Effect of Surface Free Energy Anisotropy on Dendrite Tip Shape
Effect of Surface Free Energy Anisotropy on Dendrite Tip Shape
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DOI：
10.1016/s1359-6454(00)00105-1
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发表时间：
1999-08
期刊：
影响因子：
9.4
通讯作者：
G. McFadden;S. Coriell;R. Sekerka
中科院分区：
文献类型：
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作者：
G. McFadden;S. Coriell;R. Sekerka
在以前的工作中，近似解被发现抛物面具有扰动与四重轴对称，以模拟立方材料中的枝晶生长。这些解决方案提供了自洽的修正，通过二阶的形状参数ε的佩克莱数与Ivantsov解决方案的过冷关系。参数ε与从Ivantsov旋转抛物面测量的对枝晶形状的四倍校正的幅度成比例。计算了各向异性二阶表面自由能的平衡形状。ε的值通过比较枝晶尖端形状与生长方向附近的平衡形状部分[001]来确定，对于形式为γ=γ0[1+4ε4（n14+n24+n34）]的各向异性表面自由能，其中ni是晶体表面的单位法线的分量。这个比较的结果是ε=−2ε4−24ε42+O（ε43），与Peclet数无关。从ε4的实验值发现，ε =-0.012 ±0.004，与拉科姆贝等人（Phys. Rev. E，1995，52，2778）的测量值ε ε =-0.008非常一致。
In previous work, approximate solutions were found for paraboloids having perturbations with four-fold axial symmetry in order to model dendritic growth in cubic materials. These solutions provide self-consistent corrections through second order in a shape parameter ε to the Peclet number vs supercooling relation of the Ivantsov solution. The parameter ε is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. The equilibrium shape for anisotropic surface free energy to second order in the anisotropy is calculated. The value of ε is determined by comparing the dendrite tip shape with the portion of the equilibrium shape near the growth direction, [001], for anisotropic surface free energy of the form γ=γ0[1+4ε4(n14+n24+n34)], where the niare components of the unit normal of the crystal surface. This comparison results in ε=−2ε4−24ε42+O(ε43), independent of the Peclet number. From the experimental value of ε4, it is found that ε≈−0.012±0.004, in good agreement with the measured value ε≈−0.008 of LaCombe et al. (Phys. Rev. E, 1995, 52, 2778)