Microstructural shape evolution of γ′ in nickel-based superalloys by stress-assisted diffusion

γ′ precipitates in nickel-based alloys are usually observed to form as spherical particles and later to evolve into cube-shaped, star-shaped or plate-shaped precipitates; this evolution is believed to be a path of descending free energy. We hypothesized that, at each stage, the instantaneous elastic stress fields generated by each precipitate guide its evolution towards the next morphology. The elastic fields generated by cube-, sphere- and plate-shaped precipitates due to pure dilatational transformation strains were calculated in the framework of linear elasticity. It is found that the trace of the stress tensor generates favoured sites for the equilibrium accumulation of solute atoms near the precipitates and forms preferred paths for stress-assisted diffusion. Diffusion of atoms of misfit sign similar to that of the precipitate, from the favoured sites along the preferred paths, will indeed tend to alter the morphology of an existing precipitate towards that of the next local minimum of the elastic energy. This is illustrated for the transitions from a sphere-shaped to a cube-shaped and then to a star-shaped precipitate. A plate-shaped precipitate is found to be stable against shape changes. The ordering of precipitates can also be explained along these routes. The present findings shed light on recent numerical simulations of the shape evolution of γ′ precipitates, by revealing the mechanisms and predicting the tendencies involved during shape evolution, based on the static elastic solutions of ‘inclusion’ problems.