Nonequilibrium Interface Kinetics During Rapid Solidification
- PDF / 939,787 Bytes
- 14 Pages / 420.48 x 639 pts Page_size
- 41 Downloads / 226 Views
NONEQUILIBRIUM INTERFACE KINETICS DURING RAPID SOLIDIFICATION MICHAEL J. AZIZ Division of Applied Sciences, Harvard University, Cambridge MA 02138 ABSTRACT The deviations from local equilibrium at a rapidly moving solid-liquid interface are well documented. The fraction of solute atoms in the liquid at the interface that joins the crystal during rapid solidification approaches unity and the interface temperature drops. Experimental and theoretical work on impurity incorporation and interfacial undercooling is reviewed. Past and future experiments to test the theories are discussed. INTRODUCTION Rapid solidification experiments have reached a crystal growth regime where deviations from local equilibrium are obvious and interface motion is no longer strictly heat-flow limited. These experiments allow us the opportunity to study the interface reaction kinetics in highmobility systems for the first time. In the first part of this paper, I review evidence for the departure from local equilibrium. I then describe a simple model, applicable to both metals and semiconductors, for the kinetics of the fundamental atomic processes occurring at the interface during rapid solidification of binary alloys. The result is a pair of "interface response functions" which predict (a) how much solute should be incorporated into the solid, and (b) how fast the interface should move; in terms of the local conditions at the interface, namely undercooling and composition. I then describe some recent experiments regarding question (a) that until recently have been possible only in semiconductors; the results support one model and rule out others. Finally, the predictions of a model for question (b) are presented for an ideal solution and for a simple eutectic system. Consider what happens when a liquid alloy is cooled very slowly, as shown in Fig. 1(a). If the cooling rate is so slow that compositional equilibrium can be maintained throughout the bulk of the liquid and the solid phases, then the phase diagram tells us what we need to know: a solid of uniform composition given by the equilibrium solidus will coexist with a liquid of uniform composition given by the equilibrium liquidus. As the temperature decreases, the fraction of solid material increases according to the lever rule. Under normal processing conditions, this scenario never occurs. Rather, composition gradients in the solid and often also in the liquid are created and are governed by the laws of long-range mass transport. It is still possible, however, that the atoms in each phase immediately adjacent to the interface still have enough time to establish a local equilibrium across the interface itself. With this popular assumption of local equilibrium, the phase diagram is used as an interface conditiondiagramas in Fig. l(b). That is, although the composition is nonuniform throughout the bulk of the two phases, given a composition of the liquid at the interface, the solid grows at the equilibrium temperature, with the equilibrium solidus composition. Now during rapid solidifica
Data Loading...
