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Free energy of the bcc–liquid interface and the Wulff shape as predicted by the phase-field crystal model
journal contributionposted on 06.11.2017, 12:44 by Frigyes Podmaniczky, Gyula TothGyula Toth, Tamas Pusztai, Laszlo Granasy
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 EA½0,0:5 . While the maximum free energy corresponds to the f100g orientation for all E values, the minimum is realized by the f111g direction for smaller Eðo0:13Þ, and by the f211g orientation for higher E. 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 stereographic plots displaying the anisotropy of the interface free energy. We have also derived the corresponding Wulff shapes that vary with increasing E 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.
This work has been supported by the EU FP7 Collaborative Project 'EXOMET' (contract no. NMP-LA-2012-280421, co-funded by ESA), and by the ESA MAP/PECS projects 'MAGNEPHAS III' (ESTEC Contract No. 4000105034/11/NL/KML) and 'GRADECET' (ESTEC Contract No. 4000104330/11/NL/KML).
- Mathematical Sciences