MORPHOLOGICAL INSTABILITIES OF LAMELLAR EUTECTICS

We present the results of a numerical study based on the boundary inte gral technique of interfacial pattern formation in directional solidif ication of thin-film lamellar eutectics at low velocity. Microstructur e selection maps that identify the stability domains of Various steady -state and nonsteady-state growth morphologies in the spacing-composit ion (lambda - C-0) plane are constructed for the transparent organic a lloy CBr4-C2Cl6 and for a model eutectic alloy with two solid phases o f identical physical properties. In CBr4-C2Cl6, the basic set of insta bilities that limit steady-state growth is richer than expected. It co nsists of three primary instabilities, two of which are oscillatory, w hich bound the domain of the commonly observed axisymmetric lamellar m orphology, and two secondary oscillatory instabilities, which bound th e domain of the nonaxisymmetric (tilted) lamellar morphology. The latt er is predicted to occur over a hypereutectic range of composition whi ch coincides well with experiment. Moreover, the steady tilt bifurcati on lies between but does not directly bound either of these two domain s, which are consequently disjoint. Four stable oscillatory microstruc tures, at least three of which have been seen experimentally, are pred icted to occur in unstable regimes. In the model alloy, the structure is qualitatively similar, except that a stable domain of tilted steady -state growth is not found, in agreement with previous random-walk sim ulations, Furthermore, the composition range of stability of the axisy mmetric morphology decreases sharply with increasing spacing away from minimum undercooling but extends further off-eutectic than predicted by the competitive growth criterion. In addition, oscillations with a wavelength equal to two lambda lead to lamella termination at a small distance above the onset of instability, The implications of these two features for the eutectic to dendrite transition are examined with th e conclusion that in the absence of heterogeneous nucleation, this tra nsition should be histeritic at small velocity and temperature gradien t.