Faceting of High-Angle Grain Boundaries in Titanium-Excess BaTiO3

The grain boundaries in BaTiO₃ with excess Ti of 0.5, 0.3, and 0.1 at.% sintered at 1300° or 1250°C have been examined by scanning electron microscopy (SEM), electron backscattered diffraction pattern (EBSP), and transmission electron microscopy (TEM). In the 0.1% Ti-excess specimen, large grains growing abnormally form high-angle grain boundaries when they impinge on each other as verified by EBSP. A large fraction of these grain boundaries are faceted with hill-and-valley shapes. In the 0.5% Ti-excess specimen, large grains growing abnormally are elongated in the directions of their {111} double twins. These grains often form flat grain boundaries parallel to their {111} planes with the fine matrix grains, and the grain-boundary segments between the large impinging grains with high misorientation angles are often also parallel to the {111} planes of one of the grains. These grain boundaries are expected to be singular. Most of the grain boundaries between the randomly oriented fine-matrix grains in the 0.3 at.% Ti-excess specimen are also faceted with hill-and-valley shapes at finer scales when observed under TEM. The facet planes are parallel to {111}, {011}, and {012} planes of one of the grain pairs and are also expected to be singular. These high-angle grain boundaries lying on low index planes of one of the grain pairs are similar to those observed in other oxides and metals.     

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.     

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.     

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.     

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.     

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.     

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).     

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.     

Dependence of Grain Shape and Growth on PT Content in PbO-Excess PMN–PT

When Pb(Mg_1/3Nb_2/3)O₃ (PMN) with 40 wt% excess PbO is sintered at 1050°C, the grains grow normally and have flat {100} surface segments with round edges. As PbTiO₃ (PT) is added up to 8 mol%, the grain growth is still nearly normal, characterized by time invariant normalized size distributions, but the grain edges become more sharply curved. This normal growth behavior is consistent with relatively small surface step free energy as indicated by the round grain edges. As the PT content is increased above 10–35 mol%, the grain edges become sharp and abnormal grain growth occurs. This is consistent with the step free energy increasing with the PT content as indicated by the sharpening grain edges.     

{111} Twin Formation and Abnormal Grain Growth in Barium Strontium Titanate

Two series of experiments were performed to study the experimental conditions for the formation of {111} twins and related microstructures in barium strontium titanate ((Ba, Sr)TiO₃). In the first series, the phase equilibria in the BaTiO₃–SrTiO₃–TiO₂ system were determined. XRD and WDS analysis, done in the BaTiO₃-rich region, of 45(Ba,Sr)TiO₃–10TiO₂ samples annealed at 1250°C for 200 h in air showed that (Ba,Sr)TiO₃ was in equilibrium with Ba₆Ti₁₇O₄₀ (B₆T₁₇) and Ba₄Ti₁₃O₃₀ phases with strontium solubility (Sr/(Ba + Sr)) of ∼0.02 and 0.20, respectively. In the second series the microstructures of samples consisting of a mixture of (Ba,Sr)TiO₃ and 2.0 mol% TiO₂, were observed after sintering at 1250°C for 100 h in air. {111} twins formed only in the samples with faceted B₆T₁₇ second phase particles, similar to the case of BaTiO₃. In these samples, abnormal grain growth occurred in the presence of the {111} twins. In contrast, no {111} twins formed and no abnormal grain growth occurred in the samples containing second phase particles other than B₆T₁₇. With an increased substitution of strontium for barium, the aspect ratio of abnormal grains containing {111} twin lamellae was reduced. This result was attributed to a reduction in the relative stability of the {111} planes with the strontium substitution.     

The mechanism of abnormal grain growth in polycrystalline diamond during high pressure-high temperature sintering

The abnormal grain growth (AGG) in polycrystalline diamond (PCD) during high pressure-high temperature sintering (6 GPa; 1600 °C) was investigated. Some grains grew to a size of several hundreds of micrometers in PCD manufactured with 2-μm diamond powder. However, the AGG distribution was inhomogeneous possibly due to the inhomogeneous pressure distribution. When the initial average particle diameter of diamond powder was 4 μm, no AGG was observed within the experimental range (1 h) due to an increase in the diffusion distance. Electron backscattered diffraction technique was used to show that the abnormally grown grains were single crystals with and without their twins with the {1 1 1} twinning planes. The {1 1 1} faceted planes developed in the abnormally grown crystals, suggesting that AGG in PCD could be explained by the 2D nucleation mechanism.     

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.     

Seeded Growth from Twinned and Untwinned Abnormal Grains of Pb(Mg1/3Nb2/3)O3–35 mol% PbTiO3 in a Matrix Containing PbO Additions

The growth of abnormal grains of PMN–35PT containing Σ3 twin boundaries was compared with that of untwinned abnormal grains of PMN–35PT. It was thought that the twinned abnormal grains might have a growth advantage because of the presence of reentrant edges. The aforementioned types of grains were embedded in a PMN–35PT polycrystalline matrix with 3 vol% excess PbO, and grown by annealing in an oxygen atmosphere at 1150°C for varying times. It was found that abnormal grains containing Σ3 boundaries showed a comparable degree of growth to that of the untwinned grains. Furthermore, for the twinned seed crystals, the extent of growth was independent of whether there was any initial entrapped porosity within the abnormal grain.     

Strategies and practices for suppressing abnormal grain growth during liquid phase sintering

Abnormal grain growth (AGG), where a small number of grains grow to sizes much larger than the neighboring matrix grains, is a frequent occurrence in liquid phase sintering of ceramics and cermets. As AGG can be detrimental to the material properties, a considerable amount of research on the nature, causes and suppression of AGG has been carried out. In this review, we outline the mixed control theory of grain growth and the principle of microstructural evolution that have been developed by Kang and coworkers over the last two decades. The theory and the principle, which are based on theories of crystal growth from a liquid, state that grain growth behavior is controlled by the nature of the solid-liquid interfaces, either atomically rough (macroscopically rounded) or smooth (macroscopically faceted). For grains with atomically rough solid-liquid interfaces, growth is controlled by diffusion of solute through the liquid phase and normal grain growth always occurs. For grains with faceted solid-liquid interfaces (or a mixture of rough and faceted interfaces), growth is interface reaction-controlled and diffusion-controlled below and above a critical driving force for growth, respectively. Depending on the relative values of the critical driving force for growth Δg_c and the maximum driving force for the largest grain in the system Δg_max, pseudo-normal, abnormal, and stagnant grain growth can take place. Based on this theory and principle, we present strategies for suppressing AGG by adjusting Δg_c and Δg_max to avoid AGG and examples of the successful use of these strategies.     

Abnormal Grain Growth and Intergranular Amorphous Film Formation in BaTiO3

The effect of abnormal grain growth on the formation of amorphous films at grains boundaries was studied in a model system BaTiO₃. 0.4 mol% TiO₂-excess BaTiO₃ powder compacts were sintered at 1380°C for various times up to 16 h. During the sintering, abnormal grains formed. With the growth of the abnormal grains, amorphous films formed and eventually thickened up to 19.2 nm at grain boundaries. The film formation is attributed to the accumulation of Ti solutes at grain boundaries with the grain growth, while the film thickening is mostly caused by the redistribution of liquid at triple junctions. Extended annealing of the 16-h-sintered sample at 1350°C for 15 days resulted in a thinning of the film to nearly 1.7 nm without a change in the grain size, showing an equilibrium thickness. This result demonstrates that the film thickness observed during the growth of the grain may not be the equilibrium thickness. The result further suggests that the shape of the abnormal grains, even when equiaxed, can differ from the equilibrium shape.     

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).     

Effect of SiO2 and TiO2 Addition on the Morphology of Abnormally Grown Large Pb(Mg1/3Nb2/3)O3–35 mol% PbTiO3 Grains

Abnormal grain growth (AGG) during the sintering of Pb(Mg_1/3Nb_2/3)O₃–35 mol% PbTiO₃ was investigated. When a small amount of SiO₂ was added, large abnormal grains with the penetration twin characteristic were observed to appear. AGG, in this case, is because of the twin plane re-entrant edges that provide coarsening advantage. When TiO₂ was added, on the other hand, the abnormal grains were simple cubic in morphology with well-developed {100} planes. In this case, the coarsening advantage is suggested to be because of grain boundary re-entrant edges.     

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.     

Effect of Grain Coalescence on the Abnormal Grain Growth of Pb(Mg1/3Nb2/3)O3-35 mol% PbTiO3 Ceramics

Abnormal grain growth (AGG), which occurred during the heat treatment of Pb(Mg_1/3Nb_2/3)O₃-35 mol% PbTiO₃ (PMN-35PT) with excess PbO, was investigated. AGG has been suggested to be the consequence of grain coalescence that results in the formation of Σ3 coincidence site lattice and low angle grain boundaries. Because of reentrant edges appearing at the ends of these boundaries, the coarsening rate of grains was significantly enhanced and AGG occurred.     

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.