New broken-parity state and a transition to anomalous lamellae in eutectic growth

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Abstract
We discover that a eutectic system exhibits pseudobicritical features corresponding to the simultaneous birth of two different broken-parity states. The first branch is the known tilted-growth mode, global parity breaking; it bifurcates from the usual lamellar symmetric state. At approximately the same criticial point, a second brach merges close to the second fold we found previously. The two states thus bifurcate from different basic states. This new branch owes its existence to the underlying degeneracy of the usual broken-parity state. It consists of a structure where one lamella assumes a right-traveling and the other a left-traveling state. As a consequence, the drift velocity (or equivalently the tilt angle) is smaller for the new branch. Close to the bicritical point, the bifurcation is described by a Landau theory with the tilt angle being the order parameter. From general considerations we can state that the new branch is locally stable in the kinetic sense, but less stable than the usual branch. This result is consistent with the conventional criterion based on comparison of undercooling, since the new branch has a higher undercooling. We propose a simple experimental protocol to have access to the new state. Finally, when the two lamellae have equivalent properties (a symmetric case) the new state is not traveling while each lamella is asymmetric with respect to its center and is a mirror image of the other lamella. This corresponds to the so-called anomalous cells observed in noneutectic systems. We develop an analytic theory, in the same spirit as the one used for the parity breaking, to account for the transition to the anomalous state. The results are in qualitative agreement with the full numerical calculation.