The motion of a grain boundary separating 2 otherwise stationary domains of hexagonal symmetry was studied. Starting from an order parameter equation, a multiple scale analysis led to an analytical equation of motion for the boundary that shared many properties with that of a crystalline solid. It was found that defect motion was generically opposed by a pinning force that arose from non-adiabatic corrections to the standard amplitude equations. The magnitude of this force depended sensitively upon the misorientation angle between adjacent domains. The most easily pinned grain boundaries were those with a low angle (typically 4 to 8°).

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