An expression for the anisotropy of the solid-liquid interfacial energy has been determined experimentally by an inverse method for the $\mathrm{Al}\text{−}43.4\mathrm{wt}\%\mathrm{Zn}\text{−}1.6\mathrm{wt}\%\mathrm{Si}$ 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 (${\epsilon }_1$, ${\epsilon }_2$, and ${\epsilon }_3$, respectively) satisfying the following relationships: ${\epsilon }_2∕{\epsilon }_1=-0.188$; ${\epsilon }_3∕{\epsilon }_1=-0.00776$. The corresponding interface stiffness function shows 24 minima lying along directions between $⟨100⟩$ and $⟨110⟩$. The minima are located at 28.5° from $⟨100⟩$ and only 5.1° from $⟨320⟩$, which was the growth direction suggested by Sémoroz et al. 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.

• Received 10 April 2006
• Publisher error corrected 29 August 2006

DOI:https://doi.org/10.1103/PhysRevE.74.021604