Tilt grain boundary instabilities in three dimensional lamellar patterns

Details Tilt grain boundary instabilities in three dimensional lamellar patterns Tilt grain boundary instabilities in three dimensional lamellar patterns

2004-11-10

arxiv.org/abs/cond-mat/0411284v1

Phys. Rev. E 71, 031501 (2005)

Physics

Condensed Matter

Soft Condensed Matter

11 pages, 7 figures, to be published in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.71.031501

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.

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