Cooperative two-phase growth from solid solution via interphase and grain boundary diffusion

A new approach is proposed to the problem of pattern selection in discontinuous precipitation from solid solution by interphase boundary and grain boundary diffusion. The model relies on the simultaneous calculation of growth velocities for both the precipitate lamellae and the interlamellar solid solution phase, and on the recognition that the processes of diffusional transport along grain boundaries and interphase boundaries are fundamentally different. The growth of the new phase lamellae is driven by a gradient of curvature; the growth of the interlamellar solid solution is a consequence of gradients of concentration. It is shown that the simple hypotheses of thermodynamic equilibrium and diffusive flux continuity at the triple junction between the precipitate lamella and the initial and depleted parent phases (along with the requirement that the two phases grow at the same rate) is sufficient to remove the degeneracy of the problem; it provides a selection of spacing and transformation front velocity consistent with the experimental results in the literature. The conditions for the existence of a front with constant interlamellar spacing propagating with constant velocity are expressed in terms of the thermodynamic properties of the alloy system and of the supersaturation.