Free surface relaxation of a semicoherent interface in an isotropic thin plate

• A semicoherent interface inclined in a thin crystalline plate relaxes elastically.
• The addition of appropriate fields cancels free surface stresses.
• Numerical applications illustrate the results for a thin silicon bicrystal.
• It is expected that these 3D-dimensional effects influence HRTEM imaging.

A method leading to an explicit evaluation of the elastic field of a planar semicoherent interface placed in a thin isotropic plate is proposed. It is assumed that the interface contains a single family of straight, periodically distributed, misfit dislocations. The known properties of continuous distributions of dislocations and periodic elastic fields in an unbounded medium are used to solve the problem. Surface stresses are cancelled from the addition of appropriate fields applying to an infinite medium. Numerical applications illustrate, for a near Σ9{122} semicoherent grain boundary in silicon, the dependence of the deformation field on the plate thickness and on the orientation parameters of the interface.