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

Mark Bowick, Homin Shin, Alex Travesset

Research output: Contribution to journalArticle

19 Scopus citations

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.

Original languageEnglish (US)
Article number021404
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume75
Issue number2
DOIs
StatePublished - Feb 22 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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