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Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
journal contribution
posted on 2023-06-08, 21:53 authored by Mariapia Palombaro, Giuliano Lazzaroni, Anja SchlömerkemperIn the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of G-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.
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series SISSN
1937-1632Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
1Volume
10Page range
119-139Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2015-07-27First Open Access (FOA) Date
2018-05-25First Compliant Deposit (FCD) Date
2018-05-25Usage metrics
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