A Self-Consistent Theory of Steady-State Lamellar Solidification in Binary Eutectic Systems.

摘要

The potential theoretic methods developed recently at NRL for solving the diffusion equation are applied to the free-boundary problem which describes lamellar solidification in binary eutectic systems. By using these techniques, the original free-boundary problem is reduced to a set of coupled nonlinear integro-differential equations which when solved yield the shape of the solid/liquid interface and the solute concentration on the interface. The behavior of the solution to these equations is discussed in a qualitative fashion, leading to some interesting interferences regarding the nature of the eutectic solidification process. Using the information obtained from the analysis, an approximate theory of the lamellar-rod transition is formulated. The predictions of the theory are shown to be in qualitative agreement with experimental observations of this transition. In addition a simplified version of the general integro-differential equations is developed and used both to assess the effect of interface curvature on the interfacial solute concentrations and to check the new theory for consistency with experiment.