Experimental and computational investigations of binary solidification

Abstract

The topic of this dissertation is the solidification of a binary melt. The investigation is separated into three portions: An experimental investigation on the NH₄Cl--H₂O system; the development of a Cellular Automata code; and the development of a pair of coupled partial differential equations governing the evolution of an array of dendrites. Any necessary concepts are reviewed in the introduction. The experimental investigation focuses on the morphological transition from "slow" <100> dendrites to "fast" <111> dendrites. It is shown how the very complicated structures occurring during the transition actually have a simple explanation. The "slow-to-fast" transition has been previously investigated in the literature, and the relationships obtained in those studies can not account for the data collected in the present study. When "slow" dendrites are cooled into the "fast" regime, a curious stagnation of growth has also been observed. Additionally, two mechanisms are proposed as possible contributions to the order-of-magnitude jump in speed at the slow-to-fast transition. One mechanism is that of a "herringbone structure", and the other is that of a vortical fluid flow occurring at the tip of the dendrite. A relationship is also found which further indicates the importance of fluid flow. The cellular automata model developed in this dissertation has proven to be a valuable tool in gaining insight into the solidification process. The simulated growth is governed predominantly by the diffusion of solute and the Gibbs-Thomson effect. Solutal diffusion, is accurately treated, diffusing differently through liquid than through solid. The interface curvature is approximated using a template method, into which crystalline anisotropy has also been introduced. Several features were added to explore interface kinetics, solute partitioning, and fluid flow due to shrinkage. Simulations on a 100 x 100 system typically required less than a minute on a workstation, and only qualitative agreement with the experiments was sought. The partial differential equations for the evolution of a growing array of dendrites are derived taking into account only diffusion. It is explicitly shown how the non-conservative equations conserve all of the material in the solidifying system.