Atomic-scale mechanism of grain boundary motion in graphene

Grain boundaries (GBs) in graphene can migrate when irradiated by electron beams from a transmission electron microscope (TEM). Here, we present an ab initio study on the atomic scale-mechanism for motion of GB with misorientation angle of ∼30° in graphene. From total energy calculations and energy barrier calculations, we find that a Stone–Wales (SW)-type transformation can occur more easily near GBs than in pristine graphene due to a reduced energy barrier of 7.23 eV; thus, this transformation is responsible for the motion of GBs. More interestingly, we find that a mismatch in the crystalline orientation at GBs can drive the evaporation of a carbon dimer by greatly reducing the corresponding overall energy barrier to 11.38 eV. After evaporation of the carbon dimer, the GBs can be stabilized through a series of SW-type transformations that result in GB motion. The GB motion induced by evaporation of the dimer is in excellent agreement with recent TEM experiments. Our findings elucidate the mechanism for the dynamics of GBs during TEM experiments and enhance the controllability of GBs in graphene.     

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.     

Anomalous mechanical characteristics of graphene with tilt grain boundaries tuned by hydrogenation

Grain boundaries (GBs) as typical defective graphene structure have significant influence on its mechanical properties. The fracture strength of hydrogenated graphene with tilt GBs composed of pentagon–heptagon defects are systematically investigated using classical Molecular Dynamics (MD) method. Anomalous mechanical characteristics are revealed for graphene with hydrogenation either on or near the GBs. For graphene sheets with hydrogenation on tilt GBs under perpendicular pulling, the strength of hydrogenated GBs with large tilt angle is anomalously stronger than low-angle tilt boundary having fewer defects because of the interaction between polar stress fields of hydrogenated pentagon–heptagon defects. For graphene with hydrogenation near the GBs, the interaction between GBs and hydrogenated domains at different distance intervals is investigated. The strength is found to be governed by the peak normal stress in hydrogenated domain, and an exponential relationship between the normal strength and distance interval is revealed as a result of the stress field overlap between GB and hydrogenation interface. Our results gain meaningful insight into the effects of hydrogenation on the strength of graphene with tilt GBs, and provide guidelines for designing high-quality hydrogenated graphene-based nanodevices.     

Edge effect on electronic transport properties of graphene nanoribbons and presence of perfectly conducting channel

Numerical calculations have been performed to elucidate unconventional electronic transport properties in disordered nanographene ribbons with zigzag edges (zigzag ribbons). The energy band structure of zigzag ribbons has two valleys that are well separated in momentum space, related to the two Dirac points of the graphene spectrum. The partial flat bands due to edge states make the imbalance between left- and right-going modes in each valley, i.e. appearance of a single chiral mode. This feature gives rise to a perfectly conducting channel in the disordered system, i.e. the average of conductance 〈g〉 converges exponentially to 1 conductance quantum per spin with increasing system length, provided impurity scattering does not connect the two valleys, as is the case for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through inter-valley scattering, display ordinary localization behavior. Symmetry considerations lead to the classification of disordered zigzag ribbons into the unitary class for long-range impurities, and the orthogonal class for short-range impurities. The electronic states of graphene nanoribbons with general edge structures are also discussed, and it is demonstrated that chiral channels due to the edge states are realized even in more general edge structures except for armchair edges.     

Anomalous thermal transport along the grain boundaries of bicrystalline graphene nanoribbons from atomistic simulations

We investigate the thermal transport properties of bicrystalline graphene nanoribbons (bi-GNRs) with different symmetric tilt grain boundaries (GBs) by using the molecular dynamics (MD) simulations. It is found that the bi-GNR with the 10.98° GB (the highest dislocation density) has an anomalously enhanced thermal conductivity for the heat flux along the GB compared to other ribbons with lower dislocation densities. This is in strong contrast to the behavior of thermal conductivity across the GB, which decreases monotonically with increasing the dislocation density. We attribute this counterintuitive phenomenon to its non-folding structure and lower edge stress, which can reduce the phonon scatterings induced by GBs and rough edges. In addition, we also examine the effects of the characteristic length and temperature on the thermal conductivity of the bi-GNRs through the phonon Boltzmann transport equation. At any given temperature and characteristic length, the low-dislocation-density bi-GNR are shown to be much more efficient in suppressing the thermal conductivity, and has a higher tailoring rate. These facts reveal the bi-GNR with a lower dislocation density is more promising to be a high figure of merit thermoelectric material.     

A molecular dynamics survey of grain boundary energy in uranium dioxide and cerium dioxide

Uranium dioxide (UO₂) is the primary fuel material that is used in current nuclear reactors. As one of the most fundamental material parameters, grain boundary (GB) energy strongly influences many fuel properties, and the influences depend on the characters and properties of individual GBs. Using molecular dynamics simulations, a high throughput survey of GB energy in UO₂ was carried out for the purpose of elucidating the roles of GB geometry such as misorientation and inclination, as well as the bonding nature of UO₂, in affecting GB energy. GB energies in CeO₂ were calculated as well for comparison with UO₂ to investigate the generality of GB energy anisotropy in fluorite phase oxides. The results show significant GB energy anisotropy in both UO₂ and CeO₂ that is associated with the cubic symmetry of the fluorite structure. More interestingly, the GB anisotropy is found to be dependent not only on the crystal structure but also the ionic bonding. As such, the GB energy anisotropy in fluorite oxides has significant differences compared with that in fcc metals. The data obtained and the increased knowledge on GB anisotropy will facilitate GB engineering for nuclear fuels with improved 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 shear response of <001> tilt grain boundary in titanium nitride

The equilibrated structures and shear responses of <001> titanium nitride (TiN) symmetric tilt grain boundaries (GBs) are investigated using molecular dynamics simulation. The equilibrated GBs are only composed of the kite-shaped structures connected with edge dislocation cores. From the shear response analysis of TiN GBs, we find that there exist two major deformation modes, i.e., GB sliding and shear deformation coupled with GB motion (shear-coupling). GB sliding may finally lead to the GB fracture and the shuffling of GB atoms. The shear-coupling could be further divided into the ideal and non-ideal ones. For the ideal shear-coupling, the shear deformation coupling with GB motion can be exactly described by a factor solely dependent on the GB tilt angle. However, it is not if the additional shear deformations caused by GB sliding or vacancy emission occur during the shear-coupling. Based on the geometrical analysis of atomic deformation mechanism in GB, we propose two theoretical coupling factors to describe the shear-coupling with the additional GB shear deformations. In addition, the deformation mode of GBs could be changed by elevating the temperatures and adding vacancies into GBs.     

Detailed temperature dependence of the space charge layer width at grain boundaries in acceptor-doped SrTiO3-ceramics

The influence of temperature and the donor-type grain boundary (GB) states on the width of the space charge layer d_GB at GBs in SrTiO₃ ceramics was investigated by comparing numerical simulation results with experimental data. According to recent results for the potential barrier height at the GB, the temperature behaviour of d_GB can be divided into two different regimes. For lower temperatures, d_GB is independent of the temperature, for higher temperatures it decreases with rising temperature due to a change in the occupation of the electronic GB donor states. By decorating the GB with suitable dopants, the space charge layer width and its temperature dependence can be influenced. This is due to a change of the effective GB charge.     

CSL grain boundary distribution in alumina and zirconia ceramics

The distributions of general and coincidence site lattice (CSL) grain boundaries (GBs) in texture-free alumina and zirconia ceramics sintered at two different temperatures were investigated based on electron backscatter diffraction (EBSD) measurements. Results were compared with the distributions obtained from random 2D spatial models and with calculated random distributions reported in the literature. All alumina samples independent on sintering temperature show the same characteristic deviations of the measured general GB distributions from the random model. No such features can be seen in zirconia. The total fractions of CSL GBs in alumina and zirconia samples are clearly larger, for both sintering temperatures, than those observed in the random simulations. A general GB prominence factor, similar to the twin prominence factor for fcc metals, was defined to simplify the representation of the CSL GB content in zirconia. The observed deviations from the random model show no dependence on sintering temperature nor on lattice geometry. In alumina, however, the change in the CSL GB character distribution with sintering temperature seems to be crystallographically controlled, i.e. directly dependent on the orientation of the CSL misorientation axis.     

Conductance of Graphene Nanoribbon Junctions and the Tight Binding Model

Planar carbon-based electronic devices, including metal/semiconductor junctions, transistors and interconnects, can now be formed from patterned sheets of graphene. Most simulations of charge transport within graphene-based electronic devices assume an energy band structure based on a nearest-neighbour tight binding analysis. In this paper, the energy band structure and conductance of graphene nanoribbons and metal/semiconductor junctions are obtained using a third nearest-neighbour tight binding analysis in conjunction with an efficient nonequilibrium Green's function formalism. We find significant differences in both the energy band structure and conductance obtained with the two approximations.     

Molecular Dynamics Simulation of Oxygen Ion Diffusion in Yttria Stabilized Zirconia Single Crystals and Bicrystals

Molecular dynamics simulation studies have been performed to study the oxygen ion diffusion in yttria stabilized zirconia single crystals and bicrystals separated by tilt grain boundaries (GBs). Two types of GBs which are Σ 5 (3 1 0) and Σ 13 (5 1 0) are studied at temperatures between 1,000 K and 2,000 K. The effect of grain size, which is the distance between two GBs, and the effect of GB orientations are systematically investigated in this study. The oxygen diffusion in the bicrystals is found to be blocked by the GB, and the blocking effect increases with decreasing grain size and is affected by different grain orientations. In addition, the oxygen diffusion along the GB plane is most hindered.     

Atomic Structure of ZnO Σ13 [0001]/{130} Symmetric Tilt Grain Boundary

Zinc oxide (ZnO) is used for a wide range of electrical applications, where its grain boundaries (GBs) possibly influence the physical properties. It is important to determine the GB structure in atomic scale to understand GB effects on the electrical properties. In this study, the atomic structure of a ZnO GB is investigated in detail by scanning transmission electron microscopy and theoretical calculations. It is shown that the atomic structure of ZnO Σ13 [0001]/{130} 32.2° symmetric tilt GB is constructed as an array of structural units (SUs) of six‐ and eight‐membered rings. The GB has two different SU alignments. The dominant structure of the GB is the zig‐zag SU alignment and the secondary one is the straight SU alignment. The relation between the SU alignment and the rotation angle has been determined.     

Experimental and numerical assessment of grain boundary energies in polycrystalline uranium dioxide

Uranium dioxide ceramics are widely used as nuclear fuels. Thus, it is important to understand the role of the grain boundaries (GBs) which decisively govern the properties of these polycrystalline materials and subsequently determine their performances. Here, we report a coupled numerical - experimental approach enabling to assess GB energies. Firstly, GB formation energies (γ_gb) were computed for 34 symmetric tilt GBs in UO₂ with molecular dynamics simulations at 1700 K. The surface energies (γ_S) relative to the respective planes of these GBs were calculated as well. The Herring relation was then used to assess the dihedral angles Ψ of the corresponding GB grooves. Secondly, a UO₂ ceramic sample was annealed at 1673 K to obtain GB grooves. The CSL GBs of interest were identified by EBSD and their Ψ angles determined by AFM. Computed and measured Ψ values were found to be very close.     

Distribution of Σ3 misorientations in polycrystalline strontium titanate

SrTiO₃ is a potential electrolyte material for solid-oxide fuel cells due to its high ion conductivity. Grain boundaries (GBs) play an important role in bulk ion conductivity. It has been reported that the resistance of Σ3 GBs is much lower than the general GB in SrTiO₃. In order to clarify the conflicting reports on the prevalence of Σ3 GBs in SrTiO₃, grain size and GB misorientations in Nb-doped and undoped SrTiO₃ have been investigated as a function of annealing time. The observations suggest that the prevalence of both low-angle GBs and Σ3 GBs is strongly correlated to both abnormal grain growth and annealing time. In particular, the Σ3 GB population approaches that predicted by the Mackenzie random distribution when abnormal grain growth dominates.     

Effects of dislocation densities and distributions on graphene grain boundary failure strengths from atomistic simulations

The failure strengths of graphene grain boundaries, over a range of misorientation angles from 0° to 60°, are investigated by molecular dynamics simulations. A correlation between the level of bond pre-strain and bond rupture is revealed. It is shown that the distribution of grain boundary dislocations is, in addition to the misorientation angle, also an important factor in determining the failure strength. For grain boundaries featuring a uniform dislocation distribution, a higher misorientation angle will yield a higher failure strength as a result of overlapping and mutual cancelation of the strain fields of neighboring dislocations. For grain boundaries with a non-uniform dislocation distribution, however, local structural inhomogeneity introduces large local tensile stresses and the failure strength decreases significantly. Therefore, a complicated interplay exists between the dislocation density and distribution, and the failure strength of graphene grain boundaries.     

First-principles study of spin-dependent transport through graphene/BNC/graphene structure

First-principles study on the electronic structure and transport property of the boron nitride sheet (BNC) structure, in which a triangular graphene flake surrounded by a hexagonal boron nitride sheet, is implemented. As the graphene flake becomes small and is more isolated by the boron nitride region, the magnetic ordering of the flake increases. When the BNC structure is connected to the graphene electrodes, the spin-polarized charge-density distribution appears only at the triangular graphene flake region, and the electronic structure of the graphene electrode is not spin polarized. First-principles transport calculation reveals that the transport property of the BNC structure is spin dependent.     

Electron hopping conduction in highly disordered carbon coils

Carbon coils of micrometer to nanometer wire diameter were grown bi-directionally by catalyst-assisted chemical vapor deposition. Electron microscope images showed the highly disordered structure of the carbon coils. Chemical compositions of the coils were identified with elemental analysis, atmospheric pressure-laser desorption ionization-Fourier-transform ion cyclotron resonance-mass spectroscopy and secondary ion mass spectrometric characterizations, and attenuated total reflection-infrared spectroscopic examination. Micro-Raman scattering spectroscopy and electron energy loss spectroscopy were also used to study the vibrational and electronic properties of the helical structure. The electric transport in a single carbon coil was measured from ambient temperature to 64 mK. The temperature-dependent resistance was analyzed with the Efros-Shklovskii variable range hopping model, indicating three-dimensional electron hopping conduction in the disordered helical wires. The analysis also provides a basic understanding of the electron transport with an electron hopping length of ∼5 nm inside the disordered carbon coils.     

Structural analysis of carbon nanofibres grown by the floating catalyst method

Submicron vapour grown carbon fibres (carbon nanofibres) grown by the floating catalyst method (Sample A), using hydrogen sulphide and ammonia to suppress soot formation, have been subjected to a comprehensive structural analysis, by high resolution transmission electron microscopy, PEEL, X-ray diffraction and gas adsorption. Results were compared to those obtained from an industrial sample (Sample B). Both fibres were found to be hollow but with different internal and external diameters. Sample A comprised approximately 90% fibres and 10% soot, which could not easily be separated; the fibres consisting of disordered graphene planes (with the c axis approximately perpendicular to the length of the fibre axis) which became more ordered after heat treatment (2730°C). Sample B consisted of fibres with a complex duplex structure also exhibiting disordered graphene planes; upon heat treatment there was a loss of the duplex structure and an increase in graphitic ordering. The graphitisability was similar for both fibres. Although Sample B had the greater diameter it also displayed the highest BET area.