ANALYTIC THEORY FOR PARITY BREAKING IN LAMELLAR EUTECTIC GROWTH

An extensive analytic analysis of tilted lamellar growth is presented. We first confine ourselves to a situation where both solid phases are identical and the concentration is maintained at the eutectic composi tion far ahead of the solidification front. A Rapid Communication has already been devoted to this case [C. Misbah and D. E. Temkin, Phys. R ev. A 46, R4497 (1992)]. Here, we first focus on an extensive analysis of this problem and a comparison with the full numerical calculation. We find good agreement between the two situations, a fact which confe rs confidence in the applicability of our analytic results to real sit uations. In the second line of this work, we shall analyze the effect of an off-eutectic composition. We show, contrary to some previous wor k based on a random-walker method, that the effect of the homogeneous boundary layer (which plays the role of a total net charge in an elect rostatic analogy) does not play a crucial role for parity breaking, in agreement with our previous numerical work in the continuous limit. F inally, the effect of crystalline anisotropy is analyzed. It is shown that the bifurcation equation, which is of pitchfork type in the isotr opic case, becomes imperfect.