EQUILIBRIUM CONFIGURATIONS OF TWO-DIMENSIONAL STRESSED DOMAINS ON THE SURFACE OF ISOTROPIC AND CUBIC CRYSTALS

In this paper, we derive analytical formulations of the elastic energy of a stressed domain on a crystalline substrate. Taking care of the singularity of the elastic Green function at r = 0, we obtain a universal expression for the isotropic case. By using the analogy between electric dipolar and elastic interactions, we developed similar analytical calculations for the (001) surface of a cubic crystal.We showed that the anisotropy of the boundary energy and the anisotropy of the substrate govern the shape of the domains, favoring either compact shapes or stripe configurations. The analytical approach adopted in this paper also allows us to discuss the role of elastic anisotropy for the existence of attractive interactions between domains.