Diffusion-Induced Oscillations of Extended Defects
  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. 
Alexander L. Korzhenevskii, Richard Bausch, Rudi Schmitz
cond-mat.mes-hall cond-mat.mtrl-sci cond-mat.stat-mech