A theoretical model was described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multi-layered system deposited on a thick substrate. Each layer was regarded as having differing elastic and lattice constants, and the system was subject to biaxial in-plane mechanical loading. A stress transfer methodology was developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations were of a pure edge configuration. Energy methods were used to determine equilibrium distributions of the dislocations for given external applied stress states. It was shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model was used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It was shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, could lead to critical thicknesses being underestimated by 15 to 18%. The application of uniaxial tensile stresses increased the value of critical thicknesses. The model could be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of

analysis permitted the prediction of the deformation of metallic multi-layers subject to mechanical and thermal loading.

Prediction of Dislocation Formation in Epitaxial Multilayers Subject to In-Plane Loading. L.N.McCartney: Philosophical Magazine, 2005, 85[15], 1575-610