Shape instability during precipitate growth in coherent solids

Abstract The effect of coherent elastic strain on shape instabilities during growth of a single precipitate in an elastically anisotropic cubic system is examined. A general phenomenological field approach to phase transformation kinetics is employed. Emphasis has been given to understanding the formation of concave interfaces of a coherent γ′ particle in the Ni-based superalloys. It is shown by a two-dimensional computer simulation that the infinite-range and highly anisotropic strain-induced interaction results in a shape transition from circle to faceted square with 10 habits and rounded corners at the early stage of growth. Then the divergence of solute atom supply at the corners enhances their growth which results in a concave morphology. Vanishing of the supersaturation (transition to the coarsening stage) causes a diffusional relaxation of the concave interfaces back into flat ones, indicating that the concave square is a nonequilibrium shape. A semi-quantitative criterion for the formation of concave shapes is derived. The concentration profile inside the misfitting particle is found to be nonuniform during its growth and coarsening.

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