Inverse method for the determination of a mathematical expression for the anisotropy of the solid-liquid interfacial energy in Al-Zn-Si alloys.
An expression for the anisotropy of the solid-liquid interfacial energy has been determined experimentally by an inverse method for the Al-43.4 wt%Zn-1.6 wt%Si system. Assuming that dendrite growth directions correspond to the minima of the surface stiffness, the anisotropy of the solid-liquid interfacial energy could be described by minimizing the errors between the calculated minima of a parametric interface stiffness function and experimentally measured growth directions of dendrites in thin coatings. In order to adequately describe the interfacial energy, it is found that a cubic harmonic expansion up to the third order is necessary to obtain the minima of interface stiffness along directions that depart from <100> or <110>. Best agreement with observed growth directions is obtained for first, second, and third harmonic coefficients (epsilon1, epsilon2, and epsilon3, respectively) satisfying the following relationships: epsilon2/epsilon1 = -0.188; epsilon3/epsilon1 = -0.00776. The corresponding interface stiffness function shows 24 minima lying along directions between <100> and <110>. The minima are located at 28.5 degrees from <100> and only 5.1 degrees from <320>, which was the growth direction suggested by Sémoroz for this alloy [A. Sémoroz, Y. Durandet, and M. Rappaz, Acta Mater. 49, 529 (2001).]. It was also found that the strength of the effective in-plane anisotropy is directly reflected by the morphology of the dendritic microstructure.
Niederberger
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C
Computational Materials Laboratory, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Station 12, CH-1015 Lausanne, Switzerland. christoph.niederberger@epfl.ch
Michler
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J
Jacot
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A