Defects in Crystals

Crystals have two types of order, translational and orientational, and hence they have two types of defects. Translational order is associated with dislocations, which are very common and important for technology. Orientational order is associated with disclinations, which are much less common but are still important concepts in the theory of crystals. This chapter presents the topology and energetics of dislocations and disclinations, emphasizing how they are both analogous to the defects in previous chapters. It shows that a dislocation is a dipole of two opposite disclinations, and uses this concept to explain the KTHNY theory of 2D melting. Finally, it discusses how both dislocations and disclinations are coupled with curvature of flexible membranes.