Analysis of stability of a planar solid-liquid interface in a dilute binary alloy

This paper reconsiders the question of stability of a planar solid-liquid interface in an undercooled alloy melt without making the restrictive assumption of no heat flow in the solid (i.e., Gs = 0). The results of this analysis indicate that, provided the thermal gradient on the solid side of the interface, Gs, is positive, stability can be achieved in an undercooled alloy melt for growth rates R greater than Ra (where Ra is the absolute stability limit of Mullins and Sekerka, 1964). Thus, the absolute stability criterion for steady-state planar growth in an undercooled alloy melt is the same as derived earlier by Mullins and Sekerka for directional solidification. Relaxing the restrictive assumption of Gs = 0 also reveals that there is a regime of stability for low growth rates and low supercoolings.