An analytic theory for the symmetry breaking of growth-front in lamellar eutectic growth influenced by solid-solid anisotropy

Abstract We have presented an analytic theory to get a better understanding of lamellar eutectic growth with solid-solid anisotropy during directional solidification. Using an ansatz for an asymmetric profile of the growth-front, the solution for diffusion field is obtained [A. Valance, C. Misbah, D. Temkin. PHYS REV E. 1993, 48(3): 1924.]. Imposing the Gibbs-Thomson condition, we derive a general expression for the tilt angle of surface tension force of the solid-solid interface with respect to the heat-flow direction. We found that the surface tension force of the solid-solid interface is generally not paralleled to the heat-flow direction, which indicates that the growth-front of eutectic lamellae deviates from the symmetric-pattern. Because the tilt angle of the surface tension force of the solid-solid interface is less than zero, the tilt angle of lamellar patterns is always less than the value predicted by the symmetric-pattern approximation [S. Akamatsu, S. Bottin-Rousseau, et al. ACTA MATER 2012;60:3199]. An example where the tilt angle of surface tension force and lamellar patterns under a specific anisotropy function are calculated is presented. These results give a further understanding of lamellar eutectic growth with solid-solid anisotropy.