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

TitleDynamics and instabilities of defects in two-dimensional crystals on curved backgrounds
Publication TypeJournal Article
Year of Publication2007
AuthorsBowick M, Shin H, Travesset A
Journal TitlePhysical Review E
Volume75
Pages021404
Date PublishedFeb
Type of ArticleArticle
ISBN Number1539-3755
Accession NumberISI:000244531900040
KeywordsCOLLOIDAL CRYSTALS, CRYSTALLOGRAPHY, dislocation dynamics, GRAIN-BOUNDARY SCARS, VACANCY
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.

DOI10.1103/PhysRevE.75.021404
Alternate JournalPhys. Rev. E