Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires

Palombaro, Mariapia, Lazzaroni, Giuliano and Schlömerkemper, Anja (2015) Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires. Discrete and Continuous Dynamical Systems - Series S. ISSN 1937-1632 (Accepted)

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Mariapia Palombaro
Date Deposited: 27 Jul 2015 11:29
Last Modified: 11 Mar 2017 03:04
URI: http://sro.sussex.ac.uk/id/eprint/55762

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