spherical, but the flat-surface segments still remain. The grain growth at this temperature is nearly normal because of very small surface step free energy. The surface roughening transition is reversed when a specimen initially sintered at 1820°C is heat-treated again at 1400°C, but some grains show transition shapes with nearly flat edges and slope discontinuities (shocks).     

A geometric model of growth for cubic crystals: Diamond

A mathematical and software implementation of a geometrical model of the morphology of growth in a cubic crystal system, such as diamond, is presented based on the relative growth velocities of four low index crystal planes: {100}, {110}, {111}, and {113}. The model starts from a seed crystal of arbitrary shape bounded by {100}, {110}, {111} and/or {113} planes, or a vicinal (off axis) surface of any of these planes. The model allows for adjustable growth rates, times, and seed crystal sizes. A second implementation of the model nucleates a twinned crystal on a {100} surface and follows the evolution of its morphology. New conditions for the stability of penetration twins on {100} and {111} surfaces in terms of the alpha, beta, and gamma growth parameters are presented.     

The Wulff Shape of Alumina: III, Undoped Alumina

Controlled-geometry cavities were introduced into the m{10     0} plane of undoped sapphire substrates using photolithographic methods, and subsequently internalized by diffusion bonding the etched sapphire to an undoped high-purity polycrystalline alumina. Pore-boundary separation during growth of the sapphire seed into the polycrystal entrapped the pores within the single crystal. Pores with an equivalent spherical radius of ≈1 μm reached a quasi-equilibrium shape after prolonged anneals at 1600° and 1800°C. The introduction of mechanically induced surface defects accelerated pore shape equilibration. The Wulff shape of undoped alumina was determined by characterizing the shape and facet structure of these equilibrated internal pores using optical microscopy, scanning electron microscopy, and atomic force microscopy. The observed planes in the Wulff shape of undoped alumina, c(0001), r{     012}, s{1     01}, a{11     0}, and p{11     3} planes, were consistent with those reported by Choi et al .; however, a different energy sequence is inferred. The absence of the m-plane in the Wulff shape is consistent with other experimental studies, but inconsistent with those lattice simulations that predict the m-plane to be one of the lowest energy planes in pure alumina. A comparison of Wulff shapes at 1600° and 1800°C suggests that the surface energy of undoped alumina becomes more isotropic as temperature increases.     

〈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.     

Surface Energy Anisotropy of SrTiO3 at 1400°C in Air

Geometric and crystallographic measurements of grain-boundary thermal grooves and surface faceting behavior as a function of orientation have been used to determine the surface energy anisotropy of SrTiO₃ at 1400°C in air. Under these conditions, thermal grooves are formed by surface diffusion. The surface energy anisotropy was determined using the capillarity vector reconstruction method under the assumption that Herring's local equilibrium condition holds at the groove root. The results indicate that the (100) surface has the minimum energy. For surfaces inclined between 0° and 30° from (100), the energy increases with the inclination angle. Orientations inclined by more than 30° from (100) are all about 10% higher in energy and, within experimental uncertainty, energetically equivalent. A procedure for estimating the uncertainties in the reconstructed energies is also introduced. Taken together, the orientation dependence of the surface-facet formation and the measured energy anisotropy lead to the conclusion that the equilibrium crystal shape is dominated by {100}, but also includes {110} and {111} facets. Complex planes within about 15° of {100} and 5° of {110} are also part of the equilibrium shape.