Tilt grain boundary instabilities in three dimensional lamellar patterns

TL;DR

This paper discovers a finite wavenumber instability in three-dimensional lamellar grain boundaries that is absent in two dimensions, analyzing its characteristics through stability analysis and numerical simulations.

Contribution

It identifies and characterizes a new finite wavenumber instability specific to three-dimensional lamellar grain boundaries, not present in two-dimensional cases.

Findings

Instability involves two-dimensional perturbations of the boundary.

Most unstable wavenumbers and growth rates increase with epsilon.

The instability is suppressed for purely one-dimensional perturbations.

Abstract

We identify a finite wavenumber instability of a 90$^{\circ}$ tilt grain boundary in three dimensional lamellar phases which is absent in two dimensional configurations. Both a stability analysis of the slowly varying amplitude or envelope equation for the boundary, and a direct numerical solution of an order parameter model equation are presented. The instability mode involves two dimensional perturbations of the planar base boundary, and is suppressed for purely one dimensional perturbations. We find that both the most unstable wavenumbers and their growth rate increase with $\epsilon$, the dimensionless distance away from threshold of the lamellar phase.