Ginzburg-Landau theory of the bcc-liquid interface kinetic coefficient

Abstract

We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid interfaces [Wu {\it et al.}, Phys. Rev. B \textbf{73}, 094101 (2006)] outside of equilibrium. We use this extension to derive an analytical expression for the kinetic coefficient, which is the proportionality constant $\mu (\hat{n})$ between the interface velocity along a direction $\hat{n}$ normal to the interface and the interface undercooling. The kinetic coefficient is expressed as a spatial integral along the normal direction of a sum of gradient square terms corresponding to different nonlinear density wave profiles. Anisotropy arises naturally from the dependence of those profiles on the angles between the principal reciprocal lattice vectors ${\vec{K}}_i$ and $\hat{n}$. Values of the kinetic coefficient for the$(100)$, $(110)$ and $(111)$ interfaces are compared quantitatively to the prediction of linear Mikheev-Chernov (MC) theory [J. Cryst. Growth \textbf{112}, 591 (1991)] and previous molecular dynamics (MD) simulation studies of crystallization kinetics for a classical model of Fe. Additional MD simulations are carried out here to compute the relaxation time of density waves in the liquid in order to make this comparison free of fit parameter. The GL theory predicts a similar expression for $\mu$ as the MC theory but yields a better agreement with MD simulations for both its magnitude and anisotropy due to a fully nonlinear description of density wave profiles across the solid-liquid interface. GL theory is also used to derive an inverse relation between $\mu$ and the solid-liquid interfacial free-energy. The general methodology used here to derive an expression for $\mu (\hat{n})$ also applies to amplitude equations derived from the phase-field-crystal model, which only differ from GL theory by the choice of cubic and higher order nonlinearities in the free-energy density.

References in corpus (9)

• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field crystal modeling of equilibrium bcc-liquid interfaces
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• Amplitude expansion of the binary phase field crystal model
• Renormalization group theory for the phase field crystal equation
• Ginzburg-Landau theory of crystalline anisotropy for bcc-liquid interfaces
• Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
• Amplitude equations for polycrystalline materials with interaction between composition and stress

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