A discrete to continuum analysis of dislocations in nanowire heterostructures

Lazzaroni, Giuliano, Palombaro, Mariapia and Schlömerkemper, Anja (2015) A discrete to continuum analysis of dislocations in nanowire heterostructures. Communications in Mathematical Sciences, 13 (5). pp. 1105-1133. ISSN 1539-6746

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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.

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
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Depositing User: Mariapia Palombaro
Date Deposited: 05 Aug 2014 10:25
Last Modified: 08 Mar 2017 04:44
URI: http://sro.sussex.ac.uk/id/eprint/49473

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