Consider an A-B alloy that is solidifying from left to right. You can assume that there is no diffusion in the solid phase and diffusion in the liquid phase is slow. A concentration profile is established in the liquid phase next to the solid-liquid interface in which the fraction of A component is given by:

X_A =0.02 + (0.08)e^-/2, where y is the distance from the solid-liquid interface in cm:

For X_A = 0.2, the liquidus line on the eutectic phase diagram [K] is given by T = 380-40X_A, and the partition coefficient that describes the composition ratio at the solid-liquid interface is k=X_A^solid/X_A^liquid =0.2

To the right of the interface, the temperature of the liquid [K] is given by T_liquid - T_i+3y, where T_i is the temperature at the interface [K] and y is the distance from the solid-liquid interface in cm.

Is dendrite formation expected within this system? Please explain the rationale.