Fourier synthesis predicting onset of the initial instability during directional solidification

With the combination of the Fourier synthesis method and the time-dependent linear stability analysis, a simple model was developed to describe the dynamic evolution of the initial interface instability. By using this simple model, the early instability stage of a planar interface during directional solidification of binary alloys is predicted and how the interface microstructure generates from the background infinitesimal fluctuations is also revealed. The results from this model are in good agreement with those from quantitative phase field simulations and previous experiments.