Crystallography on curved surfaces

2006/04/07 by Vincenzo Vitelli, Julius B. Lucks, David R. Nelson · 4 citations
Materials Science · Physics and Astronomy · #Block Copolymer Self-Assembly #Force Microscopy Techniques and Applications #Microstructure and mechanical properties #cond-mat.soft

paper · pdf · doi:10.1073/pnas.0602755103

published as Proceedings of the National Academy of Sciences, 103, 12323, 2006 (Free Article) · 12 Pages, 8 Figures

arxiv created 2006/04/07 · openalex publication_date 2006/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Direct visualization of dislocation dynamics in grain-boundary scars

Cited by

• Extrinsic curvature, geometric optics, and lamellar order on curved substrates
• Particles on curved surfaces: A dynamic approach by a phase-field-crystal model
• Emergent Structure of Multidislocation Ground States in Curved Crystals
• Defect formation dynamics in curved elastic surface crystals