An Analytical Model for the Critical Shell Thickness in Core/Shell Nanowires Based on Crystallographic Slip

Abstract

Employing crystal plasticity theory and micromechanics inclusion theory, we developed a full-strain relaxation model under isotropic assumption of materials properties to predict the dependence of the critical shell thickness (CST) for defect-free core/shell nanowires (NWs) on their growth direction. Unlike prior models, we consider three important factors in the energetic analysis (1) the self-energy of a dislocation loop in a finite domain, (2) the three-dimensional mismatch strains that develop in core/shell NWs (axial, radial and tangential directions) as a result of the finite NW geometry and the lattice mismatch between the core and shell materials, and (3) the three-dimensional plastic strains from misfit dislocations that nucleate to relax the mismatch strains. With these, the full-relaxation model is able to reveal that (i) the variation of the CST with growth direction depends on the core radius, (ii) misfit dislocations will not nucleate when the core radius falls below a critical value, (iii) the CST tends to a constant as the core radius increases, and (iv) the CST predicted by prior uniaxial-strain relaxation models is a lower bound.

Department(s)

Materials Science and Engineering

Keywords and Phrases

Core/shell Nanowires; Critical Shell Thickness; Crystalline Slip; Dislocations; Green's Function; Crystal Plasticity Theory; Energetic Analysis; Growth Directions; Relaxation Models; Shell Thickness; Tangential Directions

International Standard Serial Number (ISSN)

0022-5096

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2013 Elsevier Limited, All rights reserved.

Publication Date

01 Nov 2013

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