MODEL FOR EUTECTIC ORGANIZATION - THE PURELY KINETIC REGIME

We analyze the lamellar organization in the solid phase by using a purely kinetic regime based on physical first principles combined with a phenomenological Landau theory. This model has at least two advantages over the usual free-boundary-problem formulation: (i) It allows us to show from first principles the existence of a lamellar organization, which is usually taken as a starting point, and (ii) it permits us to handle analytically in a relatively simple manner the problem of the existence of these solutions. This model resembles in some way the phase-field model: the solid-fluid front is sharp, while the solid-solid interface is smooth and characterized by a continuous change in the concentration field. We analyze in detail the variety of solutions and map them to the underlying coexistence phase diagram of the three phases. We show that the growing phase with a modulated structure (the ''lamellar'' eutectic structure) has a higher velocity than any homogenous solution. The organized structure thus appears from the maximum-velocity principle as favorable against homogeneous solutions. Other questions related to various symmetry-breaking bifurcations from the simplest steady and symmetric organization are discussed, where use of the present model may become essential.