Diffusion-Induced Oscillations of Extended Defects

TL;DR

This paper models the oscillatory behavior of extended defects driven by diffusion, revealing limit-cycle solutions that explain solute band formation and banded structures in alloys.

Contribution

It derives a nonlinear oscillator equation from a diffusion-driven interface model, providing a new theoretical framework for defect oscillations and pattern formation.

Findings

Limit-cycle solutions exist in the model, indicating oscillatory interface motion.

Negative damping leads to unstable regimes with oscillations.

The model explains solute band formation and banded structures in alloys.

Abstract

From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is negative, we find limit-cycle solutions, describing an oscillatory propagation of the interface. In case of a growing solidification front this offers a transparent scenario for the formation of solute bands in binary alloys, and, taking into account the Mullins-Sekerka instability, of banded structures.