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Epitaxially grown heterogeneous nanowires present dislocations at theinterface between the phases if their radius is big. We consider acorresponding variational discrete model with quadratic pairwise atomicinteraction energy. By employing the notion of Gamma-convergence and ageometric rigidity estimate, we perform a discrete to continuum limit and adimension reduction to a one-dimensional system. Moreover, we compare adefect-free model and models with dislocations at the interface and show thatthe latter are energetically convenient if the thickness of the wire issufficiently large.

A discrete to continuum analysis of dislocations in nanowire heterostructures