Eutectic colony formation: A stability analysis

Experiments have widely shown that a steady-stare lamellar eutectic solidif ication front is destabilized on a scale much larger than the lamellar spac ing by the rejection of a dilute ternary impurity and forms two-phase cells commonly referred to as "eutectic colonies." We extend the stability analy sis of Datye and Langer [V. Datye and J. S. Langer, Phys. Rev. B 24, 4155 ( 1981)] for a binary eutectic to include the effect of a ternary impurity. W e find that the expressions for the critical onset velocity and morphologic al instability wavelength are analogous to those for the classic Mullins-Se kerka;a instability of a monophase planar interface, albeit with an effecti ve surface tension that depends on the geometry of the lamellar interface a nd, nontrivially, on interlamellar diffusion. A qualitatively new aspect of this instability is the occurrence of oscillatory modes due to the interpl ay between the destabilizing effect of the ternary impurity and the dynamic al feedback of the local change in lamellar spacing on the front motion. In a transient regime, these modes lead to the formation of large scale oscill atory microstructures for which there is recent experimental evidence in a transparent organic system. Moreover, it is shown that the eutectic front d ynamics on a scale larger than the lamellar spacing can be formulated as an effective monophase interface free boundary problem with a modified Gibbs- Thomson condition that is coupled to a slow evolution equation for the lame llar spacing. This formulation provides additional physical insights into t he nature of the instability and a simple means to calculate an approximate stability spectrum. Finally, we investigate the influence of the ternary i mpurity on a short wavelength oscillatory instability that is already prese nt at off-eutectic compositions in binary eutectics. [S1063-651X(99)18010-3 ].