A finite wave-number instability of a 90° tilt grain boundary was identified in 3-dimensional lamellar phases which was absent from 2-dimensional configurations. 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 were presented. The instability mode involved 2-dimensional perturbations of the planar base boundary and was suppressed for purely 1-dimensional perturbations. It was found that both of the most unstable wave numbers, and their growth rate, increased with the dimensionless distance from the threshold of the lamellar phase.

Tilt Grain Boundary Instabilities in Three-Dimensional Lamellar Patterns. Z.F.Huang, J.Viñals: Physical Review E, 2005, 71[3], 031501 (7pp)