Incrystallography, adisclination is aline defect in which there is compensation of an angular gap. They were first discussed byVito Volterra in 1907,[2] who provided an analysis of theelasticstrains of a wedge disclination. By analogy todislocations in crystals, the term,disinclination, was first used byCharles Frank and since then has been modified to its current usage,disclination.[3] As pointed out byJohn D. Eshelby, there is an intricate connection between disclinations and dislocations,[4][5] with dislocation motion moving the position of a disclination.[6]
Disclinations are characterized by an angular vector, called a Frank vector (similarly toBurgers vector in dislocations), and the disclination line. When the Frank vector and the disclination line are perpendicular, they are calledtwist disclinations (similarly toedge dislocations). When the vector and the disclination line are parallel, they are calledwedge disclinations (similarly toscrew dislocations), which are common indecahedralnanoparticles.[11][12]
Equally sized discs (spheres, particles, atoms) form ahexagonal crystal asdense packing in two dimensions. In such a crystal, each particle has six nearest neighbors. Local strain and twist (for example induced by thermal motion) can cause configurations where discs (or particles) have acoordination number different of six, typically five or seven. Disclinations are topological defects, therefore (starting from a hexagonal array) they can only be created in pairs. Ignoring surface/border effects, this implies that there are always as many 5-folded as 7-folded disclinations present in a perfectly plane 2D crystal. A "bound" pair of 5-7-folded disclinations is a dislocation. If myriad dislocations are thermally dissociated into isolated disclinations, then the monolayer of particles becomes anisotropic fluid in two dimensions. A 2D crystal is free of disclinations.
To transform a section of a hexagonal array into a 5-folded disclination (colored green in the figure), a triangular wedge of hexagonal elements (blue triangle) has to be removed; to create a 7-folded disclination (orange), an identical wedge must be inserted. The figure illustrates how disclinations destroy orientational order, while dislocations only destroy translational order in the far field (portions of the crystal far from the center of the disclination).
Disclinations are topological defects because they cannot be created locally by anaffine transformation without cutting the hexagonal array outwards to infinity (or the border of a finite crystal). The undisturbed hexagonal crystal has a 60° symmetry, but when a wedge is removed to create a 5-folded disclination, the crystal symmetry is stretched to 72° – for a 7-folded disclination, it is compressed to about 51,4°. Thus, disclinations store elastic energy by disturbing the director field.
Kosterlitz, J M; Thouless, D J (12 April 1973). "Ordering, metastability and phase transitions in two-dimensional systems".Journal of Physics C: Solid State Physics.6 (7). IOP Publishing:1181–1203.Bibcode:1973JPhC....6.1181K.doi:10.1088/0022-3719/6/7/010.ISSN0022-3719.
