title: Interphase anisotropy effects on lamellar eutectics: a numerical study.
abstract: 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(R) 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(R) 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.
authors.affiliation: Condensed Matter Physics, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.
authors.forename: Supriyo
authors.initials: S
authors.lastname: Ghosh
authors.affiliation: Condensed Matter Physics, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.|Department of Materials Engineering, Indian Institute of Science, 560012, Bangalore, India.
authors.forename: Abhik
authors.initials: A
authors.lastname: Choudhury
authors.affiliation: Condensed Matter Physics, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.
authors.forename: Mathis
authors.initials: M
authors.lastname: Plapp
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7588, INSP, 75005 Paris, France.|CNRS, UMR 7588, Institut des Nanosciences de Paris, 75005 Paris, France.
authors.forename: Sabine
authors.initials: S
authors.lastname: Bottin-Rousseau
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7588, INSP, 75005 Paris, France.|CNRS, UMR 7588, Institut des Nanosciences de Paris, 75005 Paris, France.
authors.forename: Gabriel
authors.initials: G
authors.lastname: Faivre
authors.affiliation: Sorbonne Universités, UPMC Univ Paris 06, UMR 7588, INSP, 75005 Paris, France.|CNRS, UMR 7588, Institut des Nanosciences de Paris, 75005 Paris, France.
authors.forename: Silvère
authors.initials: S
authors.lastname: Akamatsu