Plastic deformation of tubular crystals by dislocation glide

Daniel A. Beller and David R. Nelson
Phys. Rev. E 94, 033004 – Published 26 September 2016

Abstract

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical phyllotaxis, describing the spiral packings on cylinders commonly found in nature, have found application in all these systems. Several recent studies have examined defects in tubular crystals associated with crystalline packings that must accommodate a fixed tube radius. Here we study the mechanics of tubular crystals with variable tube radius, with dislocations interposed between regions of different phyllotactic packings. Unbinding and separation of dislocation pairs with equal and opposite Burgers vectors allow the growth of one phyllotactic domain at the expense of another. In particular, glide separation of dislocations offers a low-energy mode for plastic deformations of solid tubes in response to external stresses, reconfiguring the lattice step by step. Through theory and simulation, we examine how the tube's radius and helicity affects, and is in turn altered by, the mechanics of dislocation glide. We also discuss how a sufficiently strong bending rigidity can alter or arrest the deformations of tubes with small radii.

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  • Received 1 May 2016
  • Revised 31 August 2016

DOI:https://doi.org/10.1103/PhysRevE.94.033004

©2016 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft MatterCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel A. Beller1 and David R. Nelson2

  • 1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 94, Iss. 3 — September 2016

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