Motion of defects and stress relaxation in two-dimensional crystals

The stress relaxation of a two-dimensional solid is studied, with the assumption that defects have been trapped in the sample. The effective shear modulus and stress-strain relaxation rate are calculated for a variety of defect configurations, including large- and small-angle grain boundaries and dislocation pairs. Effects of dislocation climb on the long-term stability of the configurations are considered. The viscosity resulting from moving free dislocations and/or flow at the boundaries is described in a particular geometry. The response to a finite applied shear is discussed, in particular, nucleation of free dislocations and sliding of grain boundaries. The theory is applied to free-standing smectic-B films, and it is suggested that stress relaxation observed in these films may result from a dilute ''random neutral array'' of dislocations or from small-angle grain boundaries.