Mullins and Sekerka showed for fixed temperature gradient that the planar interface is linearly stable for all pulling speeds V above some critical value, the absolute stability limit. Near this limit, where solidification rates are rapid, the assumption of local equilibrium at the interface may be violated. We incorporate nonequilibrium effects into a linear stability analysis of the planar front by allowing the segregation coefficient and interface temperature to depend on V in a thermodynamically-consistent way. In addition to the steady cellular mode, we find a new branch of long-wavelength time-periodic states. Under certain conditions there exists a stability window separating the steady and oscillatory branches.

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