Disclinations in pentagonal quasicrystals

We develop the mathematical form of disclinations in the density-wave picture of pentagonal quasicrystals. These defects perturb the tenfold orientational order and involve both phonon and phason excitations in order that the density remain continuous. Using our earlier results on the elasticity theory of pentagonal quasicrystals, we calculate the strain fields surrounding a disclination. Also, we show that a disclination dipole, consisting of a pair of equal and oppositely charged defects, is equivalent to a single dislocation, as in a conventional crystal. The disclinations defined in this paper are equivalent to those first developed by Bohsung and Trebin using the projection technique, though the present formulation more readily allows for physical calculations.