The diffusion controlled growth rate of solid-solid interphase boundaries containing ledges

In this work the velocity of an isolated growth ledge located on an interphase boundary is solved by the method of matched asymptotic expansion where the “inner” solution is obtained by a conformal mapping procedure. In contrast to previous work, both a constant flux and local equilibrium is maintained at all points along the step face when formulating the solution. The matching procedure leads to a solvability condition for the problem, which in turn yields an analytic solution for the Peclet number as a function of supersaturation. The theoretical treatment is extended, in an approximate way, to the case of multiple steps. Predictions from the matched asymptotic expansion formulation are compared to experimental results for BCC precipitate growth in the Ni–Cr system.