Mechanism of Dendritic Branching

Theories of dendritic growth currently ascribe pattern details to extrinsic perturbations or other stochastic causalities, such as selective amplification of noise and marginal stability. These theories apply capillarity physics as a boundary condition on the transport fields in the melt that conduct the latent heat and/or move solute rejected during solidification. Predictions based on these theories conflict with the best quantitative experiments on model solidification systems. Moreover, neither the observed branching patterns nor other characteristics of dendrites formed in different molten materials are distinguished by these approaches, making their integration with casting and microstructure models of limited value. The case of solidification from a pure melt is reexamined, allowing instead the capillary temperature distribution along a prescribed sharp interface to act as a weak energy field. As such, the Gibbs-Thomson equilibrium temperature is shown to be much more than a boundary condition on the transport field; it acts, in fact, as an independent energy field during crystal growth and produces profound effects not recognized heretofore. Specifically, one may determine by energy conservation that weak normal fluxes are released along the interface, which either increase or decrease slightly the local rate of freezing. Those responses initiate rotation of the interface at specific locations determined by the surface energy and the shape. Interface rotations with proper chirality, or rotation sense, couple to the external transport field and amplify locally as side branches. A precision integral equation solver confirms through dynamic simulations that interface rotation occurs at the predicted locations. Rotations points repeat episodically as a pattern evolves until the dendrite assumes a dynamic shape allowing a synchronous limit cycle, from which the classic repeating dendritic pattern develops. Interface rotation is the fundamental mechanism responsible for dendritic branching.