Length scale correlations of cellular microstructures in directionally solidified binary system
In a cellular array, a range of primary spacing is found to be stable under given growth conditions. Since a strong coupling of solute field exists between the neighboring cells, primary spacing variation should also influence other microstructure features such as cell shape and cell length. The existence of multiple solutions is examined in this study both theoretically as well as experimentally. A theoretical model is developed that identifies and relates four important microstructural lengths, which are found to be primary spacing, tip radius, cell width and cell length. This general microstructural relationship is shown to be valid for different cells in an array as well as for other cellular patterns obtained under different growth conditions. The unique feature of the model is that the microstructure correlation does not depend on composition or growth conditions since these variables scale microstructural lengths to satisfy the relationship obtained in this study. Detailed directional solidification experimental studies have been carried out in the succino6trile-salol system to characterize and measure these four length scales. Besides the validation of the model, experimental results showed additional scaling laws to be present.