PART VI - Papers - The Dendrite-Eutectic Transition

The discussion by Tammann and Botschwar of the transition from eutectie grouth to denrdritic plus eu-tectic growth is reviewed and applied to metallic eutectic systems. Using expevimental data on the geowth rate of the Pb-Sn eutectic, and an extrapolalion of dendritic growth rate in tin and Sn-Pb alloys , qlcantitatice prerlictiotls of the extent of the eutectic region in tin-vich Sn-Pb alloys are made. There are no experimenta1 measuvements available for detailed comparison with these predictions. EUTECTIC structures form over a small range of compositions. The theory of lamellar growth presented by Jackson and Hunt' indicates that it is in principle possible to have eutectic growth over almost the complete range of compositions between the two solidus lines. This does not occur in practice. Alloys far from the eutectic composition grow dendritically followed by a eutectic as shown in Fig. I. The transition from a eutectic to a dendritic plus eutectic interface cannot be predicted from constitutional undercooling arguments because constitutional undercooling always exists ahead of the eutectic interface.' Reasonable predictions can, however, be made using arguments originally put forward by Tammanl. and Botschwar.3 These and later workers'"*6 carried out extensive experimental investigations of the extent of the eutectic range in organic materials. They concluded that the structure formed, eutectic or dendrites plus eutectic, depended on which structure grew faster at the given undercooling. This is, of course, equivalent to the structure which grows with the smallest undercooling at a given growth rate. In this paper, we will discuss these ideas briefly and then apply them to predict quantitatively the range of eutectic growth in tin-rich Pb-Sn alloys. The temperature dependence of the growth rates of dendrites and eutectic for a typical metal alloy of eutectic composition is shown schematically in Fig. 2(a). The growth rate for the eutectic increases more rapidly with undercooling than those of the dendrites because of the short diffusion path maintained in the eutectic, see Fig. 1. For an alloy off the eutectic composition on the A-rich side, the growth rates shift as shown in Fig. 2(b). The liquidus temperature of the a phase increases, that of the 3 phase decreases, and the temperature of zero growth rate for the eutectic does not change. The curves, particularly the dendritic ones, change shape as well, but for our purposes the principal effects occur because of the change in liquidus temperatures.3-6 In an isothermal system, only a dendrites will grow above TE, Fig. 2(b). If the temperature is below TE, and both phases have nucleated, a dendrites will grow ahead of the eutectic at