Formulations of van der Merwe misfit dislocation theory using a continuous distribution of infinitesimal interface dislocations

Abstract

Abstract Using the Peierls-Nabarro model for describing the equilibrium of an interfacial shear force existing between two elastically isotropic media, van der Merwe first formulated a misfit dislocation theory for critical thicknesses of strained layer systems. Recently, it has been found that the neglect of the interfacial normal force given in the original formulation leads to a slipping, as opposed to the correct welded nature for the interface. It is known that a continuous distribution of infinitesimal elastic (Volterra-type) dislocations can be used to derive the elastic fields of the corresponding Peierls-Nabarro dislocation in an infinite elastic medium. Based on this mathematical principle, it is shown here how previous elasticity solutions for a single elastic interface dislocation lying at a welded interface between two semi-infinite isotropic media can be used to derive those of the corrected van der Merwe misfit dislocation theory involving the Peierls-Nabarro model.