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

We extend the Ginzburg-Landau (GL) theory of atomically rough bcc-liquid interfaces outside of equilibrium to derive an analytical expression for the kinetic coefficient $\mu(\hat n)$. 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 and previous MD simulation studies of crystallization kinetics for a classical model of Fe. 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. In particular, the overall magnitude of $\mu$ predicted by GL theory is an order of magnitude larger than predicted by the MC theory. GL theory is also used to derive an inverse relation between $\mu$ and the solid-liquid interfacial free-energy.