On the stand-off positions of misfit dislocations

Abstract

A comparative analysis for the results obtained by force and energetic approaches, which are used in calculations of equilibrium position of misfit dislocations near interfaces, is performed. It is shown that a correct utilization of both approaches leads to similar results for the models which do not consider the finite thickness of contacting phases. The peculiarities of the dislocation motion to the equilibrium stand-off positions are considered in the framework of the force approach. In the case of climbing misfit dislocations local inelastic variation of the material volume caused by diffusive point defects is taken into account. This results in the calculated values of stand-off distances which are in a good agreement with those observed by Mader in the system Nb–Al2O3 (the system was produced by internal oxidation at high temperature). The slip of misfit dislocations in the planes inclined to the interface is proposed as another possible mechanism for the motion of misfit dislocations to their equilibrium positions (such a mechanism is peculiar to an epitaxial growth). An exact equation allowing to calculate the misfit dislocation equilibrium positions in a thin two-layer plate is derived with accounting for all the boundary conditions of the problem. A simple analytical form for a stand-off position of a gliding misfit dislocation is found. It is predicted that a stand-off distance can vary from two to four times in dependence on the ratio of the layer thicknesses. A quantitative estimate of stand-off distance gives values which are in accordance with the experimental observations by Mayer et al.