Structure, energy, and structural transformations of graphene grain boundaries from atomistic simulations

Domain/grain boundaries are often introduced into graphene during chemical vapor deposition growth processes. Here, we performed a series of hybrid molecular dynamics simulations to study the structures, energies, and structural transformations of symmetric tilt grain boundaries of graphene. The grain boundary comprises an array of edge dislocations, with the dislocation density increasing upon increasing the grain boundary misorientation angle. The dislocation in the zigzag-oriented grain boundary contains an edge-sharing pentagon/heptagon defect, whereas the dislocation in the armchair-oriented grain boundary contains two paired pentagon/heptagon defects. In some grain boundaries, out-of-plane buckling exists due to the presence of dislocations. In the transition region (the region between the zigzag- and armchair-oriented grain boundaries), the grain boundary structures feature complex mixtures of both zigzag and armchair grain boundaries. We also discuss the grain boundary transformations and migrations that occur upon adding or removing carbon atoms at the grain boundaries for all of our investigated types of grain boundaries.     

Investigation of grain boundaries influence on dielectric properties in fine-grained BaTiO3 ceramics without the core–shell structure

Grain boundaries of the Ca-doped and fine-grained BaTiO₃ (BT) ceramics were investigated in order to understand the role of grain boundaries, using a high-resolution transmission electron microscope (TEM) analyses, X-ray diffraction (XRD) and chemical etching analyses. Electrical properties and complex impedance spectroscopy of multilayer ceramic capacitors (MLCs) using Ca-doped BT were also examined to investigate with reference to the roles of grain boundaries. Doped elements were peculiarly enriched at the grain boundaries and tetragonality of the BT ceramics recovered significantly after grain boundaries were etched. It is confirmed that the grain boundaries have a significant influence in stabilizing the temperature dependence of the dielectric properties, and that the residual stress is caused by grain boundaries with the grain growth inhibited during sintering. In addition, the high reliability of BT ceramics without the core–shell structure is considered to be due to the high resistivity of the grain boundaries.     

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.     

Poling behaviour at the grain boundaries of ferroelectric PZT thin films investigated by electric scanning force microscopy

The poling behaviour of PZT(53/47) films was investigated separately at the grain boundaries and inside the grain volumes by ESFM. The films were prepared by sol-gel processing on Pt-metallized polycrystalline Al₂O₃, substrates and consisted of columnar grains with mean diameter of 220 nm. It was found that the polarization was decreased at simple grain boundaries in a border zone of 20 nm to 40 nm width, with up to 42% related to the grain volumes. At triple points, the polarization was decreased by the same amount in a border zone of 40 nm to 80 nm width with respect to the grain volumes. An asymmetric poling behaviour of the saturation polarization was found at the grain boundaries. The switchable polarization of the grain boundaries was determined to be 74% of that of the grain volumes. The coercive field was clearly increased at the grain boundaries.     

Toward Knowledge‐Based Grain‐Boundary Engineering of Transparent Alumina Combining Advanced TEM and Atomistic Modeling

Transition element dopants (e.g., Y, La) are commonly used as sintering aids in polycrystalline alumina ceramics, which segregate to the grain boundaries and control the grain‐boundary mobility. However, due to the extremely thin (<2 nm) layer of segregated dopants, the experimental characterization of the segregated alumina grain boundaries is a complex task. Computational studies have focused only on tilt grain boundaries, which are only a small fraction in a sintered alumina sample. In this study, a quantitative characterization of the segregation of Y and La at general high angle grain boundaries in transparent alumina is carried out using a unique combination of advanced TEM and near coincidence grain‐boundary atomistic simulations. The result show that high angle grain boundaries may lead to enhanced grain growth in comparison to symmetric tilt twin grain boundaries due to the reduced configuration entropy for dopant segregation and higher order grain‐boundary complexions. On the other hand, multidoping with different dopants was shown to be more beneficial than single doping due to its contribution in increasing the configurational entropy for segregation. The advanced TEM analysis showed Y and La distributions and concentrations on a series of general grain boundaries in very good agreement with the atomistic simulations. This validation of atomistic modeling technique used in this study means, as it a generic method, can be used as a predictive tool to design ceramic microstructure and properties.     

Structures and electronic properties of symmetric and nonsymmetric graphene grain boundaries

The graphene grain boundaries with periodic length up to 18 Å have been studied using density functional theory. Atomic structures, thermodynamic stabilities and electronic properties of 40 grain boundaries with symmetric and nonsymmetric structures were investigated. According to the arrangements of pentagons and heptagons on the boundary, grain boundaries were cataloged into four classes. Some nonsymmetric grain boundaries constructed here have identical misorientation angles to the experimentally observed ones. The formation energies of grain boundaries can be correlated with the misorientation angle and inflection angle. Nonsymmetric grain boundaries possess comparable formation energies to their symmetric counterparts when the periodic length along the defect line is larger than 1 nm. Analysis of electronic density of states shows that the existence of a grain boundary usually increases the density of states near the Fermi level, whereas some symmetric grain boundaries can open a small band gap due to local sp²-to-sp³ rehybridization.     

Structure and Chemistry of Yttria-Stabilized Cubic-Zirconia Symmetric Tilt Grain Boundaries

The atomic structures of two symmetric [001] tilt grain boundaries in yttria-stabilized cubic-zirconia, Σ5 (310) and near-Σ13 (510), are studied by Z -contrast scanning transmission electron microscopy. Both boundaries are composed of periodic arrays of highly symmetric structural units, with a distinct unit for each boundary. Oxygen K -edge electron energy-loss spectra show that the oxygen coordination is similar between the bulk and grain boundary, indicating that oxygen ions within the grain boundary reside in distorted tetrahedral sites. Atomic models of the grain boundaries are proposed that are consistent with the experimental data. The core structures are different from previously studied metal or oxide grain boundaries and are unique to the fluorite structure. Yttrium segregation to the grain boundaries is also investigated by electron energy-loss spectroscopy. Yttrium is found to segregate preferentially to the Σ5 grain boundary, and the spatial distribution of the segregation layer is confined to within 1 nm of the boundary plane.     

Grain Orientation Dependence of the PTCR Effect in Niobium-Doped Barium Titanate

The positive temperature coefficient of resistivity (PTCR) effect is directly measured in single grain boundaries in 0.1-mol%-Nb-doped BaTiO₃ with 1 mm coarse grains. The PTCR effect largely depends on grain boundary structure. Random grain boundaries exhibit the PTCR effect as in polycrystalline samples, but the PTCR effect does not appear in highly coherent boundaries such as small-angle boundaries, twin boundaries, and coincidence site lattice (CSL) boundaries with low Σ values. For Σ= 3 boundaries, the resistance increase above the Curie temperature is a function of deviation angle. A small PTCR effect is observed in Σ= 3 boundaries with a deviation angle of about 9° in contrast with ideal Σ= 3 boundaries and boundaries with a deviation of about 4°.     

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.     

Formation of Grain Boundaries in Liquid-Phase-Sintered WC–Co Alloys

The origin of WC/WC grain boundaries in liquid-phase-sintered WC–Co alloys has been investigated in a WC–Mo₂C–Co model system using coarse WC polygrain powder. The evolution of grain shape during liquid phase sintering was able to be identified by observing a growth layer that contained Mo. During liquid phase sintering, most of the grain boundaries in the powder were penetrated by a Co liquid but some of them were not. Electron backscattered diffraction analysis confirmed that some boundaries in the powder, in particular, Σ2 twist boundaries and Σ97 special boundaries, remained intact during liquid phase sintering. These experimental results confirm that the grain boundaries of WC grains in liquid-phase-sintered WC–Co alloys originated from those present in the starting powder.     

The impedance of ceramics with highly resistive grain boundaries: validity and limits of the brick layer model

Impedance spectroscopy is an important tool to investigate the electrical properties of grain boundaries. For the analysis of the impedance spectra cubic grains, laterally homogeneous grain boundaries and identical properties of all grain boundaries are usually assumed (brick layer model). However, in real ceramics these assumptions are generally violated. Using the finite element method we calculated the impedance of several polycrystals exhibiting highly resistive grain boundaries with microstructures and grain boundary properties deviating from the simple brick layer model. Detours around highly resistive regions (e.g. due to high grain boundary density or enhanced grain boundary resistivity) can play an important role and lead to grain-boundary semicircles depending on bulk properties and even to additional semicircles. Conditions are discussed within which the brick layer model allows for a reasonable evaluation of the spectra.     

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.     

Varistor Behavior at Twin Boundaries in ZnO

The electrical behavior of commercial ZnO varistor devices has been examined with voltage contrast microscopy and point contact dc electrical measurements. Nonlinear voltage-dependent behavior has been observed across both of the major crystalline boundary types present in the system: Bi₂O₃ layer containing ZnO grain boundaries (or grain boundaries) and antimony spinel layer internal ZnO inversion twin boundaries (or twin boundaries). Twin boundaries, which bisect practically every grain in a typical commercial device, possess potential barriers with higher average breakdown voltages than do grain boundaries. Certain zinc antimonate spinel (Zn₇Sb₂O₁₂) grains are electrically isolated from the matrix, whereas others are conductive within the matrix.     

Strain enhanced defect reactivity at grain boundaries in polycrystalline graphene

Grain boundaries dominate the property of polycrystalline graphene. We report first-principles calculations and classical molecular dynamics simulations that reveal enhanced defect reactivity induced by an inhomogeneous strain field at grain boundaries. Strained carbon bonds located at heptagons and pentagons can accumulate interstitials and single vacancies, respectively. We find that recombination of vacancies and interstitials can occur locally at grain boundaries, which serve as effective sinks, resulting in efficient annealing of defects. The enhanced defect reactivity indicates that grain boundaries may be manipulated by point defects.     

Domain wall-grain boundary interactions in polycrystalline Pb(Zr0.7Ti0.3)O3 piezoceramics

Interactions between grain boundaries and domain walls were extensively studied in ferroelectric films and bicrystals. This knowledge, however, has not been transferred to polycrystalline ceramics, in which the grain size represents a powerful tool to tailor the electromechanical and dielectric response. Here, we relate changes in dielectric and electromechanical properties of a bulk polycrystalline Pb(Zr_0.7Ti_0.3)O₃ to domain wall interactions with grain boundaries. Samples with grain sizes in the range of 3.9–10.4 μm were prepared and their microstructure, crystal structure, and dielectric/electromechanical properties were investigated. A decreasing grain size was accompanied by a reduction in large-signal electromechanical properties and an increase in small-signal relative permittivity. High-energy diffraction analysis revealed increasing microstrains upon decreasing the grain size, while piezoresponse force microscopy indicated an increased local coercive voltage near grain boundaries. The changes in properties were thus related to strained material volume close to the grain boundaries exhibiting reduced domain wall dynamics.     

Electron-beam damage and point defects near grain boundaries in cerium oxide

Cerium oxide is a technologically important ceramic with applications in catalysis and potentially as an electrolyte for solid-oxide fuel cells (SOFCs). The technological interest is largely due to the behavior of oxygen vacancies in this material. Grain boundaries play an important role in oxygen vacancy diffusion and, although not completely understood, the influence of grain boundaries has been attributed to both a space-charge effect and the segregation of impurities. In this paper, results from spatially resolved electron-energy-loss spectroscopy (EELS) near grain boundaries in doped CeO₂ in a transmission electron microscope (TEM) are reported. The data are interpreted as the result of beam damage that varies as the electron beam is scanned across grain boundaries and suggest a spatially varying concentration of oxygen vacancies near the grain boundaries.     

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.     

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.     

Interface Character Distributions in WC–Co Composites

The geometric and crystallographic characteristics of interfaces in WC–Co composites with a range of grain sizes and carbide volume fractions have been comprehensively characterized. The carbide crystals are most frequently terminated by (0001) and     surfaces. The average number of carbide vertices per grain and the basal-to-prismatic face area ratio of the WC–Co interfaces increase with the carbide volume fraction. The three most frequently occurring WC/WC grain boundaries are 90° twist boundaries about     , 30° twist boundaries about [0001], and asymmetric 90° boundaries about     . The boundary populations do not vary with grain size or carbide volume fraction, suggesting that they are determined by the grain boundary energy anisotropy.     

Study of the local environment around zirconium ions in polycrystalline α-alumina in relation with kinetics of grain growth and solute drag

The aim of the present work, made up of two parts, consists in studying the behaviour of the local environment of the doping zirconium, in the polycrystalline α-alumina related to the material microstructure. At first, the kinetics of grain growth has been studied, and local chemical analyses on thin foils at grain boundaries using the energy dispersive X-ray spectroscopy (EDXS) technique, were performed. In the second part, we shall consider the evolution of the local order around the doping element, related to the microstucture, by X-ray absorption spectroscopy (XAS) measurements. This study was performed on doped α-polycrystalline alumina (0.03 wt% ZrO₂) samples. According to the experimental results, we can show a great interaction between the zirconium and the grain boundaries of the alumina: during the grain growth, grain boundaries drag most of the doping element in solid solution. A transition in the environmental configuration around the doping in grain boundaries is observed, when the segregation ratio of the zirconium in grain boundaries reaches the value of about (4±2)×10³. In these conditions, a change in the local order is observed, around the segregated zirconium. This change varies from a statistical disorder to an ordered state, and can be described as an assembly of nanocrystalline metastable, tetragonal zirconia particles. This transition of the environmental configuration in grain boundaries is correlated to the increase of the grain growth velocity, according to the kinetics studies.