A discrete to continuum analysis of dislocations in nanowire heterostructures

TL;DR

This paper analyzes dislocations in nanowire heterostructures by transitioning from a discrete atomic model to a continuum limit, revealing conditions under which dislocations are energetically favorable.

Contribution

It introduces a discrete to continuum analysis of dislocations in nanowires using Gamma-convergence and geometric rigidity, including a comparison of defect-free and dislocated models.

Findings

Dislocations become energetically favorable in thicker nanowires.

A rigorous discrete to continuum limit is established for the model.

Dislocation presence depends on the nanowire's geometric parameters.

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.