A simple model for spherical growth in alloy solidification

During alloy solidification, spherical growth is the initial growth stage immediately after heterogeneous nucleation but before the morphological instability for dendritic growth. A number of analytical solutions are available for spherical growth and Zener's approximation has been used in nearly all such models. These models, however, are only applicable to solidification with very small supersaturation. In this paper, based on the theoretical analysis of precipitation growth in solid state we present a simplified analytical expression for spherical growth applicable to solidification with an entire range of supersaturation.