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.

中文翻译：

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固-固各向异性影响层状共晶生长前缘对称性破缺的解析理论

摘要 为了更好地理解定向凝固过程中具有固固各向异性的层状共晶生长，我们提出了一种解析理论。使用 ansatz 获得不对称的生长前沿剖面，获得扩散场的解决方案（Valance 等人，1993 年）。施加 Gibbs-Thomson 条件，我们推导出固-固界面表面张力相对于热流方向的倾斜角的一般表达式。我们发现固-固界面的表面张力通常不平行于热流方向，这表明共晶薄片的生长前沿偏离了对称模式。因为固-固界面表面张力的倾角小于零，层状图案的倾斜角总是小于对称图案近似预测的值（Akamatsu 等，2012）。给出了计算特定各向异性函数下表面张力和层状图案的倾斜角的示例。这些结果进一步了解具有固-固各向异性的层状共晶生长。