On misfit dislocations in the diffusion zone of a bicrystal system

Abstract

The problem of the diffusion-induced change in a bicrystal system of two different pure, perfect crystalline substances which are in parallel orientation and completely miscible, is treated in this paper. The interdiffusion transforms the abrupt change of crystal parameters at the bicrystal interface into a continuous change distributed throughout the diffusion zone. A general model for the description of this transformation is formulated. Basic properties of the model are: linear dependence of lattice constant on concentration, redistribution of the original interfacial or misfit dislocations into sub-interfaces, laws of conservation of the number and of the localization of misfit dislocations and the introduction of a so-called linear deformation. For the mathematical analysis of the model it is necessary to make certain simplifying approximations concerning the concentration gradient, the dependence of crystal parameters on it and the form of the sub-interfaces. An expression for the energy of linear deformation is derived. The model is used, in conjunction with this expression and those derived by Read and van der Merwe, to evaluate and compare energies of possible intermediate dislocation configurations since such information presumably gives an indication of the degree of instability of these configurations.