CRITICAL SPLITTING OF THE SOLIDIFYING INTERFACE GEOMETRICAL MODEL OF SPACING SELECTION DURING DIRECTIONAL SOLIDIFICATION OF LAMELLAR EUTECTICS

The steady-state coupling equations of directional solidification of A l-Al2Cu (epsilon = 0.94), Sn-Pb (epsilon = 0.59) and Al-Si (epsilon = 0.17)eutectics have been solved numerically. The profiles, splitting f eatures and supercooling of the solidifying interface were investigate d in detail as functions of the lamellar spacing. It was found that wh en supercooling, DELTAT0, at the three-phase conjunction point reaches its minimum value, min (DELTAT0), the solidifying interface prof ile of one lamellar phase was in the critical splitting state (marginally stable state) and that of the other lamella was super-stable. Langer's marginal stability theory of lamellar eutectic solidification with a planar interface was extended to the case with a curved interface, and a geometrical model of the spacing selection has been suggested (crit ical splitting state of one lamella's solidifying interface). The gene ral scaling law of the spacing, derived according to this theory, was found to be consistent with the similarity law recently derived by Kas sner and Misbah; it is also supported by experimental results. Another geometrical model of the spacing selection was found, where the solid ifying interface profile of one lamella became split and other lamella 's profile was in the critical splitting state. The experimental data for directional solidification of Al-Si eutectic showed that the irreg ular eutectics have a spacing selected according to this mode.