Coupling between crystalline anistropy and spontaneous parity breaking in lamellar eutectic growth

Recently, we demonstrated that the liquid-solid interface of the isotropic model of lamellar eutectic growth may undergo a parity-breaking transition from a symmetric to a tilted state. We found that the bifurcation to the asymmetric state is supercritical. Now we have solved the full boundary integral equation of the system assuming anisotropic surface tension. We observe that generically the supercritical bifurcation becomes imperfect, as could be expected from a simple phenomenological picture. In order to study whether finite domains of tilted states can exist under these circumstances, we consider a simple model for the coupling between tilt angle and phase dynamics that exhibits an imperfect bifurcation. We find that if the anisotropy is not too strong, the coupling leads to a picture that retains many of the qualitative features of the phenomenological approach given by Coullet, Goldstein, and Gunaratne [Phys. Rev. Lett. 63, 1954 (1989)] for subcritical bifurcations. Furthermore, we offer a natural explanation for the experimental finding that on creation of a tilted state lamellae of a given grain preferentially tilt in one direction, not in the opposite one.