A DISCRETE TO CONTINUUM ANALYSIS OF DISLOCATIONS IN NANOWIRE HETEROSTRUCTURES

Abstract. Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a correspond-ing variational discrete model with quadratic pairwise atomic interaction energy. By employing the notion of Gamma-convergence and a geometric rigidity esti-mate, we perform a discrete to continuum limit and a dimension reduction to a one-dimensional system. Moreover, we compare a defect-free model and mod-els with dislocations at the interface and show that the latter are energetically convenient if the thickness of the wire is sufficiently large