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Previous diffusion-controlled quantitative phase-field simulations of Al-4wt.%Cu alloy during the initial transient directional solidification have demonstrated that the shape of the non-planar solid-liquid interface varies with the instantaneous growth parameters;in particular, above a critical value of tip velocity, cell/dendrite tips undergo Mullins-Sekerka morphological instability resulting in tip splitting and transition from cells or dendrites to seaweeds [1].