Adiabatic hypercooling of binary melts.

A binary melt is hypercooled when it is cooled to a temperature below its solidus. In the isothermal limit planar solidification fronts propagate at a constant velocity determined by the kinetic undercooling and are subject to a long-wavelength morphological instability if speeds fall below a critical value. Here we examine the adiabatic limit where the accumulation of a small latent heat release causes the velocity of the interface to slowly decrease through its critical value. The evolution of the hypercooled interface is governed by a damped Kuramoto-Sivashinsky (dKS) equation with coefficients that vary as the interface decelerates. Using this equation we show that morphological transitions are delayed by an amount that reflects both the time the system spends in a stable state and the magnitude of the damping. For a sufficiently large latent heat of fusion the long-wavelength morphological instability is annihilated. Finally, the adiabatic dKS equation predicts late-stage coarsening of the microstructure with length scales that increase as t(1/2). In finite systems this coarsening removes the morphological instability.