The nature of the planar instability and pattern selection mechanisms attending directional thin film alloy solidification

Abstract

This reports on a study of the planar instability and the dynamics of the subsequent cellular pattern evolution on oriented and non-oriented alloy single crystals of succinonitrile-salol (S-Sa), succinonitrile-acetone (S-A) and pivalic acid-ethanol (P-E) alloys in directional solidification. Stable and unstable patterns for a total of 200 combinations of composition X 0, gradient G and velocity v have been recorded. The detailed systematics is reported elsewhere. In the near marginal range the wavelength and amplitude increase with v, both entering a decreasing mode at higher v. Upon jump-starting, it has been found that the planar breakdown invariably emanates from the ever-present adjacent grain or domain boundary positions. The microscopic imperfection at a boundary position spontaneously grooves as the velocity is jumped from zero and ultimately induces a non-uniform finite amplitude perturbation with sidebands of Mullins and Sekerka scale across an adjacent interface which contains a rich mix of wavenumbers. As the amplitude reaches the order of the wavelength, Ostwald ripening usually ensues wherein roughly every second wave is overgrown. For high supersaturations this wavelength doubling is repeated. The growth velocity for onset of a planar instability observed experimentally is close to that predicted by the constitutional supercooling criterion and by the thin film version of Mullins and Sekerka linear stability analysis. Within the long-lived transient state, tip-splitting, overgrowth and solitons generated spontaneously in oriented crystals ultimately adjust the cellular wavelength, amplitude and tip radius to relatively uniform, stable endpoint values. Kink manifestations or solitons which are almost stationary in the crystal frame of reference play a critical role in the final stages of a selected pattern whose wavelength is always larger than that of the initiating perturbation.