TY - RPRT
T1 - Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
Y1 - 2015
A1 - Giuliano Lazzaroni
A1 - Mariapia Palombaro
A1 - Anja Schlomerkemper
AB - In 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 large
PB - SISSA
UR - http://urania.sissa.it/xmlui/handle/1963/7494
U1 - 7623
ER -