Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
| Autor: | Giuliano Lazzaroni, Anja Schlömerkemper, Mariapia Palombaro |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Geometric rigidity
Rod theory Gamma-convergence Nonlinear elasticity Nanowire Dislocations Discrete to continuum Crystals 01 natural sciences Lattice mismatch Condensed Matter::Materials Science Mathematics - Analysis of PDEs Rigidity (electromagnetism) Settore MAT/05 - Analisi Matematica FOS: Mathematics Heterostructures QA299 Discrete Mathematics and Combinatorics Dimension reduction Non-interpenetration 0101 mathematics Scaling Mathematics Delaunay triangulation Applied Mathematics Dimensionality reduction 010102 general mathematics Mathematical analysis Heterojunction 010101 applied mathematics Voronoi diagram Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Discrete & Continuous Dynamical Systems - S. 10:119-139 |
| ISSN: | 1937-1179 1937-1632 |
| DOI: | 10.3934/dcdss.2017007 |
| Popis: | In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of $\Gamma$-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. |
| Databáze: | OpenAIRE |
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