Disclination

Formation of two disclinations (right) out of a dislocation (left) on an otherwise hexagonal background

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 an affine 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.