Abstract
We present a numerical study of the effect of a free-energy anisotropy of the solid- solid interphase boundaries on the formation of tilted lamellar microstructures during directional solidification of nonfaceted binary eutectic alloys. We used two different methods - phase-field (PF) and dynamic boundary-integral (BI) - to simulate the growth of periodic eutectic patterns in two dimensions. For a given Wulff plot of the interphase boundary, which characterizes a eutectic grain with a given relative orientation of the two solid phases, the lamellar tilt angle depends on the angle between the thermal axis z and a reference crystallographic axis. Both PF and BI results confirm the general validity of a recent approximate theory which assumes that, at the trijunctions, the surface tension vector of the interphase boundary is parallel to z. In particular, a crystallographic locking of the lamellae onto a direction close to a deep minimum in the Wulff plot is well reproduced in the simulations.
Highlights
In many nonfaceted eutectic alloys, two-phase microstructures that are delivered by coupledgrowth front patterns during directional solidification (DS) present a marked morphological dependence on the crystal orientation of the two solid phases [1, 2, 3]
The simulations confirm the semi-quantitative validity of the SP approximation that assumes that the surface tension vector of the interphase boundary at the trijunctions is parallel to the main growth axis
The most salient result is that a strong locking phenomenon associated with the existence of a sharp minimum in the Wulff plot is well reproduced by the simulations
Summary
In many nonfaceted eutectic alloys, two-phase microstructures that are delivered by coupledgrowth front patterns during directional solidification (DS) present a marked morphological dependence on the crystal orientation of the two solid phases [1, 2, 3]. A strong locking of the lamellae onto the direction of the peaked minimum of the anisotropy function is well reproduced in both BI and PF simulations. 2. The symmetric-pattern approximation The relative orientation of the α and β crystals (constant within a grain) determines the interphase boundary free energy and its anisotropy.
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