Modeling of crystal growth during rapid solidification
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I.
INTRODUCTION
THE development of new
materials with improved performance has always been a challenge to material scientists. Therefore, in recent years, the route of rapid solidification processing (RSP) has received considerable attention due to its potential to produce metastable structures with new interesting properties. Among the new materials produced by RSP, perhaps the metallic glasses are the ones attracting most attention. Therefore, the prediction of the glass-forming ability of metallic alloy systems has been a subject of extensive research. [~1 It is recognized that the retention of the amorphous structure when cooling a liquid depends on a combination of thermodynamic and kinetic factors. These factors determine the driving forces for and the rates of crystal nucleation and growth. The final product produced utilizing RSP techniques is not necessarily a metallic glass. It may as well be stable or metastable crystalline, microcrystalline, or quasicrystalline products that form either directly during RSP or during subsequent annealing. In principle, it is possible to obtain many different structures in a sample produced by RSP techniques, and therefore, it is desirable to have some method of predicting what phases and morphologies are likely to appear. A number of more or less empirical methods, e.g., glass-forming maps, t2] have been developed. However, from a more fundamental point of view, it is interesting to model mathematically the different RSP techniques under specific conditions and to make predictions from the models. In general, the modeling of phase transformations of alloys is a quite difficult task. A detailed knowledge of the interface reactions is required, and many questions have to be answered. Such questions are, for example: what is the growth morphology; what is the potency of the nucleation sites; what is the value of the surface energy between the different phases; and what is the driving force for the reaction. Due to our limited knowledge, we have to rely on many approximations when treating these types of problems. The purpose of this article is to study, within the framework of such approximations, the relative roles of nucleation, heat transfer, and growth rates on the evolution of microstructures during RSP. In parBJORN JONSSON, Doctor, Research Associate, is with the Division of Physical Metallurgy, Royal Institute of Technology, S-10044 Stockholm, Sweden. Manuscript submitted May 24, 1990. METALLURGICAL TRANSACTIONS A
ticular, by ~ a solute-drag model recently presented by Agren, [3J the effect of solute trapping during crystal growth will be considered. This allows us to distinguish between two different modes of growth and to make predictions about the transitions between the two. We find partitioned growth in a cellular or dendritic morphology at low supersaturations and partitionless growth with a planar interface at large supersaturations. Furthermore, we will restrict our discussion to two different geometries. In the first model (model I), we will assume a uni
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