Quantitatively comparing phase-field modeling with direct real time observation by synchrotron X-ray radiography of the initial transient during directional solidification of an Al–Cu alloy Original Research Article

The initial transient during directional solidification of an Al–4 wt.% Cu alloy was simulated by a quantitative phase-field model solved with the adaptive finite element method. The simulated solidification process was compared with the related analytical theory and in situ and real time observations by means of X-ray radiography at the European Synchrotron Radiation Facility. The simulated velocity of the planar interface and solute profile ahead of the solidification front in the liquid are close to the predictions of the Warren–Langer model of the initial planar solidification transient, but in fair quantitative agreement with experimental results only at early stages of planar solidification. After the accelerated flat interface lost its stability a transition to cellular solidification was initiated. The initial cell spacing predicted by the phase-field simulation agreed well with the experimental observations in the region where the cell growth direction was perpendicular to the fluid flow, whereas a discrepancy was obvious in the corners where the fluid flow was parallel to growth. An analytical relation describing the wavelength of the initial solid–liquid interface corrugations under diffusion-limited transport is screened out by comparing the phase-field simulation data with expressions based upon the Mullins–Sekerka linear stability analysis theory or derived for primary spacing. The gravity-driven natural convection in the experiment resulted in misfits between the phase-field predictions and the experimental observations in the late stage of planar solidification, onset and development of morphological instability.