Formulations of Van Der Merwe misfit dislocation theory using a continuous distribution of infinitesimal interface dislocations. .

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 the elegant misfit dislocation theory. Most recently, this theory was critically analyzed by the present author, who found that the neglect of the interfacial normal force given in part of the original formulation leads to a slipping nature for the interface rather than a welded one. Therefore, this mathematical consequence was corrected for a welded 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.