An extended morphological stability model for a planar interface incorporating the effect of nonlinear liquidus and solidus

Incorporating the effect of nonlinear liquidus and solidus, an extended morphological stability model for a planar interface was developed under local non-equilibrium conditions both at the solid/liquid interface and in the bulk liquid. The model was adopted to describe the cellular breakdown of the planar interface upon rapid solidification of Si-Sn alloys, and a quantitative agreement was obtained between the model predictions and the experimental results. It has been found that, independent of the effect of non-equilibrium liquid diffusion, two critical interface velocities V^min and V^max always occur, because of the retrograde characters of the Si-Sn phase diagram. If V^min ≤ V ≤ V^max, the so-called neutral stability curve can be evaluated in terms of the planar interface response function and the marginal stability criterion. Whereas if V > V^max or V < V^min, the calculation of the maximum solid solubility C_S^max (V) from the planar interface response function is performed. In comparison with the model assuming linear liquidus and solidus, which fails to predict the retrograde characters of the Si-Sn phase diagram both at low (k → k_e) and at high (k → 1) interface velocities, the effect of nonlinear liquidus and solidus on the cellular breakdown of the planar interface is highlighted.