Strain and defects in oblique stripe growth

TL;DR

This paper analyzes stripe formation in two-dimensional systems under directional quenching, providing analytical formulas and numerical results that describe how strain and defects develop during oblique stripe growth.

Contribution

It introduces a comprehensive analytical framework for understanding stripe formation and defect dynamics in oblique growth, including boundary effects and bifurcation analysis.

Findings

Stripe formation occurs via traveling waves at all angles.

Small angles and slow quenching rates lead to boundary dislocation glide.

A bifurcation reduces strain at small angles.

Abstract

We study stripe formation in two-dimensional systems under directional quenching in a phase-diffusion approximation including non-adiabatic boundary effects. We find stripe formation through simple traveling waves for all angles relative to the quenching line using an analytic continuation procedure. We also present comprehensive analytical asymptotic formulas in limiting cases of small and large angles as well as small and large quenching rates. Of particular interest is a regime of small angle and slow quenching rate which is well described by the glide motion of a boundary dislocation along the quenching line. A delocalization bifurcation of this dislocation leads to a sharp decrease of strain created in the growth process at small angles. We complement our results with numerical continuation reliant on a boundary-integral formulation. We also compare results in the phase-diffusion approximation numerically to quenched stripe formation in an anisotropic Swift Hohenberg equation.