By analogy to dislocations in crystals, the term, disinclination, was first used by Frederick Charles Frank and since then has been modified to its current usage, disclination.They are topological defects and play a central role in melting of 2D crystals within the KTHNY theory, based on two Kosterlitz–Thouless transitions.Equally sized discs (spheres, particles, atoms) form a hexagonal crystal as dense packing in two dimensions.Local strain and twist (for example induced by thermal motion) can cause configurations where discs (or particles) have a coordination number different of six, typically five or seven.Disclinations are topological defects because they cannot be created locally by an affine transformation without cutting the hexagonal array outwards to infinity (or the border of a finite crystal).
Formation of two disclinations (right) out of a dislocation (left) on an otherwise hexagonal background
