Dislocation screening in crystals with spherical topology
| Autor: | Piermarco Fonda, Luca Giomi, Ireth García-Aguilar |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Materials science
Condensed matter physics Field (physics) Geometrical frustration Quantitative Biology::Tissues and Organs Elastic energy FOS: Physical sciences Disclination Condensed Matter - Soft Condensed Matter 01 natural sciences 010305 fluids & plasmas Crystal 0103 physical sciences Soft Condensed Matter (cond-mat.soft) Dislocation 010306 general physics Scalar field Topological quantum number |
| Zdroj: | arXiv |
| ISSN: | 2470-0053 |
| Popis: | Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes, or fullerenes. Such a geometrical frustration gives rise to large elastic stresses, which render the crystal unstable when its size is significantly larger than the typical lattice spacing. Depending on the compliance of the crystal with respect to stretching and bending deformations, these stresses are alleviated either by a local increase of the intrinsic curvature in proximity of the disclinations or by the proliferation of excess dislocations, often organized in the form of one-dimensional chains known as "scars." The associated strain field of the scars is such as to counterbalance the one resulting from the isolated disclinations. Here we develop a continuum theory of dislocation screening in two-dimensional closed crystals with genus one. Upon modeling the flux of scars emanating from a given disclination as an independent scalar field, we demonstrate that the elastic energy of closed two-dimensional crystals with various degrees of asphericity can be expressed as a simple quadratic function of the screened topological charge of the disclinations, at both zero and finite temperature. This allows us to predict the optimal density of the excess dislocations as well as the minimal stretching energy attained by the crystal. |
| Databáze: | OpenAIRE |
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