Dislocations as Flexible Objects: Interactions and Unbinding Transition

Abstract

The elastic interactions between dislocations in a finite lamellar system of N layers are calculated as a function of the size of the system, surface tension and lamellar elastic constants. For large surface tension the in-plane interactions are repulsive for like dislocations and attractive for opposite ones, decaying exponentially with the decay length proportional to √N. Their strength is inversely proportional to √N. For small surface tension the elastic interactions are attractive at large distances for like dislocations and repulsive for opposite ones. In thin films with small surface tension like dislocations are stabilized at finite separations (∼ √N), while in thick films they unbind due to Helfrich forces. The unbinding transition is extremely sensitive to the surface tension and surface bending elastic constant.