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

Abstract

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.