SPONTANEOUS PARITY-BREAKING TRANSITION IN DIRECTIONAL GROWTH OF LAMELLAR EUTECTIC STRUCTURES

A full study of parity-broken states in the directional solidification of lamellar eutectics is performed within the boundary-integral formulation. Symmetric states cease to exist at a wavelength lambda, which is approximately twice that corresponding to their minimum undercooling, whereas solutions with a broken parity, drifting transversely to the growth front, appear as a forward bifurcation. Our results suggest that if one effectively doubles the wavelength of the initially symmetric state-a situation that can be achieved via a sudden jump of the velocity V by a factor of about 4, since lambda-2V congruent-to const-then tilted lamellae should appear as extended states and not as "solitons." We find here that parity-broken states exist for hypereutectic as well as for hypoeutectic and eutectic compositions. We have extended the derivation of the similarity equation derived previously [K. Kassner and C. Misbah, Phys. Rev. Lett. 66, 445 (1991)] to the present situation. This case involves additional subtleties, due to the loss of reflection symmetry about the growth axis. Among other results, we find that the tilt angle phi should depend on sigma = d0l/lambda-2 and CHI = l/l(T) only, where d0, l, and l(T) are the capillary, diffusion, and thermal lengths, respectively, and lambda is the wavelength of the pattern. At large enough growth velocities V, phi congruent-to phi(sigma), while at small V the dependence on CHI is strong. These predictions can be tested experimentally.