Primary spacing in directional solidification

A new analytical model is developed to explain the variation in primary spacing lambda with growth velocity V. In this model, dendrite growth is resolved into two parts: the growth of the center core and that of the side arms, which are separately treated. In contrast to the assumption in the current models, it is only the dendrite core, not the entire dendrite, whose curvature radius at the tip is directly related to dendrite tip radius R. The primary spacing is considered to be the sum of core diameter and twice the sidearm length. As long as the growth of side arms is suppressed, it becomes cellular growth. As a result, this model gives a reasonable dependence of cell and dendrite spacing on the process parameters. The proposed model has been applied to several alloys to compare its predictions both with experimental data and with the analytical expression of the Hunt-Lu model.