| The perfect graphene has perfect properties.However,due to the restrictions in graphene manufacturing,the presence of defects is inevitable,especially the topological defects-dislocation.One of the unique properties of the graphene lattice is its ability to reconstruct by forming nonhexagonal rings.These defects have huge influence on the materials.The studies about the topological defects in graphene are hot issues now.Most of the physical properties of a dislocation and physical effects induced by dislocations are dominated by its structure.Only when we know how the dislocation looks like,do we understand how they affect with the properties of materilas.The lattice theory for the structure of dislocations has been developed recently based on the Peierls-Nabarro model and the lattice dynamics.The discrete dislocation equation with the γ-potential of graphene is used to determine the mismatch field that represent abrupt leap between the bilateral sides of the cut-line.The mismatch field is explicitly obtained through variational principle.The structure of dislocation is described by the distribution of the dislocation density,which is related to the gradient of the mismatch field.The stress field of the defect can be dominated by the density distribution that is actually the source of the field.The theoretical results have been compared with that obtained by the first principle calculation.It is found that when the correction of bond formation is taken into account,the theory provides a satisfactory description to the dislocation feature,such as formation energy,structure and displacement field.The topology defect in a material always acts as the source of the internal stress.The positive values of internal stress represent the stretching and the negative values represent the extrusion.Because the graphene is typical two-dimension material,and there is no limit on the third dimension,graphene can easily buckle into the third dimension.The approximate solution of the buckling is obtained based on the internal stress distribution and is proved to be suitable by the simulation method.The position of the highest buckling is confirmed from the theory to be at the vertex of the pentagon far away from the heptagon.The critical stress 1.36cσ =μ is obtained,as well as the breadth of the buckling 1.83aη =.The buckling is strongly influenced by the internal stress and the distance between the extrusive area and stretching area.While the dislocation structure in the ground state is known,an important question naturally arises: what is the structure of a moving dislocation? Unfortunately,atomic-scale investigations of the core evolution for moving dislocation in a bulk material are beyond the spatial and temporal limits of current characterization techniques.The intermediate state of the moving dislocation in graphene is obtained theoretically in this paper.Similar to the experimental case,where the dislocation is firstly excited from the energy valley to high energy state by the electron irradiation and then falls freely to the new energy valley,we initially calculate the excitation state located at the saddle point of the energy landscape.This special excitation state is an unstable equilibrium structure of the dislocation.The dislocation at the saddle point falls freely to the energy valley along the path determined by the dynamics laws.As the dislocation falls to the bottom of the valley,it moves forward a distance that equals half a Burgers vector.The creation and annihilation of SW defects are also studied based on the intermediate state.There exist a platform,rapid drop and slowly varying tail in the energy curve.The unusual behavior of the energy curve is mainly originated from the breaking and forming of the covalent bonds located at the dislocation core.It is possible that the similar behavior would appear commonly in the energy curves of the covalent materials.The shape of the energy curve may provide deep insight to the mechanism of the brittle feature of covalent materials. |
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