Characterization of morphology transitions in diffusion-controlled systems.

Abstract

We provide a theoretical and experimental study of the nature of morphology transitions in diffusion-controlled systems. The interplay of surface tension and kinetic anisotropy is found to determine the selected morphology in an anisotropic Hele-Shaw cell experiment, and in theoretical computations in the boundary-layer model (BLM) for solidification. We employ the Hele-Shaw cell to demonstrate the existence of surface tension and kinetic dendrites. Using the BLM we show that the selected velocities for kinetic and surface-tension dendrites scale differently with the undercooling \ensuremath{\Delta}. A study of the selected velocity as a function of undercooling is presented for both aligned and competing anisotropies, the latter motivated by the Hele-Shaw experiment. The difference in scaling is related to the reentrant tip splitting found for the case of competing anisotropies in the BLM morphology diagram via a time-dependent solution for the interface evolution. We suggest that the nature of the transitions between morphologies should be classified by the behavior of the selected interfacial velocity as a function of driving force. For the case of the BLM, first- and second-order-like morphology transitions, by analogy to phase transitions, are discussed. We further advance the hypothesis that the fastest growing morphology, whether it be tip splitting or dendritic, emerges as the stable interfacial morphology experimentally. We support our hypotheses by drawing analogies to experimental results of growth from supersaturated solutions and by electrochemical deposition.