Equilibrium shapes of coherent precipitates near a surface

Abstract

The shape stability of a two-dimensional precipitate embedded in a matrix has been theoretically investigated when it is strained due to an anisotropic lattice mismatch between the matrix and the precipitate. In the case of a semi-infinite matrix, the precipitate is found to align perpendicularly to the free-surface direction when both lattice mismatches are equal. When the misfit is anisotropic, the precipitate far from the free-surface always align in the direction of lower misfit in absolute value. When both effects of misfit anisotropy and elastic relaxation due to the free-surface oppose, a critical distance between the precipitate and the free-surface may exist below which the precipitate, initially orientated in parallel with the surface, align along the direction perpendicular to it. The case of a precipitate located near an interface between two elastically inhomogeneous phases is also discussed and the shape modification of the precipitate due to the shear moduli has been characterized.