On velocity and spacing selection in discontinuous precipitation—I. Simplified analytical approach

A new approach is proposed to the problem of pattern selection in discontinuous precipitation. It 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 first is considered governed by lateral gradients of concentration, the second by gradients of curvature. 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; the new treatment provides a selection of spacing and transformation front velocity consistent with experimental results in the literature.