MODEL FOR EUTECTIC ORGANIZATION - THE PURELY KINETIC REGIME

We analyze the lamellar organization in the solid phase by using a pur ely 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 e xistence of these solutions. This model resembles in some way the phas e-field model: the solid-fluid front is sharp, while the solid-solid i nterface is smooth and characterized by a continuous change in the con centration field. We analyze in detail the variety of solutions and ma p them to the underlying coexistence phase diagram of the three phases . We show that the growing phase with a modulated structure (the ''lam ellar'' eutectic structure) has a higher velocity than any homogenous solution. The organized structure thus appears from the maximum-veloci ty principle as favorable against homogeneous solutions. Other questio ns related to various symmetry-breaking bifurcations from the simplest steady and symmetric organization are discussed, where use of the pre sent model may become essential.