Atomistic Determination of Anisotropic Surface Energy-Associated Growth Patterns of Magnesium Alloy Dendrites

Because of the existence of anisotropic surface energy with respect to the hexagonal close-packed (hcp) lattice structure, magnesium alloy dendrite prefers to grow along certain crystallographic directions and exhibits a complex growth pattern. To disclose the underlying mechanism behind the three-dimensional (3-D) growth pattern of magnesium alloy dendrite, an anisotropy function was developed in light of the spherical harmonics and experimental findings. Relevant atomistic simulations based on density functional theory were then performed to determine the anisotropic surface energy along different crystallographic directions, and the corresponding anisotropic strength was quantified via the least-square regression. Results of phase field simulations showed that the proposed anisotropy function could satisfactorily describe the 3-D growth pattern of the α-Mg dendrite observed in the experiments. Our investigations shed great insight into understanding the pattern formation of the hcp magnesium alloy dendrite at an atomic level.

Correlation between crystallographic anisotropy and dendritic orientation selection of binary magnesium alloys

Both synchrotron X-ray tomography and EBSD characterization revealed that the preferred growth directions of magnesium alloy dendrite change as the type and amount of solute elements. Such growth behavior was further investigated by evaluating the orientation-dependent surface energy and the subsequent crystallographic anisotropy via ab-initio calculations based on density functional theory and hcp lattice structure. It was found that for most binary magnesium alloys, the preferred growth direction of the α-Mg dendrite in the basal plane is always \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 11\bar{2}0\rangle $$\end{document}〈112¯0〉, and independent on either the type or concentration of the additional elements. In non-basal planes, however, the preferred growth direction is highly dependent on the solute concentration. In particular, for Mg-Al alloys, this direction changes from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 11\bar{2}3\rangle $$\end{document}〈112¯3〉 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 22\bar{4}5\rangle $$\end{document}〈224¯5〉 as the Al-concentration increased, and for Mg-Zn alloys, this direction changes from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 11\bar{2}3\rangle $$\end{document}〈112¯3〉 to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 22\bar{4}5\rangle $$\end{document}〈224¯5〉 or \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle 11\bar{2}2\rangle $$\end{document}〈112¯2〉 as the Zn-content varied. Our results provide a better understanding on the dendritic orientation selection and morphology transition of magnesium alloys at the atomic level.

The solid-liquid interface free-energy of Pb: comparison of theory and experiments

The solid-liquid interface free-energy γ(sl) is a key parameter controlling nucleation and growth during solidification and other phenomena. Different experimental techniques are available for its evaluation but results are often widely scattered and strongly depend on the technique used. One of the best examples in this sense is the case of elemental Pb, with values for γ(sl) differing by as much as 150% between nucleation rate experiments and contact angle data. Even using simple many-body potentials, theoretical calculations of γ(sl) can exceed this level of accuracy and thus be employed to assess the present experimental data. To this purpose, atomistic calculations are performed in conjunction with two different many-body potentials for Pb. These show good agreement with nucleation rate and depression of melting point experiments and support the case for a reassessment of the measurements reported from contact angle data. Possible sources of errors that might have affected these experiments are critically discussed, showing how the magnitude of the anisotropy in the interfacial free energies can be important in closing the gap between the different sets of experimental data.

Grain-boundary fluctuations in two-dimensional colloidal crystals

We study grain-boundary fluctuations in two-dimensional colloidal crystals in real space and time using video microscopy. The experimentally obtained static and dynamic correlation functions are very well described by expressions obtained using capillary wave theory. This directly leads to values for the interfacial stiffness and the interface mobility, the key parameters in curvature-driven grain-boundary migration. Furthermore, we show that the average grain-boundary position exhibits a one-dimensional random walk as recently suggested by computer simulations [Z. T. Trautt, M. Upmanyu, and A. Karma, Science 314, 632 (2006)]. The interface mobility determined from the mean-square displacement of the average grain-boundary position is in good agreement with values inferred from grain-boundary fluctuations.