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 Al-Sn binary system at temperatures of 300 and 500°C. Equilibrium shapes of liquid droplets entrained within the crystalline phase are measured experimentally on sequential two-dimensional sections, and the threedimensional 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 ε1=(1.81±0.36)×10−2 and ε2=(−1.12±0.13)×10−2. In addition, the corresponding normal stiffness components as well as a generalized stiffness are quantified and compared with available predictions from atomistic simulations. 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 Al-Sn binary system at temperatures of 300 and 500°C. Equilibrium shapes of liquid droplets entrained within the crystalline phase are measured experimentally on sequential two-dimensional sections, and the threedimensional 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 1 = ͑1.81± 0.36͒ ϫ 10 −2 and 2 = ͑−1.12± 0.13͒ ϫ 10 −2 . In addition, the corresponding normal stiffness components as well as a generalized stiffness are quantified and compared with available predictions from atomistic simulations.

Study of the twinned dendrite tip shape II: Experimental assessment

“…First, direct observations of the shape of the primary phase morphology near a dendrite tip that was stopped by impingement on another grain reveal the presence of a small groove. This clearly eliminates the conjecture of an edgy tip suggested by Watson and Hunt [18], conjecture that is also incompatible with the low anisotropy of the solid-liquid interfacial energy measured recently in aluminum alloys [5]. Second, using FIB reconstruction and observation, small zinc-rich particles have been found all along the twin plane of twinned Al-30 wt.% Zn dendrites.…”

“…An edgy tip would definitely give a growth advantage to twinned dendrites over regular ones, but this shape is incompatible with the very weak anisotropy measured recently for c s' in Al-Cu alloys [5]. On the other hand, a steady-state grooved dendrite tip would make solute diffusion more difficult and thus should not give it a growth advantage.…”

Influence of Cr on the nucleation of primary Al and formation of twinned dendrites in Al–Zn–Cr alloys: Can icosahedral solid clusters play a role?

“…More confusion has been brought recently by Li et al [13], who observed that the application of a static magnetic field of only 0.2 T, which is supposed to weaken convection, induces the formation of twinned dendrites in Al-Fe and Al-Zn alloys in small DC cast ingots. Finally, although twinned dendrites have a growth advantage over regular dendrites under the above-mentioned conditions, there is still some uncertainty about their tip morphology [3,12,[14][15][16][17][18]. More important, nothing is known about twin nucleation.…”

Free energy of the bcc–liquid interface and the Wulff shape as predicted by the phase-field crystal model

“…Anisotropy is needed for dendritic structures, and apparently a detailed knowledge on anisotropy is required to fully understand the growth morphology [2]. Experimentally, the anisotropy of the interface free energy can be deduced from the shape of liquid inclusions in a solid matrix (though, one needs to be careful to relax all the stresses before converting the shape into anisotropy) [3,4,5,6]. Anisotropy has also been evaluated on the basis of the assumption that the dendrite growth directions correspond to the maximum stiffness, and minimizing the deviation between the calculated minima of an appropriately parameterized interface stiffness function and the growth directions of dendrites found in thin coatings experimentally [7].…”

“…Other methods evaluate the interface free energy and its anisotropy from molecular dynamics simulations [8,9,10,11,12] using empirical model potentials such as the embedded atom potential. Whether experiment [5,6,7] or atomistic simulation [8,9,10,11,12], the anisotropic interface free energy data are usually fitted by the cubic harmonic expansion series introduced by Fehlner and Vosko [13]. Often only a few low index orientations are considered (typically {100}, {110}, and {111}), and a second-order cubic harmonic expansion is employed [5,6,7,8,9].…”