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 recently developed at NRL for solving the diffusion equation are applied to the problem of lamellar eutectic solidification. This approach leads to a set of coupled nonlinear integro- differential equations for the shape of the solid-liquid interface and the solute concentration on the interface. The general characteristics of the solutions to these equations are discussed, and in particular it is shown that lamellar solutions may not be possible when the ratio of thermal gradient to freezing rate is less than some critical value which depends on the phase properties and the phase fraction. Selected numerical results are presented for the Pb-Sn eutectic system and compared to the results of Jackson and Hunt, who assumed a planar interface model. It is shown that the planar interface model can be a source of considerable error under certain conditions, and that the self-consistent model provides additional theoretical insights.
- Properties of Metals and Alloys