Stability of a planar interface during solidification of a multicomponent system

A fully time-dependent analysis of the morphological stability of a planar interface during directional solidification of a multicomponent alloy at constant velocity is carried out for a simple model in which each solute acts independently. We show that there are no linearly unstable modes that are oscillatory in time (principle of exchange of stabilities in strong form) under any of the following conditions: (1) equal thermal properties in crystal and melt, (2) equal temperature gradients in crystal and melt, or (3) the thermal steady-state approximation. The stability-instability demarcation is analyzed in the thermal steady-state approximation. Numerical results are presented for ternary alloys in terms of a stability surface that becomes planar in the limits of modified constitutional supercooling and absolute stability.