The velocity of plate precipitates growing by the ledge mechanism

Experiments have shown that plate-shaped precipitates in alloys most often grow by a ledge mechanism where mobile steps at the particle–matrix interface propagate at constant velocity in the growth direction and the steps are separated by immobile terraces. In this work the concentration field in the matrix phase during growth is formulated by a boundary integral technique, which correctly accounts for the step-terrace structure. By examining the behavior at the precipitate tip and using a stability criterion to determine the plate thickness, a relationship is established between the growth velocity, the radius of curvature of the plate tip and the supersaturation. When compared with previous theoretical treatments based on the Horvay–Cahn, Ivantsov, Trivedi solution, the boundary integral result is able to describe the velocities obtained in previous experiments on the Al–Ag system more accurately, and the improved agreement does not depend on the assumption of a finite kinetic attachment term. However, the new criterion is not able to reproduce data for Fe–C alloys. Possible reasons for the discrepancy are discussed.