Ginzburg-Landau theory of crystalline anisotropy for bcc-liquid interfaces
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abstract
The weak anisotropy of the interfacial free-energy $\gamma$ is a crucial
parameter influencing dendritic crystal growth morphologies in systems with
atomically rough solid-liquid interfaces. The physical origin and quantitative
prediction of this anisotropy are investigated for body-centered-cubic (bcc)
forming systems using a Ginzburg-Landau theory where the order parameters are
the amplitudes of density waves corresponding to principal reciprocal lattice
vectors. We find that this theory predicts the correct sign,
$\gamma_{100}>\gamma_{110}$, and magnitude, $(\gamma_{100}-\gamma_{110}) /
(\gamma_{100}+\gamma_{110})\approx 1%$, of this anisotropy in good agreement
with the results of MD simulations for Fe. The results show that the
directional dependence of the rate of spatial decay of solid density waves into
the liquid, imposed by the crystal structure, is a main determinant of
anisotropy. This directional dependence is validated by MD computations of
density wave profiles for different reciprocal lattice vectors for $\{110\}$
crystal faces. Our results are contrasted with the prediction of the reverse
ordering $\gamma_{100}<\gamma_{110}$ from an earlier formulation of
Ginzburg-Landau theory [Shih \emph{et al.}, Phys. Rev. A {\bf 35}, 2611
(1987)].
