Lazzaroni, GiulianoPalombaro, MariapiaSchlomerkemper, Anja2015-01-302015-01-302015-01https://openscience.sissa.it/handle/1963/7494In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is largeenNonlinear elasticityDiscrete to continuumDimension reductionRod theoryGeometric rigidityNon-interpenetrationGamma-convergenceCrystalsDislocationsHeterostructuresPreprint