Three-dimensional crystal-melt Wulff-shape and interfacial stiffness in the Al-Sn binary system

Abstract

The quantitative determination of the three-dimensional Wulff shape for a metallic crystal-melt system is reported here. The anisotropy of crystal-melt interfacial free energy is experimentally measured for the $\mathrm{Al}--\mathrm{Sn}$ binary system at temperatures of 300 and $500\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. Equilibrium shapes of liquid droplets entrained within the crystalline phase are measured experimentally on sequential two-dimensional sections, and the three-dimensional Wulff plot is reconstructed. For this system, it is found that a single-parameter description of anisotropy is not sufficient, and the anisotropy is reported using the leading terms of the relevant cubic harmonics. Accordingly, the anisotropy coefficients are determined to be ${\ensuremath{\epsilon}}_{1}=(1.81\ifmmode\pm\else\textpm\fi{}0.36)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and ${\ensuremath{\epsilon}}_{2}=(\ensuremath{-}1.12\ifmmode\pm\else\textpm\fi{}0.13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$. In addition, the corresponding normal stiffness components as well as a generalized stiffness are quantified and compared with available predictions from atomistic simulations.