A theory of thin lamellar eutectic growth with anisotropic interphase boundaries

We present a semiempirical theory of the effects of an orientation dependence of the surface free energy of interphase boundaries (interphase boundary anisotropy) on lamellar eutectic growth in thin samples. We show that, to a good approximation, thin lamellar eutectic patterns with a strong interphase boundary anisotropy travel along the growth front at such a velocity - or, equivalently, at such an inclination angle of the lamellae left behind in the solid - that the surface tension force of the interphase boundary is nearly parallel to the applied thermal gradient. This explains, among other things, the crystallographic locking of lamellar eutectic patterns that occurs in those eutectic grains, which have cusp singularities in the Wulff plot of the interphase boundary. Based on this theory, we show that the rotating directional solidification method, by which a thin sample is rotated with respect to a fixed unidirectional thermal gradient, must yield eutectic lamellae whose trajectories are nearly homothetic to the two-dimensional Wulff form of the interphase boundary. This opens up new possibilities for the experimental study of interphase boundary anisotropy in eutectic alloys.