The elastic fields of translation and misfit dislocations were investigated for 2 types of inhomogeneous material. One was a multilayer which was made up of parallel hetero-interfaces or free surfaces and which contained a periodic array of interfacial misfit dislocations. In the simpler case of a thin layer on a substrate, analytical solutions could be found for the displacement field relative to a single, or hexagonal periodic array of, misfit dislocations. In the less simple case of a thin bicrystal and a layer which was sandwiched between 2 semi-infinite media, explicit solutions could still be extracted. In the general case of a multilayer material which involved more than 2 hetero-interfaces, the analytical expressions became intractable. Solutions could nevertheless be obtained via numerical inversion of linear equations which expressed the limiting boundary conditions along the hetero-interfaces. Another case which was considered was that of a thin bicrystal which contained a hetero-interface that was perpendicular to the 2 free surfaces of a foil. Starting from the elastic field of an edge translation dislocations, parallel to the free surfaces, it was shown how one could derive a coherent hetero-interface, a semi-coherent hetero-interface which contained a single misfit dislocation or 2 close parallel coherent hetero-interfaces.

Misfit Dislocations in Limited Inhomogeneous Media - a Review. R.Bonnet: Interface Science, 1996, 4[3-4], 169-79