Convective and interfacial instabilities during unidirectional solidification of a binary alloy

Abstract

The onset of coupled convective and constitutional interfacial instabilities during the directional solidification of a single phase binary alloy at constant velocity vertically upwards (positive z-direction) is treated by a linear stability analysis. We consider a system for which the temperature gradient alone would cause a negative density gradient and the solute gradient alone would cause a positive density gradient. The temperature and concentration fields are coupled through the hydrodynamic equations. The solidification boundary conditions at the solid-liquid interface couple the hydrodynamic and interfacial stability phenomena. Specific calculations were made for physical properties appropriate to the solidification of lead containing tin. Results indicate that the stability-instability criterion differs substantially from the criterion of a net neutral density gradient. For a temperature gradient in the liquid of 200 K/cm and for velocities in the range 1–40 μm/s, a convective-like long wavelength instability occurs at a critical concentration that increases with velocity; whereas for V > 40 μm/s, the concentration at which instability occurs decreases as velocity is increased and the values of concentration and wavelength at the onset of instability correspond to the predictions of previous morphological stability theory in which density changes and convection are neglected. Application of a vertical static magnetic field increases the critical concentration for convective instabilities but a field of a tesla (10 4 gauss) is needed to cause an order of magnitude change.