Growth Kinetic Limitations during Rapid Solidification
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GROWTH KINETIC LIMITATIONS DURING RAPID SOLIDIFICATION
William J. Boettinger Metallurgy Division, National Bureau of Standards,
Washington, DC 20234,
USA
ABSTRACT The importance of growth kinetics in the development of the microstructure of rapidly solidified alloys is described. Growth kinetics are conveniently divided into diffusion kinetics and interface attachment kinetics. The former, which are used extensively for the analysis of slow rate solidification, can be extended to high solidification rates to predict some microstructural features; e.g., the limitations on eutectic growth rate which can promote the formation of metallic glass, and the reduction of microsegregation. At the highest rates interface attachment kinetics must be included. Some microstructural effects of the velocity dependence of the partition coefficient will be described.
INTRODUCTION The details of the nucleation and growth kinetics of solid phases from the liquid state generate the wide variety of microstructures observed in cast materials. Nucleation has a dual role: it provides the initial phase selection among the various possibilities and also, when significant undercooling is achieved prior to nucleation, it provides a supercooled liquid into which crystal growth can occur rapidly. Given the wide temperature spectrum of catalytically potent nucleation sites that exists in alloys [1], and the differences in the growth rates of the phases observed, microstructures may in many cases be the results of the competition of various forms of crystal growth. A simple example is found in the columnar zone of a casting where a strong preferred grain orientation is developed even though the chill zone contains a random distribution of grain orientations. The focus of this paper is to describe some growth kinetic limitations that exist for different types of crystallization from the liquid. These limitations can have a strong influence on the microstructure of rapidly quenched alloys. In all cases we will assume that the phases present, whether stable or metastable, have been previously specified. In the present paper the term growth kinetics will be used in its broadest sense; i.e., it will include heat flow, diffusion, and interface attachment kinetics. INTERFACE CONDITIONS The analysis of the growth of a single crystalline phase into a two component liquid requires the solution of a complex moving boundary problem. In the absence of fluid flow, diffusion equations for solute and heat must be solved in the liquid and solid phases subject to conservation equations at the liquid-solid interface and a pair of response functions [2]. Of the various choices for dependent and independent variables in these functions, a convenient pair establishes the interface temperature, TI, and the solid composition at the interface,
CS,
as functions of the liquid composition at the interface,
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CL,
the interface mean curvature,
K, and the normal interface velocity, v. In
their general form, the response functions can include many other variabl
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