Theory of Microstructural Development During Rapid Solidification

Abstract

Some of the fundamental factors which play important roles in determining microstructures under rapid solidification condition are described. It is shown that the interface stability analysis needs to be extended to include the possibility of high thermal as well as high solute undercoolings. Furthermore, appropriate descriptions of solute and thermal fields for high speed transformations need to be developed.

An extension of the linear perturbation analysis is proposed which takes into account the high thermal undercooling condition. It is found that above a certain critical velocity (or undercooling), a planar interface will always be stable with respect to any arbitrary perturbations in its shape. Thus, an absolute velocity is predicted for pure and alloy under- cooled melts. A general stability criterion is developed for a planar interface stability and this criterion is valid for small as well as large growth rates.

The results of the stability analysis are applied to study the micro- structural changes which occur as a function of undercooling. For this prediction we consider the length scale of the microstructure to correspond to the marginally stable wavelength for a planar interface stability. The application of this criterion to dendritic growth phenomena shows that a limiting condition is achieved at the unit dimensionless landercooling value where the velocity approaches the absolute velocity value, and the radius of dendrite tip approaches infinity. Furthermore, the function VR², which is constant at low undercooling conditions, is found to increase sharply as the undercooling is increased.

The theoretical model is extended to understand microstructural changes which occur under constrained growth conditions. At high growth rates, appropriate stability criterion is coupled with the solute trapping effect to predict microstructural features as a function of velocityFurthermore, at high growth rates, the undercooling can become sufficiently large so that the diffusion coefficient variation with temperature must also be taken into account. In addition, any changes in phase diagram characteristics with temperature should also be examined. The effects of all these variables on interface curvature and on solute compostion in solid have been examined, and their influence on microstructural characterization under rapid solidification conditions have been evaluated. The model is applied to the Ag-Co system for which detailed experimental microstructural analysis has been published in the literature. A reasonable agreement between the theory and the experimental data is found.

The theoretical model is also extended to predict eutectic characteristics under rapid solidification conditions. It is found that a coupled eutectic growth can occur only below a certain critical velocity. The effect of phase diagram characteristics on this critical velocity is examined.