Novembre 28th 2013, GSSI
Maria Pia Palombaro, University of L'Aquila
Dislocations represent an important class of defects in crystalline solids and their presence influences the behavior of materials in many ways. For example, in semiconductor electronics dislocations play a crucial role in the development of nanowire heterostructures, which can be defined as the combination of two or more materials within the same nanowire structure. Indeed, a large lattice mismatch between the materials of interest may result in poor quality interfaces with high misfit dislocation density. We present a rigorous mathematical analysis showing that, for a given mismatch, formation of dislocations is energetically more favorable than purely elastic deformations when the radius of the cross-section is sufficiently large. The analysis is performed in the framework of Gamma-convergence both in the continuous and in the discrete setting.