INITIAL FRONT TRANSIENTS IN DIRECTIONAL SOLIDIFICATION OF THIN SAMPLES OF DILUTE ALLOYS

We study the dynamics of recoil of a planar front in a directional sol idification process, following a sudden jump from rest to a constant p ulling velocity V. To this end, we solve numerically the full integral equation describing the front dynamics in the one-sided model. We fin d, in particular, that the asymptotic (respectively initial) regimes, for which we derive analytical expressions for the front position, are restricted to such long (respectively short) times that they are in p ractice irrelevant for the analysis of experiments. We show that the r esults obtained from the heuristic approximation recently proposed by Warren and Langer are in remarkably good agreement with the exact ones in the regimes relevant to planar recoil experiments. Equally good ag reement is found for the velocity threshold and the critical wavelengt h of the cellular instability after a large velocity jump, as calculat ed in the adiabatic approximation.