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 ϵ∈[0,0.5]ϵ∈[0,0.5]. While the maximum free energy corresponds to the {100}{100} orientation for all ϵϵ values, the minimum is realized by the {111}{111} direction for smaller ϵ(<0.13)ϵ(<0.13), and by the {211}{211} orientation for higher ϵϵ. 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 ϵϵ 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.

► A mapping of the bcc–liquid interfacial free energy is performed with the PFC model.
► The interfacial free energy is consistent with the respective mean field exponent.
► The data are fitted by an expression based on the Kubic harmonics expansion.
► Wulff shapes are constructed based on the interfacial free energy data.
► The Wulff shape at large reduced temperatures differs from a rhombo-dodecahedron.