Grain boundary curvatures in polycrystalline SrTiO3: Dependence on grain size,topology, and crystallography

By mapping grain orientations on parallel serial sections of a SrTiO₃ ceramic, it was possible to reconstruct three-dimensional orientation maps containing more than 3000 grains. The grain boundaries were approximated by a continuous mesh of triangles and mean curvatures were determined for each triangle. The integral mean curvatures of grain faces were determined for all grains. Small grains with fewer than 16 neighbors mostly have positive mean curvatures while larger grains with more than 16 neighbors mostly have negative mean curvatures. It is also possible to correlate the mean curvature of individual triangles with the crystallographic characteristics of the grain boundary. The mean curvature is lowest for grain boundaries with (100) orientations and highest for grain boundaries with (111) orientations. This trend is inversely correlated to the relative areas of grain boundaries and directly correlated to the relative grain boundary energy. The direct correlation between the energy and curvature is consistent with the expected behavior of grain boundaries made up of singular orientations. Furthermore, because both the relative energy and curvature of grain boundaries with (100) orientations are minima in the distributions, these boundaries also have the lowest driving force for migration.     

Normal and Abnormal Grain Growths in BaTiO3 Fibers

The grain growth mechanisms along the BaTiO₃ fibers were studied between 1150°C and 1250°C. The normal grain growth always reached a stagnant stage after certain heat‐treatment duration caused by the surface pinning effect. However, the abnormal grain growth (AGG) was not pinned by such surface effect, and can grow continuously. The confined normal grain (or matrix grain) size provides the driving force for AGG. The fiber diameter has an important influence on the grain growth behaviors. Submicrometer fibers have relative small stagnant grain sizes, resulting in large driving force for AGG. Abnormal grain growth occurred below 1200°C in the submicrometer diameter fibers, but was not observed at the same temperature in the fibers with diameter of above 1 μm. Due to the large AGG driving force, large number densities of abnormal grains were observed in submicrometer fibers, resulting in “bamboo‐like” microstructure. Fibers with diameters of 1–2 μm were able to be converted into single crystal fibers up to several tens of micrometers due to the relative small AGG driving forces.     

Engineering grain boundary anisotropy to elucidate grain growth behavior in alumina

Current grain growth models have evolved to account for the relationship between grain boundary energy/mobility anisotropy and the five degrees of grain boundary character. However, the role of grain boundary networks on overall growth kinetics remains poorly understood. To experimentally investigate this problem, a highly textured Al₂O₃ was fabricated by colloidal casting in a strong magnetic field to engineer a unique spatial distribution of grain boundary character. Microstructural evolution was quantified and compared to an untextured sample. From this comparison, a prevalence of (0001)/(0001) terminated grain boundaries with anisotropic networks were identified in the textured sample. These boundaries and their networks were found to be driving grain growth at a faster rate than predicted by models. These findings will allow better modelling of grain growth in real systems by experimentally exploring the impact thereon of grain boundary plane anisotropy and relative energy/mobility differences between neighboring boundaries.     

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.     

Mechanical energy losses in commercial crosslinked low-density polyethylene in the temperature range between 200 and 400 K

Aging treatments in water and in air and controlled neutron irradiation were performed on commercial crosslinked low-density polyethylene (XLPE) for promoting different mesostructural arrangements of crystallites and crosslinking degree. Infrared spectroscopy, differential scanning calorimetry, differential thermal analysis, thermogravimetry, and dynamic mechanical analysis were used as characterization techniques. The relaxation peak related to the mobility of the grain boundaries from crystalline zones in XLPE was identified at around 260 K (at 7 Hz), involving an activation energy of 90 ± 4 kJ mol⁻¹. The usual equation for describing the grain boundary mobility in metals involving the movement of grain boundary dislocations was adapted for studying the mobility of the boundaries among the crystalline zones, successfully. In addition, a new mechanical relaxation peak that appears at around 300 K (at 7 Hz), which involves an activation energy of 94 ± 5 kJ mol⁻¹, was found. The driving force controlling this peak was determined as the dragging of the polymer chains at the amorphous zones adjacent to the crystals controlled by the mobility of the crystallites boundaries. The chains movement was done with break away from the physical pinning points. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47605.     

Energy of Grain Boundaries in Halite

Relative grain boundary energy measurements were made by the tracrystal method for [100] tilt boundaries in NaCl. The dependence of boundary energy on grain misorientation was similar to that in metals; however, the presence of significant torque term effects, i.e. dependence of the boundary energy on boundary orientation, is indicated. A method of measuring the relative magnitudes of the torque terms by applying a driving force to boundaries in bi-crystals is described.     

Influence of Excess PbO Additions on {111} Single-Crystal Growth of Pb(Mg1/3Nb2/3)O3–35 mol% PbTiO3 by Seeded Polycrystal Conversion

The influence of additions of excess PbO to Pb(Mg_1/3Nb_2/3)O₃–35 mol% PbTiO₃ (PMN–35PT) on {111} single-crystal growth by seeded polycrystal conversion was studied in the range of 0–5 vol% PbO. PbO volatilization and hence weight loss during annealing was controlled effectively by a double-crucible type of arrangement. PbO additions increased boundary mobility significantly in PMN–35PT, thus facilitating single-crystal growth by seeded polycrystal conversion (SPC). This is attributed to the formation of a boundary wetting PbO-based liquid phase. The growth process occurs very rapidly initially, after which it slows down. This is presumably due to both a decrease in the driving force for boundary migration because of an increase in matrix grain size, and a transition to lower mobility facets. It is also shown that for a given annealing time, the size of the grown crystal scales with the lateral dimensions of the seed crystal.     

Grain boundary energies in yttria-stabilized zirconia

The three-dimensional microstructure of 8% yttria-stabilized zirconia (YSZ) was measured by electron backscatter diffraction and focused ion beam serial sectioning. The relative grain boundary energies as a function of all five crystallographic grain boundary parameters were determined based on the assumption of thermodynamic equilibrium at the internal triple junctions. Grain boundaries with (100) orientations have low energies compared to boundaries of other orientations, and all [100] twist boundaries have relatively low energies. Other classes of boundaries with lower than average energies include [100] symmetric tilt boundaries with disorientations less than 40° and [111] twist boundaries with disorientations greater than 20°. At fixed misorientations, the relative areas of boundaries are inversely correlated to the relative grain boundary energy. The results suggest that texturing microstructures to increase the relative areas of [100] twist boundaries might increase the oxygen ion conductivity of YSZ ceramics.     

Electric Field‐Enhanced Solid‐State Conversion of Ceramic Sr5(PO4)3F to Crystals

The single crystal solid‐state conversion of fluorapatite‐type Sr₅(PO₄)₃F (Sr‐FAP) has been achieved by spark plasma sintering with the assistance of NaF additive. NaF was determined to act as both a sintering aid and impurity solute along the grain boundaries (GBs), controlling both the space charge and GB migration rate. Postsintering isothermal annealing was performed to examine the effect of DC electric field on grain growth. From the space charge potential determined from impedance spectra measurements, in combination with the theoretical contribution of space charge to grain‐boundary energy reduction, it was concluded that the magnitude of the space charge in Sr‐FAP is temperature dependent. As such, a moderate decrease in polycrystalline GB driving force is the main cause for the increased single crystal migration length that was observed in this study.     

Grain growth in strontium titanate in electric fields: The impact of space-charge on the grain-boundary mobility

This study investigates grain growth in the perovskite oxide strontium titanate in an electric field. The seeded polycrystal technique was chosen as it provides a sensitive and controlled setup to evaluate the impact of different parameters on grain growth due to the well-defined driving force for grain growth. Current blocking electrodes were used to prevent Joule heating. The results show faster grain growth, and thus, higher grain-boundary mobility at the negative electrode. It is argued that the electric field causes point-defect redistribution, resulting in a higher oxygen vacancy concentration at the negative electrode. The local oxygen vacancy concentration is suggested to affect the space-charge potential at the grain boundaries. A thermodynamic treatment of the grain-boundary potential at a grain boundary without field shows that for a high oxygen vacancy concentration less space-charge and less accumulation of cationic defects to the boundary occurs. Therefore, at the negative electrode, a higher oxygen vacancy concentration results in less space-charge and less accumulation of cationic defects. The lower degree of defect accumulation requires less diffusion of segregated defects during grain-boundary migration, so that at the negative electrode faster grain growth is expected, as found in the experiments.     

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.     

Mechanism of "Solid-State" Single-Crystal Conversion in Alumina

Single crystals of Al₂O₃ were reproducibly grown from an MgO-doped polycrystalline precursor. The single crystals were grown through controlled abnormal grain growth at temperatures between 1670° and 1945°C. It was observed that CaO impurities segregated to the boundary between the single crystal and the polycrystalline region, and formed a wetting intergranular film. This type of film is required to produce the highly mobile grain boundaries that facilitate single-crystal conversion. The measured grain boundary mobilities correspond reasonably well with the mobilities calculated from data for a grain boundary containing a film with properties of the bulk glass, although some deviation from bulk behavior is indicated by the difference in activation energy. The grain boundaries are the most highly mobile alumina grain boundaries measured to date. This suggests that extrinsic effects produce the highest grain boundary mobility, rather than intrinsic behavior, which has conventionally been assumed to be the fastest.     

Texture Development by Templated Grain Growth in Liquid-Phase-Sintered α-Alumina

The distribution and orientation of platelet-shaped particles of α-alumina in a fine-grained alumina matrix is shown to template texture development via anisotropic grain growth. The textured microstructure ranges from 4 wt% oriented platelet particles in calcined samples to nearly 100% oriented α-Al₂O₃ grains after sintering at 1400°C. A CaO + SiO₂ liquid phase creates favorable thermodynamic and kinetic conditions for anisotropic grain growth and grain reorientation during sintering. Important criteria for templated grain growth include (1) anisotropic crystal structure and growth, (2) high thermodynamic driving force for template grain growth, and (3) modification of diffusion in the system to continuously provide material to the anisotropically growing template grains.     

Three-Dimensional Simulation of Grain Growth in the Presence of Mobile Pores

A kinetic, three-dimensional Monte Carlo model for simulating grain growth in the presence of mobile pores is presented. The model was used to study grain growth and pore migration by surface diffusion in an idealized geometry that ensures constant driving force for grain growth. The driving forces, pore size, and pore mobilities were varied to study their effects on grain-boundary mobility and grain growth. The simulations captured a variety of complex behaviors, including reduced grain-boundary velocity due to pore drag that has been predicted by analytical theories. The model is capable of treating far more complex geometries, including polycrystals. We present the capabilities of this model and discuss its limitations.     

Epitaxial Aluminum-Doped Zinc Oxide Thin Films on Sapphire: II, Defect Equilibria and Electrical Properties

The electrical transport properties of epitaxial ZnO films grown on different orientations of sapphire substrates have been measured as a function of partial pressure of oxygen. After equilibration, the carrier concentration is found to change from a p ^-1/4_O2 to a p ^-3/8_O2 dependence with increasing oxygen partial pressure. The partial pressure dependence is shown to be consistent with zinc vacancies being the rate-controlling diffusive species. In addition, the carrier concentration in ZnO films grown on A-, C-, and M-plane sapphire are the same but that of R-plane sapphire is systematically lower. Electron Hall mobility measurements as a function of carrier concentration for all the substrate orientations exhibit a transition from "single-crystal" behavior at high carrier concentrations to "polycrystalline" behavior at low carrier concentrations. This behavior is attributed to the effective height of potential barriers formed at the low-angle grain boundaries in the epitaxial ZnO films. The trap density at the grain boundaries is deduced to be 7 × 10¹²/cm². The electron mobility, at constant carrier concentration, varies with the substrate orientation on which the ZnO films were grown. The difference is attributed to the difference in dislocation density in the films produced as a result of lattice mismatch with the different sapphire orientations.     

Driving Force of Crystallization Based on Diffusion in the Boundary and the Integration Layers

Crystal growth rates are notoriously difficult to predict and even experimental data are often inconsistent. By allowing for mass and energy diffusion through the molecular and thermal layers surrounding a growing crystal and for the heat effect of crystallization, a new model of crystal growth from solution is proposed and applied to crystallization of potassium chloride from aqueous solution. The driving force for crystal growth was calculated using the solubility at the interface temperature in contrast to the conventional one based on bulk temperature. A positive heat effect at the crystal interface as well as the resistances to the mass and energy transfer processes to and from the crystal surface can reduce the conventional driving force for crystal growth by more than 20 %.     

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.     

Modeling of Grain-Boundary Segregation Behavior in Aluminum Oxide

It is believed that the segregation of oversized dopant ions to grain boundaries in Al₂O₃ hinders grain-boundary diffusion, thereby reducing the tensile creep rate in this system by ∼2–3 orders of magnitude. In order to explain this improvement in creep behavior, it is helpful to characterize both the effective cation and interstitial volumes at grain boundaries, because the relative openness of some boundary structures suggests a great accommodation of oversized ions. In this study, the boundary volume is determined by a spatially local Voronoi construction, which highlights cation (Al³⁺) substitutional sites as well as large interstitial voids. In particular, we examine the spatial distribution of free volume near grain boundaries and, in addition, the dependence of the driving force for segregation on misfit strain in doped Al₂O₃. We interpret our results in light of recent evidence that selective codoping can provide a more efficient means of filling available space near boundaries, thereby further enhancing creep resistance.     

Cation-Aided Joining of Surfaces of β-Silicon Nitride: Structural and Electronic Aspects

An atomic-scale approach has been applied to the examination of both the physical and electronic structures of stable surfaces of β-Si₃N₄. Sterical constraints prevent the (001) surface from effective chemical reaction with the interface. The theoretical surface-to-surface bonding is investigated by using a periodical tight-binding approach. Based on the interpretation of the density of states, the balance of the number of states and electrons is performed for stoichiometric Si₃N₄, ideal N-terminated (110) surfaces, oxygen-overlayered (110) slabs, and the metal monolayer with which the slabs are brought into contact. The stable electronic configuration, which is attained when the cation binds to the interface, represents the electronic driving force behind the diffusion of the additive and/or impurity atoms toward grain boundaries. The different bonding propensities of the (001) and (110) surfaces imply that effective bonding of the planes parallel to the c -direction to the interphase restrains the crystal from growth in the lateral direction. Conversely, geometry-constrained bonding of the (001) planes allows the crystal growth that produces the rod-shaped β-grains.     

Structure of Sapphire Bicrystal Boundaries Produced by Liquid-Phase Sintering

The structure and composition of sapphire bicrystal boundaries produced by liquid-phase sintering depended on the crystallographic misorientation of the crystals across the boundary and on the orientation of the boundary. Basal twist boundaries of 15° or 30° were not wetted by glass, but contained significant amounts of Ca and Si at the boundary. For tilt boundaries of 7° or 12°, the glass wetted segments of boundaries that contained the basal plane of either crystal. Boundary segments with orientations of 40° or more from the basal plane, however, were dewetted (i.e., "dry"). Boundary segments oriented less than ∼40° from the basal orientation were partially wetted, consisting of segments of wetted and dry grain boundaries. For the 12° tilt boundary, Ca and Si could be detected on portions of the boundary that contained no glass. For bicrystal boundaries having tilts of ≤4°, dewetting occurred for all observed boundary orientations. Basal-oriented segments in these small angle tilt boundaries contained noticeable concentrations of adsorbed Ca and Si, while nonbasal segments were apparently free of Ca and Si. Most results could be explained based on a combined Wulff plot construction, which predicts partially wetted grain boundaries and "missing" angles for unwetted grain boundaries. Results that could not be explained by the construction included growth step ledges bounded by nonequilibrium facet planes.