A discrete to continuum analysis of dislocations in nanowire heterostructures

2013/08/15 by Giuliano Lazzaroni, Lazzaroni, Giuliano, Mariapia Palombaro +3 · 1 citation
Computer Science · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Force Microscopy Techniques and Applications #Microstructure and mechanical properties #math.AP

paper · pdf · doi:10.48550/arxiv.1308.3505

openalex publication_date 2013/08/15 · arxiv created 2013/10/01 · arxiv updated 2013/10/02 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By employing the notion of Gamma-convergence and a geometric rigidity estimate, we perform a discrete to continuum limit and a dimension reduction to a one-dimensional system. Moreover, we compare a defect-free model and models with dislocations at the interface and show that the latter are energetically convenient if the thickness of the wire is sufficiently large.

Citations

• Continuum limits of discrete thin films with superlinear growth densities
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

Cited by

• Derivation of variational membrane models in the context of anisotropic nonlocal hyperelasticity

Related

• Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires
• Collective formation of misfit dislocations at the critical thickness for equilibrium nanowire heterostructures
• Interactions beyond nearest neighbours and rigidity of discrete energies: a compactness result and an application to dimension reduction
• Continuum model for dislocation structures of semicoherent interfaces
• A scaling law for a model of epitaxially strained elastic films with dislocations