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.
|Titolo:||Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires|
|Autori:||Lazzaroni G; Palombaro M; Schlömerkemper A|
|Rivista:||DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||10.3934/dcdss.2017007|
|Appare nelle tipologie:||1.1 Journal article|