SPACING SELECTION FOR AN SN-PB LAMELLAR EUTECTIC DURING DIRECTIONAL SOLIDIFICATION

The spacing selection for an Sn-Pb lamellar eutectic during directiona l solidification was studied in detail by solving numerically the stea dy-state coupling equations of directional solidification. The equatio ns treat separately the solidification of the two lamellar solid phase s: alpha and beta. The calculations show that for each of the two phas es, the profile of the solidifying interface experiences a splitting e volution with increasing lamellar spacing lambda, which corresponds to a transition of the interface from a stable profile to an unstable pr ofile. It is argued that the critical splitting state (CSS) is a margi nally stable state for the solidifying interface. This predicts that d ynamically there are two operating points, which differ from each othe r and constitute the limits of a selection band of spacings, although only one of the two operating points is stable. A detailed comparison of the calculated results with experiments supports the present theore tical model. A more general scaling law than the classic law is propos ed. Finally, the dependence of faults in the solidified structure on t he solidifying rate and width of the selection band is presented.