01420nas a2200133   4500008004100000245009400041210006900135260001000204520094900214100002401163700002401187700002501211856005001236       2015                        en  d00aRigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires0 aRigidity of threedimensional lattices and dimension reduction in  bSISSA3 aIn 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 large1 aLazzaroni, Giuliano1 aPalombaro, Mariapia1 aSchlomerkemper, Anja  uhttp://urania.sissa.it/xmlui/handle/1963/7494