Stability of thin lamellar eutectic growth

Abstract

We have performed a stability analysis for the Jackson-Hunt model of a directionally solidifying, thin-film, lamellar eutectic. Allowed perturbations include displacements of the solid-solid-liquid triple points in directions both parallel and perpendicular to the direction of growth. These displacements are coupled in such a way that growth of each lamella is always perpendicular to the local orientation of the solidification front. The discrete approach adopted here allows us to compute a full spectrum of stability eigenmodes, including modes whose periodicities are of the order of the lamellar spacing. We find that for all values of melt composition or temperature gradient, there is a long-wavelength instability at lamellar spacings less than a critical value which corresponds to minimum undercooling. Thus, minimum undercooling coincides exactly with marginal instability in this model. At sufficiently off-eutectic melt compositions there occurs a second, oscillatory instability with a wavelength equal to twice the lamellar spacing. There is experimental evidence for the existence of such modes.