Dislocations in nanowire heterostructures: from discrete to continuum

We discuss an atomistic model for heterogeneous nanowires, allowing for dislocations at the interface. We study the limit as the atomic distance converges to zero, considering simultaneously a dimension reduction and the passage from discrete to continuum. Employing the notion of Gamma-convergence, we establish the minimal energies associated to defect-free configurations and configurations with dislocations at the interface, respectively. It turns out that dislocations are favoured if the thickness of the wire is sufficiently large