Theoretical Investigation Of Misfit Dislocation And Dislocation Induced Buckling

The function of the material is determined by its structure.Materials usually have defects,and dislocation as a line defect can be found in a large number of crystalline materials,so people can use transmission electron microscopy(TEM)to observe the microscopic images of the dislocation in the materials.Dislocation can be regarded as the dividing line between the slipped part and the un-slipped part of the crystal.As a kind of topological defects,it will greatly affect the physical properties of the material,especially the change of mechanical properties.With the development of science and technology,people are no longer satisfied with traditional materials composed of single elements,which makes the research and development of composite materials become a hot topic.Composite materials are usually composed of two or more kinds of materials.There are often a large number of dislocations at the adhesive interface,which causes the change of material ductility,deformation resistance and high temperature resistant.Interfaces play crucial roles in determining the properties and performance of materials,this has also led to a lot of research on it.In fact,studies of the properties of the interfaces between dissimilar materials began in the middle of the twentieth century,partly with the aim of controlling the properties of materials by gaining an understanding of their atomic structure and adhesive energy.In this thesis,a generalized Frenkel-Kontorova model is used to investigate the chain buckling induced by a topological defect.Since then,based on the solution of the balance problem for a semi-infinite lattice,we propose a generalization of the Peiels-Nabarro equation and apply it to a boron nitride/aluminum nitride heterostructure with a large lattice mismatch.The main works are as follow:(1)Buckling induced by a topological defect in a chainConsider that the appearance of dislocation in the material will cause a corresponding stress field around it.When internal compressive stress caused by the dislocation is large enough,the material will be buckle into a new dimension to reduce the stress and lower the elastic energy.In fact,Yakobson's group discussed the relationship between buckled behavior in graphene and the stress field generated by dislocations in it.Since then,based on the elastic theory and lattice theory of dislocation,Shaofeng Wang et al.have theoretically investigated buckling of dislocation in graphene.To understand the micro-mechanism of defect-induced buckling,we extended earlier work on F-K model by Frenkel and Kontorova to study the behavior of atomic chain buckling which was caused by internal stress.By using the generalization of the F-K model which is allowed to release the transverse displacement,the dynamics of the defect-induced Euler buckling is investigated for a flexible chain.In fact,Landau's theory can clearly illustrate the evolution process of kink-induced buckling,which is composed of the gestation stage and growth stage.The integration constant in the solution of Landau theory represents the gestation time.At the gestation stage,the unstable mode struggles to emerge from the initial random fluctuation.It is usually considered as a coarsening process.The growth stage describes the macroscopic mode grows with the time,and it grows by obeying the macroscopic laws until it finally arrives at the new stable equilibrium.The spatial pattern of the buckling induced by the anti-kink is an antisymmetric shape regarding the maximum stress point.For the internal compressive stress generated by anti-kink under the given width of kink,we find that the condition of chain self-buckling depends on the chain length and the yield constant,and this phase transition curve is a linear function.When the yield constant is closer to the critical constant,it will occur critical slowing down.(2)Generalized Peierls-Nabarro model for studying misfit dislocationFor the misfit occurring at the interface between two dissimilar materials,theoretical investigation of interfacial misfit dislocation has been investigated through the solution of the balance problem for a semi-infinite crystal.Following the Peierls-Nabarro approach,when two semi-crystals glue together along a given surface,the misfit dislocation equation is obtained by the Fourier transforms.This generalization of the P-N equation describes the relationship between the relative displacement of the adhesive surface and the effective interaction force.In addition to the generalization of the P-N equation similar to the equation derived by Yao et al.,the relationship between the mass center displacement and the relative displacement has been presented explicitly.Based on the solution of the misfit dislocation equation,it provides a theoretical basis for determining interfacial atomic configuration in a heterostructure.It is found that the interfacial atomic positions and the energy of misfit dislocation depend on a parameter? that represents the combined effect of three factors: the misfit,the elastic constants and the interfacial bond strength.This theory is applied to a BN/Al N heterostructure,where the lattice mismatch between BN and Al N is larger than 20%,the misfit dislocation structure and misfit dislocation energy have been studied in detail.The misfit dislocation energy cannot be obtained directly by the first-principles calculation,here we introduce the adhesive work which is the key to understand the microscopic mechanism controlling the strength and fracture of composite materials.In order to verify the reliability of the theoretical results,the adhesion energy of the BN/Al N heterostructure has also been evaluated,and the theoretical result coincides with that obtained from the first-principles calculation.(3)Modification of the P-N model for misfit dislocationPrevious studies on misfit dislocations have been based on the theory of continuum elasticity theory,it can be used to describe the long-range deformation of a dislocation at length scales outside the core field of the dislocation line.However,it is clearly unrealistic to view a solid as a continuous medium,which ignores the discrete nature of the crystal lattice.At present,the theoretical analysis of misfit dislocation is mainly through molecular dynamics simulations and local density function simulations.However,as in the original P-N model,when the upper and lower semi-crystals are glued together along a given surface,the effect of lower semi-crystal on the bottom surface of the upper semi-crystal is ignored,as is the effect of the upper semi-crystal on the top surface of the lower semi-crystal.Furthermore,the change of the interfacial spacing caused by misfit dislocation has been ignored in previous studies.To accurately describe the misfit dislocation structure on the atomic scale,a discreteness correction to misfit dislocation equation can be derived by modifying the displacement fields that satisfy the balance equation.There is an extra term proportional to the second-order derivative,which originates from a discrete feature,it is used to reflect the formation that occurs near to the dislocation core.To facilitate comparison of the differences between before and after discrete correction,the improved P-N equation has been applied to the investigation of interfacial misfit dislocation for a BN/Al N heterostructure.The interfacial displacement can be obtained from the relationship between the mass center displacement and relative displacement.Through the approximate solution of misfit dislocation equation,we find that the theoretical calculation result for the interface displacement along the glide direction is close to the numerical result.To estimate the change in interfacial spacing caused by the misfit dislocation between the misfit planes,we consider the change of the generalized stacking fault energy along the direction of interfacial spacing.Although we have taken into account the change in interfacial spacing that induced by misfit dislocation,it can be seen that there are some discrepancies between the theoretical and numerical results for the interface displacement along the direction of interfacial spacing,and so the agreement between the results of analytical theory and those of numerical calculation needs to be further improved.At the same time,the misfit dislocation energy under the correction for the effects of discreteness is given.For the BN/Al N heterostructure,the dislocation energy after the discrete correction is reduced by 10% compared with that before.