Lamella / Rod Transformation as described by the Criterion of Minimum Entropy Production

Abstract

A general theory for the lamella -> rod transformation is presented. The analysis has been developed in two steps: first, taking into account the condition of minimum Gibbs' free energy, next, using the criterion of minimum entropy production together with the concept of marginal stability. The present theory provides a justification for theoretical determination of a threshold growth rate at which solidification begins to form a rod-like structure instead of a lamellar one. Additionally, the so-called operating range for transformation is justified by the oscillation between the trajectory of minimum entropy production and the trajectory of marginal stability. A model of the evolution of the mechanical equilibrium is introduced to satisfy some changes of the curvature of the solid / liquid interface with increasing growth rate. A consideration associated with the Gibbs' free energy allows to formulate a new criterion which predicts whether the lamellar structure is the stable form or a rod-like structure is the stable form (for a given phase diagram). An application of the criterion of minimum entropy production, together with a model of the instability of the solid/liquid interface (referred to as marginal stability), allows for determining a/ a trajectory at which a regular structure is forming and b/ a trajectory of marginal stability at which the maximum destabilization of the s/l interface of the non-faceted phase is observed together with the faceted phase branching.

Keywords

• spacing oscillation; marginal stability; attractor; threshold rate for the lamella / rod transformation

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