Splitting of coherent precipitates caused by elastic non-equilibrium

Abstract

During the process of nickel-based superalloys, gamma prime particles often split into doublets, quartets, or octets. It is an interesting instability phenomenon as it defies conventional surface thermodynamics. Particle splitting is examined through the discrete atom method, which is based on the combination of statistical mechanics and linear elasticity. Splitting phenomena may be classified into two: commensurate elastic instability and incommensurate elastic instability. In the former, the elastic anisotropy of a coherent particle is commensurate with that of the matrix phase, and a non-equilibrium elastic state may cause particle splitting provided that relaxation of the elastic strain energy can exceed the accompanying interfacial energy increase. Incommensurate elastic instability arises when the anisotropy ratios of the precipitate and matrix phase have opposite signs, for example, when the elastically soft direction of the matrix is parallel to the hard direction of the particle phase. The strain energy tends to relax along the elastically soft directions of both phases: thus the particle stretches along its own soft directions while yielding its hard directions to the matrix phase. Such a splitting can end up with a symmetry in the arrangement of particles, but requires a condition that the bulk moduli of both matrix and precipitate phase are comparable to each other.