# Influence of morphological instability on grain boundary trajectory during directional solidification

## TL;DR

This study investigates how morphological instability influences grain boundary trajectories during directional solidification, revealing that grain boundary tilt angles depend on solidification velocity and interface stability, with implications for material microstructure control.

## Contribution

It combines experiments and phase-field simulations to elucidate the effect of morphological instability on grain boundary behavior during directional solidification.

## Key findings

- Tilt angle of grain boundaries remains constant at low velocities.
- Tilt angle decreases and vanishes as cellular morphology forms at higher velocities.
- Absence of grain boundary mobility in the solid is crucial for the transition.

## Abstract

The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a transparent alloy, and by numerical simulations with the phase-field method in two dimensions. We find that low-angle grain boundaries (subboundaries) with an anisotropic interfacial free energy grow tilted at an angle $\theta_t$ with respect to the temperature gradient axis. $\theta_t$ remains essentially equal to its value imposed at equilibrium as long as the solidification velocity $V$ remains low. When $V$ increases and approaches the cellular instability threshold, $\theta_t$ decreases, and eventually vanishes when a steady-state cellular morphology forms. The absence of mobility of the subboundary in the solid is key to this transition. These findings are in good agreement with a recent linear-stability analysis of the problem.