Dynamics and instabilities of defects in two-dimensional crystals on curved backgrounds

Mark Bowick, Homin Shin, and Alex Travesset
Phys. Rev. E 75, 021404 – Published 22 February 2007

Abstract

Point defects are ubiquitous in two-dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite-length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.

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  • Received 31 October 2006
  • Corrected 27 February 2007

DOI:https://doi.org/10.1103/PhysRevE.75.021404

©2007 American Physical Society

Corrections

27 February 2007

Erratum

Authors & Affiliations

Mark Bowick1, Homin Shin1, and Alex Travesset2

  • 1Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA
  • 2Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA

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Issue

Vol. 75, Iss. 2 — February 2007

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