Computational Study of Spacing Selection in Directionally Growing Dendritic Arrays

The primary dendrite arm spacing (PDAS) is widely used in the directional solidification community as an important microstructural parameter. It is commonly accepted that the PDAS is not a single value, but that a range of stable spacing exists. The limits and the maximum of the PDAS distribution depend on the growth conditions of the PDAS array, namely the thermal gradient and the solidification velocity.
The paper focuses on modelling the competitive growth of dendrites in an array during directional solidification, and the mechanism that establish the spacing distribution, i.e. the creation of new dendrites and removal of dendrites.
For this purpose a novel mesoscale model is proposed. It is able to capture the solidification front position by tracking the positions of dendrites tips. The tracking technique is based on massless markers, each representing a dendrite tip, moving through a fixed grid. Upon changes of solidification conditions the local PDAS is adjusted, by creating new markers (dendrites) or by deleting existing ones, following sets of predefined rules. These are based on the evaluation of the spacing between each dendrite and its nearest neighbours. This yields a fast model that can take into account large numbers of dendrites.
The model has been used to study directional solidification of SCN-Acetone alloy under cyclic variation of the thermal gradient. The results are compared to experimental data previously published by Ma [1]. The model does show good agreement with the experiments, and is able to reproduce the experimentally observed hysteresis effects in the PDAS upon cycling the thermal gradient. Different sets of rules reproduce different aspects of the experimental findings.