Interphase anisotropy effects on lamellar eutectics: A numerical study
In directional solidification of binary eutectics, it is often observed
that two-phase lamellar growth patterns grow tilted with respect to the
direction z of the imposed temperature gradient. This crystallographic
effect depends on the orientation of the two crystal phases α and
β with respect to z. Recently, an approximate theory was formulated
that predicts the lamellar tilt angle as a function of the anisotropy
of the free energy of the solid(α)-solid(β) interphase boundary.
We use two different numerical methods - phase field (PF) and dynamic
boundary integral (BI) - to simulate the growth of steady periodic
patterns in two dimensions as a function of the angle θ between z
and a reference crystallographic axis for a fixed relative orientation
of α and β crystals, that is, for a given anisotropy function
(Wulff plot) of the interphase boundary. For Wulff plots without unstable
interphase-boundary orientations, the two simulation methods are in
excellent agreement with each other and confirm the general validity
of the previously proposed theory. In addition, a crystallographic
"locking" of the lamellae onto a facet plane is well reproduced in
the simulations. When unstable orientations are present in the Wulff
plot, it is expected that two distinct values of the tilt angle can
appear for the same crystal orientation over a finite θ range.
This bistable behavior, which has been observed experimentally, is
well reproduced by BI simulations but not by the PF model. Possible
reasons for this discrepancy are discussed.