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.     

Dislocation Structures of Low-Angle and Near-Σ3 Grain Boundaries in Alumina Bicrystals

Alumina bicrystals with low-angle and near-Σ3 <0001> tilt grain boundaries were fabricated using diffusion bonding to study the dislocation structures in alumina grain boundaries. The resulting grain-boundary structures were investigated using high-resolution transmission electron microscopy, and the grain-boundary energies were analyzed using theoretical calculations. It was found that partial dislocations with Burgers vectors of the type return ⅓<10[Onemacr]0> were periodically located in the boundaries and that a stacking fault between pairs of partials was formed in such boundaries. The length of the stacking fault decreased with increased misorientation angles, which was reasonably predicted by the theoretical calculation. In the case of a near-Σ3 grain boundary, an array of displacement shift complete dislocations with the Burgers vector of return ⅓<1[Onemacr]00> was periodically formed along the boundaries. These boundaries did not have stacking faults. The spacing between the dislocations decreased with increased deviation angle from the exact-Σ3 boundary with the tilt angle of 60°.     

Molecular dynamics study of UO2 symmetric tilt grain boundaries around [001] axis

Molecular dynamics and CRG empirical potential are used in this work to study the symmetrical tilt grain boundaries around the [001] axis in UO₂. The analysis of atomic structures obtained by simulation shows excellent agreement with the Read and Schokley model (Read WT, Shockley W. Dislocation Models of Crystal Grain Boundaries. Physical Review. 1950;78:275) predicting the existence of regular dislocations in these grain boundaries. We calculated their energy of formation and cleavage as well as the energy of formation of Schottky defects and incorporation of xenon and krypton atoms in their proximity. This allowed us to determine how these properties evolve for this series of grain boundaries presenting similar geometric characteristics, as a function of the misorientation angle. In addition, the boundary between small and large misorientation grain boundaries has been determined around 20°, close to the value of 15° reported in literature.     

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.     

Mechanical strength characteristics of asymmetric tilt grain boundaries in graphene

We investigate the ultimate strengths and failure types of asymmetric tilt grain boundaries (GBs) with various tilt angles with the aid of molecular dynamics simulations and analytic theory. The tensile strength of armchair-oriented graphene GBs shows a tendency to increase as the misorientation angle rises, while that of zigzag-oriented graphene GBs non-monotonically increases. The overall strength enhancement and weakening behaviors can be explained by a continuum stress analysis of pentagon–heptagon defects along GBs. Nevertheless, full atomistic analyses are required to predict the exact bonds from which mechanical failure initiate. Two different fracture types are observed in our studies; one with cracks growing along the GB and another with cracks growing away from the GB. Detailed understanding of the atomic arrangement along the GB, in addition to defect density, is necessary to ascertain the ultimate strength and rupture process of GBs.     

Geometry and Electrical Properties of Grain Boundaries in Manganese Zinc Ferrite Ceramics

For large-grained manganese zinc (MnZn) ferrite ceramics, grain misorientation determined by electron backscatter diffractions and grain-boundary resistance measured using microcontact impedance spectroscopy have been correlated. The degree of oxidation of grain boundaries and, hence, the barrier height depends on the overall grain-boundary network as well as on the individual boundary structure; therefore, a statistical analysis has been performed based on several hundreds of local measurements. When the boundaries are divided into low- and high-resistance groups, statistically significant differences in rotation axis and angle distributions are found. The misorientation distribution of the low-resistance boundary group is suggested to reflect the low-energy configurations of boundary planes in MnZn ferrites.     

Stability and Surface Energies of Wetted Grain Boundaries in Aluminum Oxide

The stability of a calcium-aluminum-silicate liquid film between two near-basal plane surfaces of sapphire at 1650°C was studied. Samples were prepared having an average basal misorientation across the interface of 6–7° about < 〈10 1 0〉. The interfaces varied in orientation from 0° to ∼38° to the [0001] direction. Three types of interfaces were observed: faceted, solid-liquid interfaces; low-angle grain boundaries consisting of aligned arrays of dislocations; and boundaries consisting of alternating regions of dislocations and faceted solid-liquid interfaces. The type of interface observed depended on the orientation of the interface and could be predicted by using a construction based on Wulff shapes. Because the type of interface depends on crystal alignment and interface angle, these results suggest an absolute method of determining the surface free energy of wetted boundaries.     

Dislocation analysis of a complex sub-grain boundary in UO2 ceramic using accurate electron channelling contrast imaging in a scanning electron microscope

In this work, accurate electron channelling contrast imaging (A-ECCI) assisted by high resolution selected area channelling patterns (HR-SACP) was used to characterize the structure of a complex low sub-grain boundary in a creep deformed uranium dioxide (UO₂) ceramic. The dislocations were characterized using TEM-style g·b = 0 and g·b × u = 0 contrast criteria. Misorientations across the boundary were measured using HR-SACPs with 0.04° precision and high accuracy EBSD. The boundary was determined to be asymmetric and mixed in nature, composed of two distinct regions with different dislocation morphologies and a misorientation below 0.5°. The A-ECCI, HR-SACP, and HR-EBSD results are consistent, confirming A-ECCI as a powerful tool for characterizing even complex dislocations structures using scanning electron microscopy. This is particularly true for UO₂, since this material is very difficult to thin, which makes TEM examination of sub-boundaries over the scale of several micrometers difficult. Furthermore, in this study, the change in dislocations arrangement along the breath of the complex low angle sub-grain boundary is related to the misorientation across the boundary.     

A theoretical evaluation of the temperature and strain-rate dependent fracture strength of tilt grain boundaries in graphene

Based on molecular dynamic simulations, we investigate the effects of temperature and strain rate on the strength of single layer graphene with tilt grain boundaries under tension. The simulation results show that temperature plays an important role in the strength of graphene with grain boundaries. The strength of graphene with grain boundaries decreases significantly as temperature increases. In particular, we confirm a previous report that graphene with large angle tilt boundaries (which has a high density of defects) may be much stronger than that with low angle boundaries. This finding holds true for temperatures from 10 to 1800 K and strain rates from 0.0001 to 0.01 ps⁻¹.     

The mechanical responses of tilted and non-tilted grain boundaries in graphene

Various mechanical characteristics of tilted and non-tilted grain boundaries in graphene were investigated under tension and compression in directions perpendicular and parallel to the grain boundaries using molecular dynamics simulation. In contrast to the non-tilted grain boundary and the pristine graphene, the mechanical response of tilted grain boundary was observed to be quite unique under perpendicular tension, exhibiting distinct crack propagation prior to tensile failure and the subsequent pattern of incomplete fracture. These features are manifested as a remarkable decrease in the slope and a rugged pattern in the stress–strain curves. The characteristic of incomplete fracture was striking especially for large misorientation angles with formation of long monoatomic carbon chains, suggesting a methodology for feasible production of the monoatomic carbon chains that have been difficult to synthesize and extract. Under perpendicular compression, the folding of the sheet occurred consistently along grain boundaries during the entire process, indicating a tunable folding, while the folding line wandered extensively for pristine graphene. Under parallel compression, we found that folding along grain boundaries disturbed the bending of the graphene substantially for intrinsic reinforcement.     

Electronic transport through ordered and disordered graphene grain boundaries

The evolution of electronic wave packets (WPs) through grain boundaries (GBs) of various structures in graphene was investigated by the numerical solution of the time-dependent Schrödinger equation. WPs were injected from a simulated STM tip placed above one of the grains. Electronic structure of the GBs was calculated by ab-initio and tight-binding methods. Two main factors governing the energy dependence of the transport have been identified: the misorientation angle of the two adjacent graphene grains and the atomic structure of the GB. In case of an ordered GB made of a periodic repetition of pentagon−heptagon pairs, it was found that the transport at high and low energies is mainly determined by the misorientation angle, but the transport around the Fermi energy is correlated with the electronic structure of the GB. A particular line defect with zero misorientation angle Lahiri et al., behaves as a metallic nanowire and shows electron–hole asymmetry for hot electrons or holes. To generate disordered GBs, found experimentally in CVD graphene samples, a Monte-Carlo-like procedure has been developed. Results show a reduced transport for the disordered GBs, primarily attributed to electronic localized states caused by C atoms with only two covalent bonds.     

High temperature deformation of a 5 wt.% zirconia-spinel composite: influence of a threshold stress

Creep experiments performed on a 5 wt.% zirconia- MgAl₂O₄ spinel material, in the stress and temperature ranges 8–200 MPa and 1350–1410°C, have shown the importance of grain boundaries in deformation of this material. Deformation can be analysed as the result of two sequential contributions. At low stress, an increase in the apparent stress exponent and the occurrence of a threshold stress, whose value roughly varies inversely proportional to spinel grain size, were observed. At high stress, grain boundary diffusion is the most likely mechanism that controls the grain boundary sliding. These observations are consistent with previous experiments showing that sliding of spinel/spinel boundaries is more difficult than sliding of spinel/zirconia boundaries in the low stress range. The plastic flow is analysed by means of grain boundary dislocations whose density increases with stress. At low stress, when the density of boundary dislocations is low, creep rates are interface-controlled while at high stress, when the boundary dislocation density is large, rates are limited by the long-range diffusion process.     

Intrinsic energy dissipation in CVD-grown graphene nanoresonators

We utilize classical molecular dynamics to study the quality (Q)-factors of monolayer CVD-grown graphene nanoresonators. In particular, we focus on the effects of intrinsic grain boundaries of different orientations, which result from the CVD growth process, on the Q-factors. For a range of misorientation angles that are consistent with those seen experimentally in CVD-grown graphene, i.e. 0° to ～20°, we find that the Q-factors for graphene with intrinsic grain boundaries are 1-2 orders of magnitude smaller than that of pristine monolayer graphene. We find that the Q-factor degradation is strongly influenced by both the symmetry and structure of the 5-7 defect pairs that occur at the grain boundary. Because of this, we also demonstrate that the Q-factors of CVD-grown graphene can be significantly elevated, and approach that of pristine graphene, through application of modest (1%) tensile strain.     

Distribution in angular mismatch between crystallites in diamond films grown in microwave plasma

High resolution electron backscattered diffraction (EBSD) has been used for analysis of grain size, texture and stress distribution on growth side of free-standing polycrystalline diamond films of different grade. The undoped and moderate boron-doped films of 0.3–0.5 mm thickness were grown by microwave plasma CVD. The highest number of stressed domains, mostly located at grain boundaries, and the largest average grain misorientation angle (θ ≈ 6°) have been found for B-doped film. Highly defected and highly [001] oriented “black” diamond exhibited much more rear stress domains, this being ascribed to angular mismatch as small as θ = 0.5° in that film. The samples of “white” diamond showed somewhat intermediate pictures, with stress observed both in bulk and on grain boundaries. Evolution of texture (columnar growth) and stress distribution with film thickness has been observed with EBSD study of film cross-sections.     

Abnormal grain growth in iron-containing SiC fibers

Understanding the role of sintering aids during microstructure evolution is critical to the manufacture of densified SiC fibers. A variety of TEM characterization techniques are combined to investigate grain growth behavior in iron-doped SiC fibers. Ultra-large SiC grains in micron size, as the self-assembly of nano sub-grains into a similar orientation, were consistently discovered at the surface and indicative of abnormal grain growth. The growth front consisted of polycrystalline nanograins wetted by iron-rich particles, where several sub-grains were found to unify their (111) planes with a misorientation angle less than 10°, indicating grain rotation at the growth front. It is proposed that iron-rich particles form a quasi-liquid interfacial phase during sintering, which facilitates coherent attachment of grains and results in fast grain growth using neighboring irregular-shaped nanograins as building blocks. The imperfect ordered coalescence of nanograins introduces structural heterogeneities, including low angle grain boundaries and porosities.     

Probing lamellar twins in spark plasma sintered CaTiO3 using Electron Backscattered Diffraction

The twinning characteristics of spark plasma sintered CaTiO₃ with orthorhombic perovskite structure is critically analysed using Electron Backscatter Diffraction (EBSD) technique. The twins are characterized by a sub-micron interlamellar spacing with a misorientation of ≈ 90°. The crystallographic relationship between the matrix and the twin has been analysed in terms of misorientation matrix using the Kikuchi patterns obtained from the EBSD scan. From the analysis of angle/axis pairs at the boundary, the twin axis was found to be of type [101]. These twins with high angle boundaries are expected to enhance fracture resistance through crack deflection and crack tip shielding mechanisms.     

Influence of Y and La Additions on Grain Growth and the Grain‐Boundary Character Distribution of Alumina

Grain‐boundary character distributions (GBCDs) were determined for spark plasma sintered Y‐ and La‐doped aluminas prepared at temperatures between 1450°C and 1600°C. La doping leads to grain boundaries that adopt (0001) orientations 3.7 times more frequently than expected in a random distribution, whereas the Y‐doped microstructures are more equiaxed. At 1500°C, some of the boundaries in the Y‐doped samples transform to a higher mobility complexion; in this microstructure, the grain‐boundary plane is 1.3 times more likely to occur than expected in a random distribution. After the fast‐growing grains impinge, the dominant plane becomes and these boundaries have areas that are 1.2 times more likely to occur than expected in a random distribution. The grain‐boundary planes in the Y‐ and La‐codoped samples preferred (0001) and orientations, combining the characteristics of the singly doped samples. Grain boundaries with a 60° misorientation about [0001] were up to six times more common than random in the Y‐doped samples. The preference for (0001) oriented grain‐boundary planes in the La‐doped sample persisted at all specific misorientations.     

Is the failure of large-area polycrystalline graphene notch sensitive or insensitive?

We perform molecular dynamics simulations on large-area polycrystalline graphene containing a pre-existing circular notch with focus on the notch effect on tensile strength and failure pattern. Our results show that the failure of polycrystalline graphene becomes notch-sensitive if there is an overlapping of stress concentration zones induced by the notch and grain boundaries (GBs); otherwise, the failure becomes notch-insensitive. More specifically, when the notch diameter is larger than the average grain size, the failure is generally notch-sensitive. However, if the notch size is smaller than the grain size, whether the failure is notch-sensitive or not depends on the notch location. These observations can be well explained by following attributes: (1) Both GBs and circular notch can create stress concentration; (2) The stress concentration created by the notch is generally weaker than that by GBs; and (3) The strength of GBs is weaker than that of the grain interior. Our work provides useful guideline for designing polycrystalline graphene for structure and device applications.     

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.