Crossover Scaling of Wavelength Selection in Directional Solidification of Binary Alloys

TL;DR

This paper investigates how the spacing of dendritic structures in binary alloys during directional solidification depends on growth conditions, revealing a crossover scaling behavior validated by experiments.

Contribution

It introduces a new crossover scaling function that describes wavelength selection from cellular to dendritic growth in alloy solidification.

Findings

Spacing exhibits a maximum as a function of pulling velocity.

Scaling function accurately describes the transition in growth modes.

Results align with experimental data on dendritic growth.

Abstract

We simulate dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with an adaptive-mesh refinement. The spacing of primary branches is examined for a range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a non-trivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers, a result validated using published experimental data.