The motion of a grain boundary separating 2 otherwise stationary domains of hexagonal symmetry were studied. Starting from an order parameter equation, a multiple scale analysis led to an analytical equation of motion for the boundary which shared many properties with that of a crystalline solid. It was found that defect motion was generically opposed by a pinning force that arises from non-adiabatic corrections to the standard amplitude equations. The magnitude of this force depends sharply on the misorientation angle between adjacent domains: the most easily pinned grain boundaries were those with a low angle (typically 4 to 8°). Although pinning effects may be small, they could be orders of magnitude larger than those present in smectic phases.

Weakly Nonlinear Theory of Grain Boundary Motion in Patterns with Crystalline Symmetry. Denis Boyer, J.Viñals: Physical Review Letters, 2002, 89[5], 055501 (4pp)