Instability of triple junctions in lamellar eutectic growth

By employing the method of multiple-scale expansions we derive a system of nonlinear ordinary differential equations to describe the dynamics of lamellar eutectic crystals in directional solidification. The equations govern the motions of trijunctions where the liquid and the two solid phases meet, and predict a critical lamellar spacing λ_c below which the solidifying fronts are unstable. When the morphological numbers are large this critical spacing agrees with the value predicted by the Jackson and Hunt's theory: Vλ_c² = constant, where V is the growth speed. As the morphological numbers decrease, the speed-spacing relationship deviates from the power law, with the predicted spacing smaller than that at the minimum undercooling point. The thermal gradient then plays an important role in determining the lamellar structures.