Stability of hexagonal solidification patterns

TL;DR

This paper uses 3D phase-field simulations to analyze the stability and dynamics of hexagonal solidification patterns, revealing how anisotropy influences stability and identifying new multiplet states.

Contribution

It introduces a detailed analysis of secondary instabilities and stability boundaries of hexagonal patterns in solidification, highlighting the role of anisotropy and perturbations.

Findings

Hexagonal patterns can be stable or unsteady depending on parameters.

Stability boundaries are strongly affected by crystalline anisotropy.

Multiplet states can be induced by specific perturbations.

Abstract

We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary instabilities of regular hexagonal arrays and find that the stability boundaries depend significantly on the strength of crystalline anisotropy. We also find multiplet states that can be reached by applying well-defined perturbations to a pre-existing hexagonal array.