Ternary eutectic dendrites: Pattern formation and scaling properties

TL;DR

This study uses phase-field modeling to explore pattern formation, scaling, and morphological transitions in ternary eutectic dendrites, revealing the influence of velocity, anisotropy, and fluctuations on their structures.

Contribution

It provides a detailed phase diagram of eutectic dendrite morphologies and confirms the Jackson-Hunt scaling law within a comprehensive ternary system model.

Findings

Eutectic dendrites exhibit various morphologies depending on pulling velocity.

The dendrite tip radius scales with interface free energy similarly for one- and two-phase structures.

Eutectic patterns include target, spiral, and flat front structures, influenced by thermal fluctuations.

Abstract

Extending previous work [T. Pusztai, L. R\'atkai, A. Sz\'all\'as, and L. Gr\'an\'asy, Phys. Rev. E {\bf 87}, 032402 (2013)], we have studied the formation of eutectic dendrites in a model ternary system within the framework of the phase-field theory. We have mapped out the domain in which two-phase dendritic structures grow. With increasing pulling velocity, the following sequence of growth morphologies is observed: flat front lamellae $\rightarrow$ eutectic colonies $\rightarrow$ eutectic dendrites $\rightarrow$ dendrites with target pattern $\rightarrow$ partitionless dendrites $\rightarrow$ partitionless flat front. We confirm that the two-phase and one-phase dendrites have similar forms, and display a similar scaling of the dendrite tip radius with the interface free energy. It is also found that the possible eutectic patterns include the target pattern, and single- and multiarm spirals, of which the thermal fluctuations choose. The most probable number of spiral arms increases with increasing tip radius and with decreasing kinetic anisotropy. Our numerical simulations confirm that in agreement with the assumptions of a recent analysis of two-phase dendrites [S. Akamatsu, S. Bottin-Rousseau, G. Faivre, and E. A. Brener, Phys. Rev. Lett. {\bf 112}, 105502 (2014)], the Jackson-Hunt scaling of the eutectic wavelength with pulling velocity is obeyed in the parameter domain explored, and that the natural eutectic wavelength is proportional to the tip radius of the two-phase dendrites. Finally, we find that it is very difficult/virtually impossible to form spiraling two-phase dendrites without anisotropy, an observation that seems to contradict the expectations of Akamatsu {\it et al.}. Yet, it cannot be excluded, that in isotropic systems two-phase dendrites are rare events difficult to observe in simulations.