Edge Dislocations In A Thin Film And Dislocation And Anti-Dislocation Array

As is well known,the edge dislocation can make a crystal bending.Finite same sign edge dislocation array with equal distance will globally bend a film evidently.However,the dislocation and anti-dislocation array wouldn't bend a crystal globally,but only deforms it periodically.This thesis aims to derive the fundamental equation which can describe the edge dislocation in a film and study the relation between the edge dislocation and plastic bending of a film.In the last,the dislocation neutralizing effect in one dimensional dislocation and anti-dislocation array is discussed.According to the idea of dislocation equation in Peierls-Nabarro model,in order to derive the edge dislocation equation of a film,the first thing should be done is solving the boundary equilibrium problem of a film.Which means that solving the boundary equation to represent the boundary displacement field with known boundary force.The static equilibrium problem of an isotropic film has not been totally solved out yet in linear elasticity theory.The exact solution of the equilibrium problem of an isotropic film is studied for arbitrary thickness and for arbitrary boundary condition.By virtue of the film symmetry,the exact solution of is simplified into an invariant form with several scalar functions to be determined.By the approximations proposed in the thesis,the equilibrium solution in real space is obtained.In the following,the displacement field in the interior of the film is obtained by using the previous boundary solution.The equilibrium solution of mid-plane under the thin film limit is compared with the existed plate theories.The relation of elastic energy and curvature is studied by using the boundary equilibrium solution when the thin film has a quasi-one dimensional small uniform deflection.The dislocation equation of a free boundary film is derived in wave-vector space based on the boundary solution.The straight edge dislocation equation is obtained in real space by a reasonable approximation.Solving the edge dislocation equation in a film by the numerical method and the suitable fitting formula of numerical results is found.Analysis the numerical solution and find that the thinner film is,the narrower dislocation.If the thickness of a film is over several nanometers,the edge dislocation is almost the same as which in an infinite crystal.The total interaction energy of edge dislocations in a thin film is studied by using the free energy functional.The curvature of a film with several dislocations is estimated by the known relation between the central displacement and relative displacement of slip plane.Compare the strain energy of a thin film with the elastic bending and dislocated plastic bending when the thin film has a certain curvature and the critical curvature is obtained.The thin film tends to be elastically bended with a small curvature.When the curvature radius decreased to about six times the thin film thickness,the plastic bending energy becomes smaller than the elastic and the edge dislocations determined the shape of the thin film appear.In the frame of Peierls-Nabarro model,a one dimensional self-organized array composed of dislocation and anti-dislocation is analytically investigated.Assume that the unknown slip field is a special periodic function,then the equation describes the dislocation and anti-dislocation array is obtained.The solution of this array is found out and the strain energy and misfit energy are calculated out as well.The stress field and displacement field of straight screw dislocation and edge dislocation array are studied by using the superposition principle.The airy stress function of the edge dislocation array is calculated out as well.The Burgers vector and Peierls stress are quantitatively analyzed by the exact solution.These quantities of a dislocation decrease due to the dislocation neutralizing effect.For example,when the distance between the dislocation and the anti-dislocation is as large as ten times of the dislocation width,the actual Burgers vector is only about 80% of an isolated dislocation.The Peierls barrier and stress weaken in the same degree as Burgers vector.The neutralizing effect originates physically from the power-law asymptotic behavior(square inverse)that is universal in regardless of the core structure of dislocation.This neutralizing effect is not negligible when a dislocation and anti-dislocation interact closely.