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 (Valance et al., 1993). 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 (Akamatsu et al., 2012). 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.