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 succinonitrile-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. In the regime where only a cellular structure is formed, the shape of the cell, the cell tip radius and the length of the cell are all found to scale individually with the local primary spacing. The presence of multiple solutions of primary spacing is also shown to influence the cell-dendrite transition that is controlled not only by the processing variables (growth velocity, thermal gradient and composition) but also by the local cell spacing. The cell-dendrite transition was found not to be sharp, but occurred over a range of processing conditions. Two critical conditions have been identified such that only cells are present below lower critics condition, and only dendrites are formed above the upper critics condition. Between these two limits, both cells and dendrites have been found to coexist. In this mixed regime, a critical local spacing is found above which a cell is unstable and forms a dendrite. An analytical expression is developed that relates the critical spacing for the cell-dendrite transition with processing conditions