Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2006-10-30
Phys. Rev. E 75 (2007) 021404
Physics
Condensed Matter
Soft Condensed Matter
9 pages, 11 eps figures, REVTeX
Scientific paper
10.1103/PhysRevE.75.021404
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.
Bowick Mark
Shin Homin
Travesset Alex
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