Small-angle grain boundaries in quasicrystals

The Read-Shockley treatment of small-angle grain boundaries in crystals is generalized to the case of quasicrystals. The dependence of the grain-boundary energy on the angle of mismatch between abutting quasicrystalline grains is calculated. It is found that, even for a symmetric tilt boundary in a quasicrystal, dislocations with at least two types of Burgers vectors are required; these dislocations have to be arranged quasiperiodically along the boundary. The possible clumping of these dislocations to form composites is discussed. Explicit calculations are presented for a pentagonal quasicrystal.