Crystallography on curved surfaces

Vincenzo Vitelli; J. B. Lucks; D. R. Nelson

doi:10.1073/pnas.0602755103

Crystallography on curved surfaces

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

^*Corresponding author for this work

Chemical and Biological Engineering

Research output: Contribution to journal › Article › peer-review

86 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	12323-12328
Number of pages	6
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	103
Issue number	33
DOIs	https://doi.org/10.1073/pnas.0602755103
State	Published - Aug 15 2006

Keywords

Dislocations
Elasticity
Geometric frustration
Topological defects

ASJC Scopus subject areas

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T1 - Crystallography on curved surfaces

AU - Vitelli, Vincenzo

AU - Lucks, J. B.

AU - Nelson, D. R.

PY - 2006/8/15

Y1 - 2006/8/15

N2 - 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.

AB - 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.

KW - Dislocations

KW - Elasticity

KW - Geometric frustration

KW - Topological defects

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U2 - 10.1073/pnas.0602755103

DO - 10.1073/pnas.0602755103

M3 - Article

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EP - 12328

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 33

ER -

Crystallography on curved surfaces

Abstract

Keywords

ASJC Scopus subject areas

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