화학공학소재연구정보센터
Journal of Crystal Growth, Vol.385, 148-153, 2014
Free energy of the bcc-liquid interface and the Wulff shape as predicted by the phase-field crystal model
The Euler-Lagrange equation of the phase-field crystal (PFC) model has been solved under appropriate boundary conditions to obtain the equilibrium free energy of the body centered cubic crystal-liquid interface for 18 orientations at various reduced temperatures in the range epsilon is an element of [0,0.5]. While the maximum free energy corresponds to the {100} orientation for all epsilon values, the minimum is realized by the {111} direction for smaller epsilon(<0.13), and by the {211} orientation for higher epsilon. The predicted dependence on the reduced temperature is consistent with the respective mean field critical exponent. The results are fitted with an eight-term Kubic harmonic series, and are used to create stet eographic plots displaying the anisotropy of the interface free energy. We have also derived the corresponding Wulff shapes that vary with increasing epsilon from sphere to a polyhedral form that differs from the rhombo-dodecahedron obtained previously by growing a bcc seed until reaching equilibrium with the remaining liquid. (C) 2013 Elsevier B.V. All rights reserved.