Equilibrium Crystal Shapes of Ideal and Random Quasicrystals

The scaling behavior of interfaces is studied for ideal and random quasicrystals in two and three dimensions, and its consequences for the equilibrium crystal shape are discussed. For a 3D decagonal phase, a facet with a fivefold symmetry axis is found to undergo a roughening transition. For a 3D icosahedral phase, such a facet is likely to stay smooth at all temperatures, $T$, in the ideal case, but is predicted to be rough on sufficiently large scales for $T>\mathrm{}0\mathrm{}$ in the random case. The singular behavior of the equilibrium crystal shape near the edge of a facet is also determined.