Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems

Abstract

Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morphology is the periodic arrangement of lamellar plates with well-defined orientations of the solid-solid interface in a given eutectic grain. It is typically believed that this form of morphology develops due to the presence of solid-solid interfacial energy anisotropy. In this paper, we provide evidence using phase-field simulations where our focus is on alloys where the minority phase fraction is low. Our aim is to establish the role of solid-solid interfacial energy anisotropy in the stabilization of broken lamellar structures in such systems in contrast to the formation of a rod microstructure. In this regard, we conduct phase-field simulations for different strengths of anisotropy in both constrained and extended settings, using which we clarify the mechanisms by which a lamellar arrangement gets stabilized in the presence of anisotropy in the solid-solid interfacial energy.

Coexistence of rod-like and lamellar eutectic growth patterns

“…The curvature effect also entailed the alignment of the subboundaries -but no crystal-orientation effects were detected [18,24], in contrast to observations reported in, e.g., Refs. [46,47]. At low velocity, a few short lamellae were observed along subboundaries, and in contact with the sample wall (Fig.…”

Role of interfacial energy and liquid diffusivities on pattern formation during thin-film three-phase eutectic growth

“…where s is the relaxation constant that controls the interface kinetics [39] and is calculated as in [45,46]. controls the diffuse interface width.…”

“…In the preceding equation 2, we have used the matrix-vector notation, where quantities in curly braces {} are vectors of size K À 1, while quantities in square brackets [] are matrices of size ðK À 1Þ Â ðK À 1Þ. The set c a ¼ ðc a A ; c a B Þ contains the concentrations of the independent components of each phase, h a ð/Þ is the interpolation function between phases (the form is chosen the same as in [46]). J at;i is the anti-trapping current (functional form is available in [45,46]), and under directional solidification at temperature gradient G T and a constant velocity v, oT ot ¼ ÀG T v. The mobility matrix M ij is linearly interpolated between the phases with gð/ a Þ ¼ / a as…”

Role of interfacial energy and liquid diffusivities on pattern formation during thin-film three-phase eutectic growth

“…where τ is the relaxation constant that controls the interface kinetics [39] and is calculated as in [45,46]. controls the diffuse interface width.…”

“…In the preceding equation 2, we have used the matrix-vector notation, where quantities in curly braces {} are vectors of size K-1, while quantities in square brackets [] are matrices of size (K-1)×(K-1). The set c α = (c α A , c α B ) contains the concentrations of the independent components of each phase, h α (φ) is the interpolation function between phases (the form is chosen the same as in [46]). J at,i is the anti-trapping current (functional form is available in [45,46]), and under directional solidification at temperature gradient G T and a constant velocity v, ∂T ∂t = −G T v. The mobility matrix M ij is linearly interpolated between the phases with g(φ α ) = φ α as…”