Crystallography on curved surfaces

Vincenzo Vitelli*, J. B. Lucks, D. R. Nelson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

109 Scopus citations


We study static and dynamical properties that distinguish 2D crystals constrained to lie on a curved substrate from their flat-space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian curvature is presented in the context of a model surface amenable to full analytical treatment. We find that glide diffusion of isolated dislocations is suppressed by a binding potential of purely geometrical origin. Finally, the energetics and biased diffusion dynamics of point defects such as vacancies and interstitials are explained in terms of their geometric potential.

Original languageEnglish (US)
Pages (from-to)12323-12328
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number33
StatePublished - Aug 15 2006


  • Dislocations
  • Elasticity
  • Geometric frustration
  • Topological defects

ASJC Scopus subject areas

  • General


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