Calculus of Variations and Geometric Measure Theory
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G. Lazzaroni - M. Palombaro - A. Schlömerkemper

A discrete to continuum analysis of dislocations in nanowire heterostructures

created by lazzaroni on 15 Aug 2013
modified on 15 Jun 2015


Published Paper

Inserted: 15 aug 2013
Last Updated: 15 jun 2015

Journal: Communications in Mathematical Sciences
Volume: 13
Pages: 1105-1133
Year: 2015


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.


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