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A Self-Consistent Theory of Steady-State Lamellar Solidification in Binary Eutectic Systems.
NAVAL RESEARCH LAB WASHINGTON D C
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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 solidliquid 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.
APPROVED FOR PUBLIC RELEASE