Spacing in solidification of dendritic arrays

A number of models of the primary dendrite spacing selection in directional solidification have been proposed based on considerations of the solutal diffusion problem. It is shown here that the primary spacing in dendritic solidification is fundamentally determined by the heat balance. Diffusion of solute affects the spacing only indirectly via selection of the tip radius. A simple solution for the spacing is derived. This analysis does not support the recent idea that the dendrite tip radius is selected by array interactions and indicates that the experimentally observed history dependence and range of spacings are due to the thermal hysteresis of the system, rather than to a range of physically allowable stable states.