Experimental determination of the stability diagram of a lamellar eutectic growth front

We present an experimental study of the growth patterns of directionally solidified thin samples of the lamellar eutectic alloy CBr${}_4$-C${}_2$Cl${}_6$ as a function of the pattern wavelength $\lambda$, the solidification velocity $V$, and the alloy concentration $C$, within the so-called planar coupled zone of the parameter space. Capillary-anisotropy effects and three-dimensional (3D) effects are minimized by an appropriate choice of the eutectic grain size, the eutectic grain orientation, and the sample thickness. We first verify the old proposition made by Jackson and Hunt [Trans. AIME 236, 1129 (1996)] that the basic patterns (i.e., the stationary, spatially periodic, reflection-symmetric, 2D patterns) of our system are stable over a finite range of $\lambda$ at given $V$ and $C$, the lower bound of which is determined by a local, lamella-termination instability. We show that the upper bound of the basic state stability range is marked by a primary Hopf bifurcation toward an oscillatory state. The nature of the oscillatory state, and the threshold value for the bifurcation, depend on $C$. Other, secondary bifurcations occur at higher $\lambda$. In total, we identify six different types of low-symmetry extended growth patterns: the already-known steady symmetry-broken, or “tilted” state [K. Kassner and C. Misbah, Phys. Rev. A 44, 6533 (1991); G. Faivre and J. Mergy, ibid., 45, 7320 (1992)], and five new types of oscillatory and/or tilted states. We determine the stability domains of the various states in the plane $(C,\lambda V^{1/2})$, and characterize the various primary and secondary bifurcations of our system. Our experimental results are in good quantitative agreement with the stability diagram numerically calculated by Karma and Sarkissian [Metall. Mater. Trans. 27A, 635 (1996)] in the frame of a 2D model without capillary anisotropy.