Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry -: art. no. 055501

We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation, a multiple scale analysis leads to an analytical equation of motion for the boundary that shares many properties with that of a crystalline solid. We find that defect motion is generically opposed by a pinning force that arises from nonadiabatic 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 are those with a low angle (typically 4degreesless than or equal tothetaless than or equal to8degrees) . Although pinning effects may be small, they can be orders of magnitude larger than those present in smectic phases.