Disclination

from Wikipedia, the free encyclopedia

A disclination is a lattice defect (defect) in a crystal in which the rotational symmetry (orientation order) is violated.

The disclination represents the analogue of the dislocation , in which the translation symmetry (translation order) is violated.

Example in 2 dimensions

Creation of two disclinations (right) from a dislocation (left) on a hexagonal background.

Disclinations and dislocations are topological defects and play a central role in describing the melting of a two-dimensional crystal by the KTHNY theory .

In two dimensions, the closest packing of disks of the same size (spheres, particles, atoms) forms a hexagonal crystal, i.e. H. each disc has six nearest neighbors. Local distortions and twists of the crystal form configurations in which one disk has a different coordination number , i.e. H. Number of neighbors, has, typically five or seven.

Since disclinations are topological defects, they can only arise in pairs, so that - apart from edge effects - there are always just as many 5s as 7s disclinations. A "bound" 5-7 pair represents a dislocation. Are there isolated disclinations in a monolayer , which e.g. B. caused by thermal fluctuations, it is an isotropic liquid in two dimensions on average over time ; a two-dimensional crystal is free from disclinations.

With the 7-way disclination (shown in orange in the picture) a "piece of cake" (blue triangle) is added, while with the 5-way disclination one is removed. In this way, many disclinations destroy the orientation order, while dislocations only disturb the translation order, as additional grid lines are inserted (blue lines).

A single disclination is a topological defect because it cannot be produced by a local, affine transformation . This means that they cannot be made individually without cutting the hexagonal crystal to infinity, or at least to its edge, in order to insert or remove a “piece of cake”. In a hexagonal crystal, the cake pieces would originally have a point with an angle of 60 °. The elongation to 72 ° with a 5-way disclination and the compression to approx. 51.4 ° with a 7-way disclination means that disclinations cost elastic energy .

See also

literature

  • JM Kosterlitz and DJ Thouless: Ordering Metastability, and Phase Transitions in Two-Dimensional Systems . In: Journal of Physics C . Volume 6, 1973, p. 1181
  • DR Nelson and BI Halperin: Dislocation-mediated melting in two dimensions . In: Physical Review B . Volume 19, 1979, pp. 2457-2484
  • AP Young: Melting and the vector Coulomb gas in two dimensions . In: Physical Review B . Volume 19, 1979, pp. 1855-1866
  • U. Gasser, C. Eisenmann, G. Maret, P. Keim: Melting of crystals in two dimensions - mini review . In: ChemPhysChem, Volume 11/5, 2010, S. (2010)
  • Nabarro: Theory of crystal dislocations. Oxford University Press 1967

Web links